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1.  Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data 
Biometrika  2009;96(3):723-734.
Considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data, which involve models for both the propensity score and the regression of outcome on covariates. The usual doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations. We propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods, even with some estimated propensity scores close to zero.
doi:10.1093/biomet/asp033
PMCID: PMC2798744  PMID: 20161511
Causal inference; Enhanced propensity score model; Missing at random; No unmeasured confounders; Outcome regression
2.  ESTIMATING TREATMENT EFFECTS ON HEALTHCARE COSTS UNDER EXOGENEITY: IS THERE A ‘MAGIC BULLET’? 
Methods for estimating average treatment effects, under the assumption of no unmeasured confounders, include regression models; propensity score adjustments using stratification, weighting, or matching; and doubly robust estimators (a combination of both). Researchers continue to debate about the best estimator for outcomes such as health care cost data, as they are usually characterized by an asymmetric distribution and heterogeneous treatment effects,. Challenges in finding the right specifications for regression models are well documented in the literature. Propensity score estimators are proposed as alternatives to overcoming these challenges. Using simulations, we find that in moderate size samples (n= 5000), balancing on propensity scores that are estimated from saturated specifications can balance the covariate means across treatment arms but fails to balance higher-order moments and covariances amongst covariates. Therefore, unlike regression model, even if a formal model for outcomes is not required, propensity score estimators can be inefficient at best and biased at worst for health care cost data. Our simulation study, designed to take a ‘proof by contradiction’ approach, proves that no one estimator can be considered the best under all data generating processes for outcomes such as costs. The inverse-propensity weighted estimator is most likely to be unbiased under alternate data generating processes but is prone to bias under misspecification of the propensity score model and is inefficient compared to an unbiased regression estimator. Our results show that there are no ‘magic bullets’ when it comes to estimating treatment effects in health care costs. Care should be taken before naively applying any one estimator to estimate average treatment effects in these data. We illustrate the performance of alternative methods in a cost dataset on breast cancer treatment.
doi:10.1007/s10742-011-0072-8
PMCID: PMC3244728  PMID: 22199462
Propensity score; non-linear regression; average treatment effect; health care costs
3.  Improved Doubly Robust Estimation when Data are Monotonely Coarsened, with Application to Longitudinal Studies with Dropout 
Biometrics  2010;67(2):536-545.
Summary
A routine challenge is that of making inference on parameters in a statistical model of interest from longitudinal data subject to drop out, which are a special case of the more general setting of monotonely coarsened data. Considerable recent attention has focused on doubly robust estimators, which in this context involve positing models for both the missingness (more generally, coarsening) mechanism and aspects of the distribution of the full data, that have the appealing property of yielding consistent inferences if only one of these models is correctly specified. Doubly robust estimators have been criticized for potentially disastrous performance when both of these models are even only mildly misspecified. We propose a doubly robust estimator applicable in general monotone coarsening problems that achieves comparable or improved performance relative to existing doubly robust methods, which we demonstrate via simulation studies and by application to data from an AIDS clinical trial.
doi:10.1111/j.1541-0420.2010.01476.x
PMCID: PMC3061242  PMID: 20731640
Coarsening at random; Discrete hazard; Dropout; Longitudinal data; Missing at random
4.  Evaluating the Effect of Early Versus Late ARV Regimen Change if Failure on an Initial Regimen: Results From the AIDS Clinical Trials Group Study A5095 
The current goal of initial antiretroviral (ARV) therapy is suppression of plasma human immunodeficiency virus (HIV)-1 RNA levels to below 200 copies per milliliter. A proportion of HIV-infected patients who initiate antiretroviral therapy in clinical practice or antiretroviral clinical trials either fail to suppress HIV-1 RNA or have HIV-1 RNA levels rebound on therapy. Frequently, these patients have sustained CD4 cell counts responses and limited or no clinical symptoms and, therefore, have potentially limited indications for altering therapy which they may be tolerating well despite increased viral replication. On the other hand, increased viral replication on therapy leads to selection of resistance mutations to the antiretroviral agents comprising their therapy and potentially cross-resistance to other agents in the same class decreasing the likelihood of response to subsequent antiretroviral therapy. The optimal time to switch antiretroviral therapy to ensure sustained virologic suppression and prevent clinical events in patients who have rebound in their HIV-1 RNA, yet are stable, is not known. Randomized clinical trials to compare early versus delayed switching have been difficult to design and more difficult to enroll. In some clinical trials, such as the AIDS Clinical Trials Group (ACTG) Study A5095, patients randomized to initial antiretroviral treatment combinations, who fail to suppress HIV-1 RNA or have a rebound of HIV-1 RNA on therapy are allowed to switch from the initial ARV regimen to a new regimen, based on clinician and patient decisions. We delineate a statistical framework to estimate the effect of early versus late regimen change using data from ACTG A5095 in the context of two-stage designs.
In causal inference, a large class of doubly robust estimators are derived through semiparametric theory with applications to missing data problems. This class of estimators is motivated through geometric arguments and relies on large samples for good performance. By now, several authors have noted that a doubly robust estimator may be suboptimal when the outcome model is misspecified even if it is semiparametric efficient when the outcome regression model is correctly specified. Through auxiliary variables, two-stage designs, and within the contextual backdrop of our scientific problem and clinical study, we propose improved doubly robust, locally efficient estimators of a population mean and average causal effect for early versus delayed switching to second-line ARV treatment regimens. Our analysis of the ACTG A5095 data further demonstrates how methods that use auxiliary variables can improve over methods that ignore them. Using the methods developed here, we conclude that patients who switch within 8 weeks of virologic failure have better clinical outcomes, on average, than patients who delay switching to a new second-line ARV regimen after failing on the initial regimen. Ordinary statistical methods fail to find such differences. This article has online supplementary material.
doi:10.1080/01621459.2011.646932
PMCID: PMC3545451  PMID: 23329858
Causal inference; Double robustness; Longitudinal data analysis; Missing data; Rubin causal model; Semiparametric efficient estimation
5.  Doubly Robust Estimation of Causal Effects 
American Journal of Epidemiology  2011;173(7):761-767.
Doubly robust estimation combines a form of outcome regression with a model for the exposure (i.e., the propensity score) to estimate the causal effect of an exposure on an outcome. When used individually to estimate a causal effect, both outcome regression and propensity score methods are unbiased only if the statistical model is correctly specified. The doubly robust estimator combines these 2 approaches such that only 1 of the 2 models need be correctly specified to obtain an unbiased effect estimator. In this introduction to doubly robust estimators, the authors present a conceptual overview of doubly robust estimation, a simple worked example, results from a simulation study examining performance of estimated and bootstrapped standard errors, and a discussion of the potential advantages and limitations of this method. The supplementary material for this paper, which is posted on the Journal's Web site (http://aje.oupjournals.org/), includes a demonstration of the doubly robust property (Web Appendix 1) and a description of a SAS macro (SAS Institute, Inc., Cary, North Carolina) for doubly robust estimation, available for download at http://www.unc.edu/∼mfunk/dr/.
doi:10.1093/aje/kwq439
PMCID: PMC3070495  PMID: 21385832
causal inference; epidemiologic methods; propensity score
6.  Doubly Robust Nonparametric Multiple Imputation for Ignorable Missing Data 
Statistica Sinica  2012;22:149-172.
Missing data are common in medical and social science studies and often pose a serious challenge in data analysis. Multiple imputation methods are popular and natural tools for handling missing data, replacing each missing value with a set of plausible values that represent the uncertainty about the underlying values. We consider a case of missing at random (MAR) and investigate the estimation of the marginal mean of an outcome variable in the presence of missing values when a set of fully observed covariates is available. We propose a new nonparametric multiple imputation (MI) approach that uses two working models to achieve dimension reduction and define the imputing sets for the missing observations. Compared with existing nonparametric imputation procedures, our approach can better handle covariates of high dimension, and is doubly robust in the sense that the resulting estimator remains consistent if either of the working models is correctly specified. Compared with existing doubly robust methods, our nonparametric MI approach is more robust to the misspecification of both working models; it also avoids the use of inverse-weighting and hence is less sensitive to missing probabilities that are close to 1. We propose a sensitivity analysis for evaluating the validity of the working models, allowing investigators to choose the optimal weights so that the resulting estimator relies either completely or more heavily on the working model that is likely to be correctly specified and achieves improved efficiency. We investigate the asymptotic properties of the proposed estimator, and perform simulation studies to show that the proposed method compares favorably with some existing methods in finite samples. The proposed method is further illustrated using data from a colorectal adenoma study.
PMCID: PMC3280694  PMID: 22347786
Doubly robust; Missing at random; Multiple imputation; Nearest neighbor; Nonparametric imputation; Sensitivity analysis
7.  Test the reliability of doubly robust estimation with missing response data 
Biometrics  2014;70(2):289-298.
Summary
In statistical inference one has to make sure that the underlying regression model is correctly specified otherwise the resulting estimation may be biased. Model checking is an important method to detect any departure of the regression model from the true one. Missing data is a ubiquitous problem in social and medical studies. If the underlying regression model is correctly specified, recent researches show great popularity of the doubly robust estimates method for handling missing data because of its robustness to the misspecification of either the missing data model or the conditional mean model, i.e. the model for the conditional expectation of true regression model conditioning on the observed quantities. However, little work has been devoted to the goodness of fit test for doubly robust estimates method. In this paper, we propose a testing method to assess the reliability of the estimator derived from the doubly robust estimating equation with possibly missing response and always observed auxiliary variables. Numerical studies demonstrate that the proposed test can control type I errors well. Furthermore the proposed method can detect departures from model assumptions in the marginal mean model of interest powerfully. A real dementia data set is used to illustrate the method for the diagnosis of model misspecification in the problem of missing response with an always observed auxiliary variable for cross-sectional data.
doi:10.1111/biom.12150
PMCID: PMC4061274  PMID: 24571677
Auxiliary; doubly robust; estimating equation; goodness of fit; missing data
8.  A new estimation with minimum trace of asymptotic covariance matrix for incomplete longitudinal data with a surrogate process 
Statistics in medicine  2013;32(27):10.1002/sim.5875.
Missing data is a very common problem in medical and social studies, especially when data are collected longitudinally. It is a challenging problem to utilize observed data effectively. Many papers on missing data problems can be found in statistical literature. It is well known that the inverse weighted estimation is neither efficient nor robust. On the other hand, the doubly robust (DR) method can improve the efficiency and robustness. As is known, the DR estimation requires a missing data model (i.e., a model for the probability that data are observed) and a working regression model (i.e., a model for the outcome variable given covariates and surrogate variables). Because the DR estimating function has mean zero for any parameters in the working regression model when the missing data model is correctly specified, in this paper, we derive a formula for the estimator of the parameters of the working regression model that yields the optimally efficient estimator of the marginal mean model (the parameters of interest) when the missing data model is correctly specified. Furthermore, the proposed method also inherits the DR property. Simulation studies demonstrate the greater efficiency of the proposed method compared with the standard DR method. A longitudinal dementia data set is used for illustration.
doi:10.1002/sim.5875
PMCID: PMC3808493  PMID: 23744541
longitudinal data; missing data; optimal; surrogate outcome
9.  The performance of different propensity-score methods for estimating differences in proportions (risk differences or absolute risk reductions) in observational studies 
Statistics in Medicine  2010;29(20):2137-2148.
Propensity score methods are increasingly being used to estimate the effects of treatments on health outcomes using observational data. There are four methods for using the propensity score to estimate treatment effects: covariate adjustment using the propensity score, stratification on the propensity score, propensity-score matching, and inverse probability of treatment weighting (IPTW) using the propensity score. When outcomes are binary, the effect of treatment on the outcome can be described using odds ratios, relative risks, risk differences, or the number needed to treat. Several clinical commentators suggested that risk differences and numbers needed to treat are more meaningful for clinical decision making than are odds ratios or relative risks. However, there is a paucity of information about the relative performance of the different propensity-score methods for estimating risk differences. We conducted a series of Monte Carlo simulations to examine this issue. We examined bias, variance estimation, coverage of confidence intervals, mean-squared error (MSE), and type I error rates. A doubly robust version of IPTW had superior performance compared with the other propensity-score methods. It resulted in unbiased estimation of risk differences, treatment effects with the lowest standard errors, confidence intervals with the correct coverage rates, and correct type I error rates. Stratification, matching on the propensity score, and covariate adjustment using the propensity score resulted in minor to modest bias in estimating risk differences. Estimators based on IPTW had lower MSE compared with other propensity-score methods. Differences between IPTW and propensity-score matching may reflect that these two methods estimate the average treatment effect and the average treatment effect for the treated, respectively. Copyright © 2010 John Wiley & Sons, Ltd.
doi:10.1002/sim.3854
PMCID: PMC3068290  PMID: 20108233
propensity score; observational study; binary data; risk difference; number needed to treat; matching; IPTW; inverse probability of treatment weighting; propensity-score matching
10.  Bias and variance trade-offs when combining propensity score weighting and regression: with an application to HIV status and homeless men 
The quality of propensity scores is traditionally measured by assessing how well they make the distributions of covariates in the treatment and control groups match, which we refer to as “good balance”. Good balance guarantees less biased estimates of the treatment effect. However, the cost of achieving good balance is that the variance of the estimates increases due to a reduction in effective sample size, either through the introduction of propensity score weights or dropping cases when propensity score matching. In this paper, we investigate whether it is best to optimize the balance or to settle for a less than optimal balance and use double robust estimation to adjust for remaining differences. We compare treatment effect estimates from regression, propensity score weighting, and double robust estimation with varying levels of effort expended to achieve balance using data from a study about the differences in outcomes by HIV status in heterosexually active homeless men residing in Los Angeles. Because of how costly data collection efforts are for this population, it is important to find an alternative estimation method that does not reduce effective sample size as much as methods that aggressively aim to optimize balance. Results from a simulation study suggest that there are instances in which we can obtain more precise treatment effect estimates without increasing bias too much by using a combination of regression and propensity score weights that achieve a less than optimal balance. There is a bias-variance tradeoff at work in propensity score estimation; every step toward better balance usually means an increase in variance and at some point a marginal decrease in bias may not be worth the associated increase in variance.
PMCID: PMC3433039  PMID: 22956891
Propensity score; Double robust estimation; HIV status; Homeless men
11.  On the joint use of propensity and prognostic scores in estimation of the Average Treatment Effect on the Treated: A simulation study 
Statistics in medicine  2013;33(20):3488-3508.
Summary
Propensity and prognostic score methods seek to improve the quality of causal inference in non-randomized or observational studies by replicating the conditions found in a controlled experiment, at least with respect to observed characteristics. Propensity scores model receipt of the treatment of interest; prognostic scores model the potential outcome under a single treatment condition.
While the popularity of propensity score methods continues to grow, prognostic score methods and methods combining propensity and prognostic scores have thus far received little attention. To this end, we performed a simulation study that compared subclassification and full matching on a single estimated propensity or prognostic score with three approaches combining estimated propensity and prognostic scores: full matching on a Mahalanobis distance combining the estimated propensity and prognostic scores (FULL-MAHAL); full matching on the estimated prognostic propensity score within propensity score calipers (FULL-PGPPTY); and subclassification on an estimated propensity and prognostic score grid with 5 × 5 subclasses (SUBCLASS(5*5)). We considered settings in which one, both or neither score model was misspecified. The data generating mechanisms varied in the degree of linearity and additivity in the true treatment assignment and outcome models.
FULL-MAHAL and FULL-PGPPTY exhibited strong to superior performance in root mean square error terms across all simulation settings and scenarios. Methods combining propensity and prognostic scores were no less robust to model misspecification than single-score methods even when both score models were incorrectly specified. Our findings support the joint use of propensity and prognostic scores in estimation of the average treatment effect on the treated.
doi:10.1002/sim.6030
PMCID: PMC3995901  PMID: 24151187
observational data; confounding; bias reduction; subclassification; full matching; Mahalanobis metric
12.  Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity-score matched samples 
Statistics in Medicine  2009;28(25):3083-3107.
The propensity score is a subject's probability of treatment, conditional on observed baseline covariates. Conditional on the true propensity score, treated and untreated subjects have similar distributions of observed baseline covariates. Propensity-score matching is a popular method of using the propensity score in the medical literature. Using this approach, matched sets of treated and untreated subjects with similar values of the propensity score are formed. Inferences about treatment effect made using propensity-score matching are valid only if, in the matched sample, treated and untreated subjects have similar distributions of measured baseline covariates. In this paper we discuss the following methods for assessing whether the propensity score model has been correctly specified: comparing means and prevalences of baseline characteristics using standardized differences; ratios comparing the variance of continuous covariates between treated and untreated subjects; comparison of higher order moments and interactions; five-number summaries; and graphical methods such as quantile–quantile plots, side-by-side boxplots, and non-parametric density plots for comparing the distribution of baseline covariates between treatment groups. We describe methods to determine the sampling distribution of the standardized difference when the true standardized difference is equal to zero, thereby allowing one to determine the range of standardized differences that are plausible with the propensity score model having been correctly specified. We highlight the limitations of some previously used methods for assessing the adequacy of the specification of the propensity-score model. In particular, methods based on comparing the distribution of the estimated propensity score between treated and untreated subjects are uninformative. Copyright © 2009 John Wiley & Sons, Ltd.
doi:10.1002/sim.3697
PMCID: PMC3472075  PMID: 19757444
balance; goodness-of-fit; observational study; propensity score; matching; propensity-score matching; standardized difference; bias
13.  Self-Administered Outpatient Antimicrobial Infusion by Uninsured Patients Discharged from a Safety-Net Hospital: A Propensity-Score-Balanced Retrospective Cohort Study 
PLoS Medicine  2015;12(12):e1001922.
Background
Outpatient parenteral antimicrobial therapy (OPAT) is accepted as safe and effective for medically stable patients to complete intravenous (IV) antibiotics in an outpatient setting. Since, however, uninsured patients in the United States generally cannot afford OPAT, safety-net hospitals are often burdened with long hospitalizations purely to infuse antibiotics, occupying beds that could be used for patients requiring more intensive services. OPAT is generally delivered in one of four settings: infusion centers, nursing homes, at home with skilled nursing assistance, or at home with self-administered therapy. The first three—termed healthcare-administered OPAT (H-OPAT)—are most commonly used in the United States by patients with insurance funding. The fourth—self-administered OPAT (S-OPAT)—is relatively uncommon, with the few published studies having been conducted in the United Kingdom. With multidisciplinary planning, we established an S-OPAT clinic in 2009 to shift care of selected uninsured patients safely to self-administration of their IV antibiotics at home. We undertook this study to determine whether the low-income mostly non-English-speaking patients in our S-OPAT program could administer their own IV antimicrobials at home with outcomes as good as, or better than, those receiving H-OPAT.
Methods and Findings
Parkland Hospital is a safety-net hospital serving Dallas County, Texas. From 1 January 2009 to 14 October 2013, all uninsured patients meeting criteria were enrolled in S-OPAT, while insured patients were discharged to H-OPAT settings. The S-OPAT patients were trained through multilingual instruction to self-administer IV antimicrobials by gravity, tested for competency before discharge, and thereafter followed at designated intervals in the S-OPAT outpatient clinic for IV access care, laboratory monitoring, and physician follow-up. The primary outcome was 30-d all-cause readmission, and the secondary outcome was 1-y all-cause mortality. The study was adequately powered for readmission but not for mortality. Clinical, sociodemographic, and outcome data were collected from the Parkland Hospital electronic medical records and the US census, constituting a historical prospective cohort study. We used multivariable logistic regression to develop a propensity score predicting S-OPAT versus H-OPAT group membership from covariates. We then estimated the effect of S-OPAT versus H-OPAT on the two outcomes using multivariable proportional hazards regression, controlling for selection bias and confounding with the propensity score and covariates.
Of the 1,168 patients discharged to receive OPAT, 944 (81%) were managed in the S-OPAT program and 224 (19%) by H-OPAT services. In multivariable proportional hazards regression models controlling for confounding and selection bias, the 30-d readmission rate was 47% lower in the S-OPAT group (adjusted hazard ratio [aHR], 0.53; 95% CI 0.35–0.81; p = 0.003), and the 1-y mortality rate did not differ significantly between the groups (aHR, 0.86; 95% CI 0.37–2.00; p = 0.73). The S-OPAT program shifted a median 26 d of inpatient infusion per patient to the outpatient setting, avoiding 27,666 inpatient days. The main limitation of this observational study—the potential bias from the difference in healthcare funding status of the groups—was addressed by propensity score modeling.
Conclusions
S-OPAT was associated with similar or better clinical outcomes than H-OPAT. S-OPAT may be an acceptable model of treatment for uninsured, medically stable patients to complete extended courses of IV antimicrobials at home.
In a propensity score-balanced retrospective cohort study, Kavita Bhavan and colleagues compare health outcomes for patients undergoing self-administered versus healthcare-administered outpatient parenteral antimicrobial therapy.
Editors' Summary
Background
Patients sometimes need lengthy courses of antimicrobial agents to treat life-threatening infections. For example, patients who develop endocarditis (an infection of the inner lining of the heart usually caused by bacteria entering the blood and traveling to the heart) need to be given antimicrobial drugs for up to six weeks. Initially, these patients require intensive diagnostic and therapeutic care in the hospital. But once the antimicrobial treatment starts to work, most patients only need regular intravenous antimicrobial infusions. Patients who stay in the hospital to receive this low intensity care occupy beds that could be used for patients requiring more intensive care. Moreover, they are at risk of catching a hospital-acquired, antibiotic-resistant infection. For these reasons, and because long-term administration of antimicrobial agents in the hospital is costly, outpatient parenteral (injected or infused) antimicrobial therapy (OPAT) is increasingly being used as a safe and effective way for medically stable patients to complete a course of intravenous antibiotics outside the hospital.
Why Was This Study Done?
In the US, OPAT is usually delivered in infusion centers, in nursing homes, or at home by visiting nurses. But healthcare-administered OPAT (H-OPAT) is available only to insured patients (in the US, medical insurance provided by employers or by the government-run Medicare and Medicaid programs funds healthcare). Uninsured people cannot usually afford H-OPAT and have to stay in safety-net hospitals (public hospitals that provide care to low-income, uninsured populations) for intravenous antibiotic treatment. In this propensity-score-balanced retrospective cohort study, the researchers investigate whether uninsured patients discharged from a safety-net hospital in Texas to self-administer OPAT at home (S-OPAT) can achieve outcomes as good as or better than those achieved by patients receiving H-OPAT. A retrospective cohort study compares recorded clinical outcomes in groups of patients who received different treatments. Because the patients were not chosen at random, such studies are subject to selection bias and confounding. Propensity score balancing is used to control for selection bias—the possibility that some members of the population are less likely to be included in a study than others. Adjustment for covariates (patient characteristics that may affect the outcome under study) is used to control for confounding—the possibility that unknown characteristics shared by patients with a specific outcome, rather than any treatment, may be responsible for that outcome.
What Did the Researchers Do and Find?
Between 2010 and 2013, 994 uninsured patients were enrolled in the hospital’s S-OPAT program, and 224 insured patients were discharged to an H-OPAT program. Patients in the S-OPAT group were trained to self-administer intravenous antimicrobials, tested for their ability to treat themselves before discharge, and then monitored by weekly visits to the S-OPAT outpatient clinic. The researchers estimated the effect of S-OPAT versus H-OPAT on 30-day all-cause readmission and one-year all-cause mortality (the primary and secondary outcomes, respectively) after adjusting for covariates and controlling for selection bias with a propensity score developed using baseline clinical and sociodemographic information collected from the patients. The 30-day readmission rate was 47% lower in the S-OPAT group than in the H-OPAT group (a significant result unlikely to have arisen by chance), and the one-year mortality rate did not differ significantly between the two groups. Notably, because the S-OPAT program resulted in patients spending fewer days having inpatient infusions, 27,666 inpatient days were avoided over the study period.
What Do These Findings Mean?
These findings indicate that, after adjusting for preexisting differences between those patients receiving S-OPAT and those receiving H-OPAT and for potential confounders, the risk of readmission within 30 days of discharge was lower in the S-OPAT group than in the H-OPAT group and the risk of dying within one year of hospital discharge did not differ significantly between the two groups (the study did not include enough participants to detect any subtle difference that might have existed for this end point). Thus, S-OPAT was associated with similar or better outcomes than H-OPAT. Note that there may be residual selection bias and confounding by characteristics not included in the propensity score. This study did not address whether S-OPAT actually improves outcomes for patients compared with H-OPAT; a randomized controlled trial in which patients are randomly assigned to receive the two treatments is needed to do this. Nevertheless, these findings suggest that S-OPAT might make it possible for uninsured, medically stable patients to have extended courses of intravenous antimicrobials at home rather than remaining in the hospital until their treatment is complete.
Additional Information
This list of resources contains links that can be accessed when viewing the PDF on a device or via the online version of the article at http://dx.doi.org/10.1371/journal.pmed.1001922.
The UK National Health Service Choices website provides basic information about the use of antibiotics, including information about when intravenous antibiotics are needed and about endocarditis
The US National Heart, Lung, and Blood Institute also provides information about endocarditis and its treatment
The Infectious Diseases Society of America provides clinical guidelines for the use of OPAT
The OPAT Initiative of the British Society for Antimicrobial Chemotherapy is a multi-stakeholder project that supports the establishment of standardized OPAT services throughout the UK; it also provides guidelines for the use of OPAT
Wikipedia has a page on propensity score matching (note that Wikipedia is a free online encyclopedia that anyone can edit; available in several languages)
doi:10.1371/journal.pmed.1001922
PMCID: PMC4686020  PMID: 26671467
14.  A robust method using propensity score stratification for correcting verification bias for binary tests 
Sensitivity and specificity are common measures of the accuracy of a diagnostic test. The usual estimators of these quantities are unbiased if data on the diagnostic test result and the true disease status are obtained from all subjects in an appropriately selected sample. In some studies, verification of the true disease status is performed only for a subset of subjects, possibly depending on the result of the diagnostic test and other characteristics of the subjects. Estimators of sensitivity and specificity based on this subset of subjects are typically biased; this is known as verification bias. Methods have been proposed to correct verification bias under the assumption that the missing data on disease status are missing at random (MAR), that is, the probability of missingness depends on the true (missing) disease status only through the test result and observed covariate information. When some of the covariates are continuous, or the number of covariates is relatively large, the existing methods require parametric models for the probability of disease or the probability of verification (given the test result and covariates), and hence are subject to model misspecification. We propose a new method for correcting verification bias based on the propensity score, defined as the predicted probability of verification given the test result and observed covariates. This is estimated separately for those with positive and negative test results. The new method classifies the verified sample into several subsamples that have homogeneous propensity scores and allows correction for verification bias. Simulation studies demonstrate that the new estimators are more robust to model misspecification than existing methods, but still perform well when the models for the probability of disease and probability of verification are correctly specified.
doi:10.1093/biostatistics/kxr020
PMCID: PMC3276270  PMID: 21856650
Diagnostic test; Model misspecification; Propensity score; Sensitivity; Specificity
15.  Collaborative Double Robust Targeted Maximum Likelihood Estimation* 
Collaborative double robust targeted maximum likelihood estimators represent a fundamental further advance over standard targeted maximum likelihood estimators of a pathwise differentiable parameter of a data generating distribution in a semiparametric model, introduced in van der Laan, Rubin (2006). The targeted maximum likelihood approach involves fluctuating an initial estimate of a relevant factor (Q) of the density of the observed data, in order to make a bias/variance tradeoff targeted towards the parameter of interest. The fluctuation involves estimation of a nuisance parameter portion of the likelihood, g. TMLE has been shown to be consistent and asymptotically normally distributed (CAN) under regularity conditions, when either one of these two factors of the likelihood of the data is correctly specified, and it is semiparametric efficient if both are correctly specified.
In this article we provide a template for applying collaborative targeted maximum likelihood estimation (C-TMLE) to the estimation of pathwise differentiable parameters in semi-parametric models. The procedure creates a sequence of candidate targeted maximum likelihood estimators based on an initial estimate for Q coupled with a succession of increasingly non-parametric estimates for g. In a departure from current state of the art nuisance parameter estimation, C-TMLE estimates of g are constructed based on a loss function for the targeted maximum likelihood estimator of the relevant factor Q that uses the nuisance parameter to carry out the fluctuation, instead of a loss function for the nuisance parameter itself. Likelihood-based cross-validation is used to select the best estimator among all candidate TMLE estimators of Q0 in this sequence. A penalized-likelihood loss function for Q is suggested when the parameter of interest is borderline-identifiable.
We present theoretical results for “collaborative double robustness,” demonstrating that the collaborative targeted maximum likelihood estimator is CAN even when Q and g are both mis-specified, providing that g solves a specified score equation implied by the difference between the Q and the true Q0. This marks an improvement over the current definition of double robustness in the estimating equation literature.
We also establish an asymptotic linearity theorem for the C-DR-TMLE of the target parameter, showing that the C-DR-TMLE is more adaptive to the truth, and, as a consequence, can even be super efficient if the first stage density estimator does an excellent job itself with respect to the target parameter.
This research provides a template for targeted efficient and robust loss-based learning of a particular target feature of the probability distribution of the data within large (infinite dimensional) semi-parametric models, while still providing statistical inference in terms of confidence intervals and p-values. This research also breaks with a taboo (e.g., in the propensity score literature in the field of causal inference) on using the relevant part of likelihood to fine-tune the fitting of the nuisance parameter/censoring mechanism/treatment mechanism.
doi:10.2202/1557-4679.1181
PMCID: PMC2898626  PMID: 20628637
asymptotic linearity; coarsening at random; causal effect; censored data; crossvalidation; collaborative double robust; double robust; efficient influence curve; estimating function; estimator selection; influence curve; G-computation; locally efficient; loss-function; marginal structural model; maximum likelihood estimation; model selection; pathwise derivative; semiparametric model; sieve; super efficiency; super-learning; targeted maximum likelihood estimation; targeted nuisance parameter estimator selection; variable importance
16.  Propensity Score Weighting with Multilevel Data 
Statistics in medicine  2013;32(19):3373-3387.
Propensity score methods are being increasingly used as a less parametric alternative to traditional regression to balance observed differences across groups in both descriptive and causal comparisons. Data collected in many disciplines often have analytically relevant multilevel or clustered structure. The propensity score, however, was developed and has been used primarily with unstructured data. We present and compare several propensity-score-weighted estimators for clustered data, including marginal, cluster-weighted and doubly-robust estimators. Using both analytical derivations and Monte Carlo simulations, we illustrate bias arising when the usual assumptions of propensity score analysis do not hold for multilevel data. We show that exploiting the multilevel structure, either parametrically or nonparametrically, in at least one stage of the propensity score analysis can greatly reduce these biases. These methods are applied to a study of racial disparities in breast cancer screening among beneficiaries in Medicare health plans.
doi:10.1002/sim.5786
PMCID: PMC3710526  PMID: 23526267
balance; multilevel; propensity score; racial disparity; treatment effect; unmeasured confounders; weighting
17.  The performance of different propensity score methods for estimating marginal hazard ratios 
Statistics in Medicine  2012;32(16):2837-2849.
Propensity score methods are increasingly being used to reduce or minimize the effects of confounding when estimating the effects of treatments, exposures, or interventions when using observational or non-randomized data. Under the assumption of no unmeasured confounders, previous research has shown that propensity score methods allow for unbiased estimation of linear treatment effects (e.g., differences in means or proportions). However, in biomedical research, time-to-event outcomes occur frequently. There is a paucity of research into the performance of different propensity score methods for estimating the effect of treatment on time-to-event outcomes. Furthermore, propensity score methods allow for the estimation of marginal or population-average treatment effects. We conducted an extensive series of Monte Carlo simulations to examine the performance of propensity score matching (1:1 greedy nearest-neighbor matching within propensity score calipers), stratification on the propensity score, inverse probability of treatment weighting (IPTW) using the propensity score, and covariate adjustment using the propensity score to estimate marginal hazard ratios. We found that both propensity score matching and IPTW using the propensity score allow for the estimation of marginal hazard ratios with minimal bias. Of these two approaches, IPTW using the propensity score resulted in estimates with lower mean squared error when estimating the effect of treatment in the treated. Stratification on the propensity score and covariate adjustment using the propensity score result in biased estimation of both marginal and conditional hazard ratios. Applied researchers are encouraged to use propensity score matching and IPTW using the propensity score when estimating the relative effect of treatment on time-to-event outcomes. Copyright © 2012 John Wiley & Sons, Ltd.
doi:10.1002/sim.5705
PMCID: PMC3747460  PMID: 23239115
propensity score; survival analysis; inverse probability of treatment weighting (IPTW); Monte Carlo simulations; observational study; time-to-event outcomes
18.  Balancing Score Adjusted Targeted Minimum Loss-based Estimation 
Journal of causal inference  2015;3(2):139-155.
Adjusting for a balancing score is sufficient for bias reduction when estimating causal effects including the average treatment effect and effect among the treated. Estimators that adjust for the propensity score in a nonparametric way, such as matching on an estimate of the propensity score, can be consistent when the estimated propensity score is not consistent for the true propensity score but converges to some other balancing score. We call this property the balancing score property, and discuss a class of estimators that have this property. We introduce a targeted minimum loss-based estimator (TMLE) for a treatment-specific mean with the balancing score property that is additionally locally efficient and doubly robust. We investigate the new estimator’s performance relative to other estimators, including another TMLE, a propensity score matching estimator, an inverse probability of treatment weighted estimator, and a regression-based estimator in simulation studies.
doi:10.1515/jci-2012-0012
PMCID: PMC4637178  PMID: 26561539
balancing score; propensity score; causal inference; matching; TMLE
19.  Doubly Robust Estimates for Binary Longitudinal Data Analysis with Missing Response and Missing Covariates 
Biometrics  2011;67(3):10.1111/j.1541-0420.2010.01541.x.
Summary
Longitudinal studies often feature incomplete response and covariate data. Likelihood-based methods such as the expectation–maximization algorithm give consistent estimators for model parameters when data are missing at random (MAR) provided that the response model and the missing covariate model are correctly specified; however, we do not need to specify the missing data mechanism. An alternative method is the weighted estimating equation, which gives consistent estimators if the missing data and response models are correctly specified; however, we do not need to specify the distribution of the covariates that have missing values. In this article, we develop a doubly robust estimation method for longitudinal data with missing response and missing covariate when data are MAR. This method is appealing in that it can provide consistent estimators if either the missing data model or the missing covariate model is correctly specified. Simulation studies demonstrate that this method performs well in a variety of situations.
doi:10.1111/j.1541-0420.2010.01541.x
PMCID: PMC3652597  PMID: 21281272
Doubly robust; Estimating equation; Missing at random; Missing covariate; Missing response
20.  A Bayesian MCMC approach to survival analysis with doubly-censored data 
Doubly-censored data refers to time to event data for which both the originating and failure times are censored. In studies involving AIDS incubation time or survival after dementia onset, for example, data are frequently doubly-censored because the date of the originating event is interval-censored and the date of the failure event usually is right-censored. The primary interest is in the distribution of elapsed times between the originating and failure events and its relationship to exposures and risk factors. The estimating equation approach [Sun, et al. 1999. Regression analysis of doubly censored failure time data with applications to AIDS studies. Biometrics 55, 909-914] and its extensions assume the same distribution of originating event times for all subjects. This paper demonstrates the importance of utilizing additional covariates to impute originating event times, i.e., more accurate estimation of originating event times may lead to less biased parameter estimates for elapsed time. The Bayesian MCMC method is shown to be a suitable approach for analyzing doubly-censored data and allows a rich class of survival models. The performance of the proposed estimation method is compared to that of other conventional methods through simulations. Two examples, an AIDS cohort study and a population-based dementia study, are used for illustration. Sample code is shown in the appendix.
doi:10.1016/j.csda.2010.02.025
PMCID: PMC2877214  PMID: 20514348
AIDS; dementia; doubly censored data; incubation period; MCMC; midpoint imputation
21.  Variable selection for confounder control, flexible modeling and Collaborative Targeted Minimum Loss-based Estimation in causal inference 
This paper investigates the appropriateness of the integration of flexible propensity score modeling (nonparametric or machine learning approaches) in semiparametric models for the estimation of a causal quantity, such as the mean outcome under treatment. We begin with an overview of some of the issues involved in knowledge-based and statistical variable selection in causal inference and the potential pitfalls of automated selection based on the fit of the propensity score. Using a simple example, we directly show the consequences of adjusting for pure causes of the exposure when using inverse probability of treatment weighting (IPTW). Such variables are likely to be selected when using a naive approach to model selection for the propensity score. We describe how the method of Collaborative Targeted minimum loss-based estimation (C-TMLE; van der Laan and Gruber, 2010) capitalizes on the collaborative double robustness property of semiparametric efficient estimators to select covariates for the propensity score based on the error in the conditional outcome model. Finally, we compare several approaches to automated variable selection in low-and high-dimensional settings through a simulation study. From this simulation study, we conclude that using IPTW with flexible prediction for the propensity score can result in inferior estimation, while Targeted minimum loss-based estimation and C-TMLE may benefit from flexible prediction and remain robust to the presence of variables that are highly correlated with treatment. However, in our study, standard influence function-based methods for the variance underestimated the standard errors, resulting in poor coverage under certain data-generating scenarios.
doi:10.1515/ijb-2015-0017
PMCID: PMC4733443  PMID: 26226129
C-TMLE; IPTW; variable reduction
22.  Continuous Subcutaneous Insulin Infusion (CSII) Pumps for Type 1 and Type 2 Adult Diabetic Populations 
Executive Summary
In June 2008, the Medical Advisory Secretariat began work on the Diabetes Strategy Evidence Project, an evidence-based review of the literature surrounding strategies for successful management and treatment of diabetes. This project came about when the Health System Strategy Division at the Ministry of Health and Long-Term Care subsequently asked the secretariat to provide an evidentiary platform for the Ministry’s newly released Diabetes Strategy.
After an initial review of the strategy and consultation with experts, the secretariat identified five key areas in which evidence was needed. Evidence-based analyses have been prepared for each of these five areas: insulin pumps, behavioural interventions, bariatric surgery, home telemonitoring, and community based care. For each area, an economic analysis was completed where appropriate and is described in a separate report.
To review these titles within the Diabetes Strategy Evidence series, please visit the Medical Advisory Secretariat Web site, http://www.health.gov.on.ca/english/providers/program/mas/mas_about.html,
Diabetes Strategy Evidence Platform: Summary of Evidence-Based Analyses
Continuous Subcutaneous Insulin Infusion Pumps for Type 1 and Type 2 Adult Diabetics: An Evidence-Based Analysis
Behavioural Interventions for Type 2 Diabetes: An Evidence-Based Analysis
Bariatric Surgery for People with Diabetes and Morbid Obesity: An Evidence-Based Summary
Community-Based Care for the Management of Type 2 Diabetes: An Evidence-Based Analysis
Home Telemonitoring for Type 2 Diabetes: An Evidence-Based Analysis
Application of the Ontario Diabetes Economic Model (ODEM) to Determine the Cost-effectiveness and Budget Impact of Selected Type 2 Diabetes Interventions in Ontario
Objective
The objective of this analysis is to review the efficacy of continuous subcutaneous insulin infusion (CSII) pumps as compared to multiple daily injections (MDI) for the type 1 and type 2 adult diabetics.
Clinical Need and Target Population
Insulin therapy is an integral component of the treatment of many individuals with diabetes. Type 1, or juvenile-onset diabetes, is a life-long disorder that commonly manifests in children and adolescents, but onset can occur at any age. It represents about 10% of the total diabetes population and involves immune-mediated destruction of insulin producing cells in the pancreas. The loss of these cells results in a decrease in insulin production, which in turn necessitates exogenous insulin therapy.
Type 2, or ‘maturity-onset’ diabetes represents about 90% of the total diabetes population and is marked by a resistance to insulin or insufficient insulin secretion. The risk of developing type 2 diabetes increases with age, obesity, and lack of physical activity. The condition tends to develop gradually and may remain undiagnosed for many years. Approximately 30% of patients with type 2 diabetes eventually require insulin therapy.
CSII Pumps
In conventional therapy programs for diabetes, insulin is injected once or twice a day in some combination of short- and long-acting insulin preparations. Some patients require intensive therapy regimes known as multiple daily injection (MDI) programs, in which insulin is injected three or more times a day. It’s a time consuming process and usually requires an injection of slow acting basal insulin in the morning or evening and frequent doses of short-acting insulin prior to eating. The most common form of slower acting insulin used is neutral protamine gagedorn (NPH), which reaches peak activity 3 to 5 hours after injection. There are some concerns surrounding the use of NPH at night-time as, if injected immediately before bed, nocturnal hypoglycemia may occur. To combat nocturnal hypoglycemia and other issues related to absorption, alternative insulins have been developed, such as the slow-acting insulin glargine. Glargine has no peak action time and instead acts consistently over a twenty-four hour period, helping reduce the frequency of hypoglycemic episodes.
Alternatively, intensive therapy regimes can be administered by continuous insulin infusion (CSII) pumps. These devices attempt to closely mimic the behaviour of the pancreas, continuously providing a basal level insulin to the body with additional boluses at meal times. Modern CSII pumps are comprised of a small battery-driven pump that is designed to administer insulin subcutaneously through the abdominal wall via butterfly needle. The insulin dose is adjusted in response to measured capillary glucose values in a fashion similar to MDI and is thus often seen as a preferred method to multiple injection therapy. There are, however, still risks associated with the use of CSII pumps. Despite the increased use of CSII pumps, there is uncertainty around their effectiveness as compared to MDI for improving glycemic control.
Part A: Type 1 Diabetic Adults (≥19 years)
An evidence-based analysis on the efficacy of CSII pumps compared to MDI was carried out on both type 1 and type 2 adult diabetic populations.
Research Questions
Are CSII pumps more effective than MDI for improving glycemic control in adults (≥19 years) with type 1 diabetes?
Are CSII pumps more effective than MDI for improving additional outcomes related to diabetes such as quality of life (QoL)?
Literature Search
Inclusion Criteria
Randomized controlled trials, systematic reviews, meta-analysis and/or health technology assessments from MEDLINE, EMBASE, CINAHL
Adults (≥ 19 years)
Type 1 diabetes
Study evaluates CSII vs. MDI
Published between January 1, 2002 – March 24, 2009
Patient currently on intensive insulin therapy
Exclusion Criteria
Studies with <20 patients
Studies <5 weeks in duration
CSII applied only at night time and not 24 hours/day
Mixed group of diabetes patients (children, adults, type 1, type 2)
Pregnancy studies
Outcomes of Interest
The primary outcomes of interest were glycosylated hemoglobin (HbA1c) levels, mean daily blood glucose, glucose variability, and frequency of hypoglycaemic events. Other outcomes of interest were insulin requirements, adverse events, and quality of life.
Search Strategy
The literature search strategy employed keywords and subject headings to capture the concepts of:
1) insulin pumps, and
2) type 1 diabetes.
The search was run on July 6, 2008 in the following databases: Ovid MEDLINE (1996 to June Week 4 2008), OVID MEDLINE In-Process and Other Non-Indexed Citations, EMBASE (1980 to 2008 Week 26), OVID CINAHL (1982 to June Week 4 2008) the Cochrane Library, and the Centre for Reviews and Dissemination/International Agency for Health Technology Assessment. A search update was run on March 24, 2009 and studies published prior to 2002 were also examined for inclusion into the review. Parallel search strategies were developed for the remaining databases. Search results were limited to human and English-language published between January 2002 and March 24, 2009. Abstracts were reviewed, and studies meeting the inclusion criteria outlined above were obtained. Reference lists were also checked for relevant studies.
Summary of Findings
The database search identified 519 relevant citations published between 1996 and March 24, 2009. Of the 519 abstracts reviewed, four RCTs and one abstract met the inclusion criteria outlined above. While efficacy outcomes were reported in each of the trials, a meta-analysis was not possible due to missing data around standard deviations of change values as well as missing data for the first period of the crossover arm of the trial. Meta-analysis was not possible on other outcomes (quality of life, insulin requirements, frequency of hypoglycemia) due to differences in reporting.
HbA1c
In studies where no baseline data was reported, the final values were used. Two studies (Hanaire-Broutin et al. 2000, Hoogma et al. 2005) reported a slight reduction in HbA1c of 0.35% and 0.22% respectively for CSII pumps in comparison to MDI. A slightly larger reduction in HbA1c of 0.84% was reported by DeVries et al.; however, this study was the only study to include patients with poor glycemic control marked by higher baseline HbA1c levels. One study (Bruttomesso et al. 2008) showed no difference between CSII pumps and MDI on Hba1c levels and was the only study using insulin glargine (consistent with results of parallel RCT in abstract by Bolli 2004). While there is statistically significant reduction in HbA1c in three of four trials, there is no evidence to suggest these results are clinically significant.
Mean Blood Glucose
Three of four studies reported a statistically significant reduction in the mean daily blood glucose for patients using CSII pump, though these results were not clinically significant. One study (DeVries et al. 2002) did not report study data on mean blood glucose but noted that the differences were not statistically significant. There is difficulty with interpreting study findings as blood glucose was measured differently across studies. Three of four studies used a glucose diary, while one study used a memory meter. In addition, frequency of self monitoring of blood glucose (SMBG) varied from four to nine times per day. Measurements used to determine differences in mean daily blood glucose between the CSII pump group and MDI group at clinic visits were collected at varying time points. Two studies use measurements from the last day prior to the final visit (Hoogma et al. 2005, DeVries et al. 2002), while one study used measurements taken during the last 30 days and another study used measurements taken during the 14 days prior to the final visit of each treatment period.
Glucose Variability
All four studies showed a statistically significant reduction in glucose variability for patients using CSII pumps compared to those using MDI, though one, Bruttomesso et al. 2008, only showed a significant reduction at the morning time point. Brutomesso et al. also used alternate measures of glucose variability and found that both the Lability index and mean amplitude of glycemic excursions (MAGE) were in concordance with the findings using the standard deviation (SD) values of mean blood glucose, but the average daily risk range (ADRR) showed no difference between the CSII pump and MDI groups.
Hypoglycemic Events
There is conflicting evidence concerning the efficacy of CSII pumps in decreasing both mild and severe hypoglycemic events. For mild hypoglycemic events, DeVries et al. observed a higher number of events per patient week in the CSII pump group than the MDI group, while Hoogma et al. observed a higher number of events per patient year in the MDI group. The remaining two studies found no differences between the two groups in the frequency of mild hypoglycemic events. For severe hypoglycemic events, Hoogma et al. found an increase in events per patient year among MDI patients, however, all of the other RCTs showed no difference between the patient groups in this aspect.
Insulin Requirements and Adverse Events
In all four studies, insulin requirements were significantly lower in patients receiving CSII pump treatment in comparison to MDI. This difference was statistically significant in all studies. Adverse events were reported in three studies. Devries et al. found no difference in ketoacidotic episodes between CSII pump and MDI users. Bruttomesso et al. reported no adverse events during the study. Hanaire-Broutin et al. found that 30 patients experienced 58 serious adverse events (SAEs) during MDI and 23 patients had 33 SAEs during treatment out of a total of 256 patients. Most events were related to severe hypoglycemia and diabetic ketoacidosis.
Quality of Life and Patient Preference
QoL was measured in three studies and patient preference was measured in one. All three studies found an improvement in QoL for CSII users compared to those using MDI, although various instruments were used among the studies and possible reporting bias was evident as non-positive outcomes were not consistently reported. Moreover, there was also conflicting results in two of the studies using the Diabetes Treatment Satisfaction Questionnaire (DTSQ). DeVries et al. reported no difference in treatment satisfaction between CSII pump users and MDI users while Brutomesso et al. reported that treatment satisfaction improved among CSII pump users.
Patient preference for CSII pumps was demonstrated in just one study (Hanaire-Broutin et al. 2000) and there are considerable limitations with interpreting this data as it was gathered through interview and 72% of patients that preferred CSII pumps were previously on CSII pump therapy prior to the study. As all studies were industry sponsored, findings on QoL and patient preference must be interpreted with caution.
Quality of Evidence
Overall, the body of evidence was downgraded from high to low due to study quality and issues with directness as identified using the GRADE quality assessment tool (see Table 1) While blinding of patient to intervention/control was not feasible in these studies, blinding of study personnel during outcome assessment and allocation concealment were generally lacking. Trials reported consistent results for the outcomes HbA1c, mean blood glucose and glucose variability, but the directness or generalizability of studies, particularly with respect to the generalizability of the diabetic population, was questionable as most trials used highly motivated populations with fairly good glycemic control. In addition, the populations in each of the studies varied with respect to prior treatment regimens, which may not be generalizable to the population eligible for pumps in Ontario. For the outcome of hypoglycaemic events the evidence was further downgraded to very low since there was conflicting evidence between studies with respect to the frequency of mild and severe hypoglycaemic events in patients using CSII pumps as compared to CSII (see Table 2). The GRADE quality of evidence for the use of CSII in adults with type 1 diabetes is therefore low to very low and any estimate of effect is, therefore, uncertain.
GRADE Quality Assessment for CSII pumps vs. MDI on HbA1c, Mean Blood Glucose, and Glucose Variability for Adults with Type 1 Diabetes
Inadequate or unknown allocation concealment (3/4 studies); Unblinded assessment (all studies) however lack of blinding due to the nature of the study; No ITT analysis (2/4 studies); possible bias SMBG (all studies)
HbA1c: 3/4 studies show consistency however magnitude of effect varies greatly; Single study uses insulin glargine instead of NPH; Mean Blood Glucose: 3/4 studies show consistency however magnitude of effect varies between studies; Glucose Variability: All studies show consistency but 1 study only showed a significant effect in the morning
Generalizability in question due to varying populations: highly motivated populations, educational component of interventions/ run-in phases, insulin pen use in 2/4 studies and varying levels of baseline glycemic control and experience with intensified insulin therapy, pumps and MDI.
GRADE Quality Assessment for CSII pumps vs. MDI on Frequency of Hypoglycemic
Inadequate or unknown allocation concealment (3/4 studies); Unblinded assessment (all studies) however lack of blinding due to the nature of the study; No ITT analysis (2/4 studies); possible bias SMBG (all studies)
Conflicting evidence with respect to mild and severe hypoglycemic events reported in studies
Generalizability in question due to varying populations: highly motivated populations, educational component of interventions/ run-in phases, insulin pen use in 2/4 studies and varying levels of baseline glycemic control and experience with intensified insulin therapy, pumps and MDI.
Economic Analysis
One article was included in the analysis from the economic literature scan. Four other economic evaluations were identified but did not meet our inclusion criteria. Two of these articles did not compare CSII with MDI and the other two articles used summary estimates from a mixed population with Type 1 and 2 diabetes in their economic microsimulation to estimate costs and effects over time. Included were English articles that conducted comparisons between CSII and MDI with the outcome of Quality Adjusted Life Years (QALY) in an adult population with type 1 diabetes.
From one study, a subset of the population with type 1 diabetes was identified that may be suitable and benefit from using insulin pumps. There is, however, limited data in the literature addressing the cost-effectiveness of insulin pumps versus MDI in type 1 diabetes. Longer term models are required to estimate the long term costs and effects of pumps compared to MDI in this population.
Conclusions
CSII pumps for the treatment of adults with type 1 diabetes
Based on low-quality evidence, CSII pumps confer a statistically significant but not clinically significant reduction in HbA1c and mean daily blood glucose as compared to MDI in adults with type 1 diabetes (>19 years).
CSII pumps also confer a statistically significant reduction in glucose variability as compared to MDI in adults with type 1 diabetes (>19 years) however the clinical significance is unknown.
There is indirect evidence that the use of newer long-acting insulins (e.g. insulin glargine) in MDI regimens result in less of a difference between MDI and CSII compared to differences between MDI and CSII in which older insulins are used.
There is conflicting evidence regarding both mild and severe hypoglycemic events in this population when using CSII pumps as compared to MDI. These findings are based on very low-quality evidence.
There is an improved quality of life for patients using CSII pumps as compared to MDI however, limitations exist with this evidence.
Significant limitations of the literature exist specifically:
All studies sponsored by insulin pump manufacturers
All studies used crossover design
Prior treatment regimens varied
Types of insulins used in study varied (NPH vs. glargine)
Generalizability of studies in question as populations were highly motivated and half of studies used insulin pens as the mode of delivery for MDI
One short-term study concluded that pumps are cost-effective, although this was based on limited data and longer term models are required to estimate the long-term costs and effects of pumps compared to MDI in adults with type 1 diabetes.
Part B: Type 2 Diabetic Adults
Research Questions
Are CSII pumps more effective than MDI for improving glycemic control in adults (≥19 years) with type 2 diabetes?
Are CSII pumps more effective than MDI for improving other outcomes related to diabetes such as quality of life?
Literature Search
Inclusion Criteria
Randomized controlled trials, systematic reviews, meta-analysis and/or health technology assessments from MEDLINE, Excerpta Medica Database (EMBASE), Cumulative Index to Nursing & Allied Health Literature (CINAHL)
Any person with type 2 diabetes requiring insulin treatment intensive
Published between January 1, 2000 – August 2008
Exclusion Criteria
Studies with <10 patients
Studies <5 weeks in duration
CSII applied only at night time and not 24 hours/day
Mixed group of diabetes patients (children, adults, type 1, type 2)
Pregnancy studies
Outcomes of Interest
The primary outcome of interest was a reduction in glycosylated hemoglobin (HbA1c) levels. Other outcomes of interest were mean blood glucose level, glucose variability, insulin requirements, frequency of hypoglycemic events, adverse events, and quality of life.
Search Strategy
A comprehensive literature search was performed in OVID MEDLINE, MEDLINE In-Process and Other Non-Indexed Citations, EMBASE, CINAHL, The Cochrane Library, and the International Agency for Health Technology Assessment (INAHTA) for studies published between January 1, 2000 and August 15, 2008. Studies meeting the inclusion criteria were selected from the search results. Data on the study characteristics, patient characteristics, primary and secondary treatment outcomes, and adverse events were abstracted. Reference lists of selected articles were also checked for relevant studies. The quality of the evidence was assessed as high, moderate, low, or very low according to the GRADE methodology.
Summary of Findings
The database search identified 286 relevant citations published between 1996 and August 2008. Of the 286 abstracts reviewed, four RCTs met the inclusion criteria outlined above. Upon examination, two studies were subsequently excluded from the meta-analysis due to small sample size and missing data (Berthe et al.), as well as outlier status and high drop out rate (Wainstein et al) which is consistent with previously reported meta-analyses on this topic (Jeitler et al 2008, and Fatourechi M et al. 2009).
HbA1c
The primary outcome in this analysis was reduction in HbA1c. Both studies demonstrated that both CSII pumps and MDI reduce HbA1c, but neither treatment modality was found to be superior to the other. The results of a random effects model meta-analysis showed a mean difference in HbA1c of -0.14 (-0.40, 0.13) between the two groups, which was found not to be statistically or clinically significant. There was no statistical heterogeneity observed between the two studies (I2=0%).
Forrest plot of two parallel, RCTs comparing CSII to MDI in type 2 diabetes
Secondary Outcomes
Mean Blood Glucose and Glucose Variability
Mean blood glucose was only used as an efficacy outcome in one study (Raskin et al. 2003). The authors found that the only time point in which there were consistently lower blood glucose values for the CSII group compared to the MDI group was 90 minutes after breakfast. Glucose variability was not examined in either study and the authors reported no difference in weight gain between the CSII pump group and MDI groups at the end of study. Conflicting results were reported regarding injection site reactions between the two studies. Herman et al. reported no difference in the number of subjects experiencing site problems between the two groups, while Raskin et al. reported that there were no injection site reactions in the MDI group but 15 such episodes among 8 participants in the CSII pump group.
Frequency of Hypoglycemic Events and Insulin Requirements
All studies reported that there were no differences in the number of mild hypoglycemic events in patients on CSII pumps versus MDI. Herman et al. also reported no differences in the number of severe hypoglycemic events in patients using CSII pumps compared to those on MDI. Raskin et al. reported that there were no severe hypoglycemic events in either group throughout the study duration. Insulin requirements were only examined in Herman et al., who found that daily insulin requirements were equal between the CSII pump and MDI treatment groups.
Quality of Life
QoL was measured by Herman et al. using the Diabetes Quality of Life Clinical Trial Questionnaire (DQOLCTQ). There were no differences reported between CSII users and MDI users for treatment satisfaction, diabetes impact, and worry-related scores. Patient satisfaction was measured in Raskin et al. using a patient satisfaction questionnaire, whose results indicated that patients in the CSII pump group had significantly greater improvement in overall treatment satisfaction at the end of the study compared to the MDI group. Although patient preference was also reported, it was only examined in the CSII pump group, thus results indicating a greater preference for CSII pumps in this groups (as compared to prior injectable insulin regimens) are biased and must be interpreted with caution.
Quality of Evidence
Overall, the body of evidence was downgraded from high to low according to study quality and issues with directness as identified using the GRADE quality assessment tool (see Table 3). While blinding of patient to intervention/control is not feasible in these studies, blinding of study personnel during outcome assessment and allocation concealment were generally lacking. ITT was not clearly explained in one study and heterogeneity between study populations was evident from participants’ treatment regimens prior to study initiation. Although trials reported consistent results for HbA1c outcomes, the directness or generalizability of studies, particularly with respect to the generalizability of the diabetic population, was questionable as trials required patients to adhere to an intense SMBG regimen. This suggests that patients were highly motivated. In addition, since prior treatment regimens varied between participants (no requirement for patients to be on MDI), study findings may not be generalizable to the population eligible for a pump in Ontario. The GRADE quality of evidence for the use of CSII in adults with type 2 diabetes is, therefore, low and any estimate of effect is uncertain.
GRADE Quality Assessment for CSII pumps vs. MDI on HbA1c Adults with Type 2 Diabetes
Inadequate or unknown allocation concealment (all studies); Unblinded assessment (all studies) however lack of blinding due to the nature of the study; ITT not well explained in 1 of 2 studies
Indirect due to lack of generalizability of findings since participants varied with respect to prior treatment regimens and intensive SMBG suggests highly motivated populations used in trials.
Economic Analysis
An economic analysis of CSII pumps was carried out using the Ontario Diabetes Economic Model (ODEM) and has been previously described in the report entitled “Application of the Ontario Diabetes Economic Model (ODEM) to Determine the Cost-effectiveness and Budget Impact of Selected Type 2 Diabetes Interventions in Ontario”, part of the diabetes strategy evidence series. Based on the analysis, CSII pumps are not cost-effective for adults with type 2 diabetes, either for the age 65+ sub-group or for all patients in general. Details of the analysis can be found in the full report.
Conclusions
CSII pumps for the treatment of adults with type 2 diabetes
There is low quality evidence demonstrating that the efficacy of CSII pumps is not superior to MDI for adult type 2 diabetics.
There were no differences in the number of mild and severe hypoglycemic events in patients on CSII pumps versus MDI.
There are conflicting findings with respect to an improved quality of life for patients using CSII pumps as compared to MDI.
Significant limitations of the literature exist specifically:
All studies sponsored by insulin pump manufacturers
Prior treatment regimens varied
Types of insulins used in study varied (NPH vs. glargine)
Generalizability of studies in question as populations may not reflect eligible patient population in Ontario (participants not necessarily on MDI prior to study initiation, pen used in one study and frequency of SMBG required during study was high suggesting highly motivated participants)
Based on ODEM, insulin pumps are not cost-effective for adults with type 2 diabetes either for the age 65+ sub-group or for all patients in general.
PMCID: PMC3377523  PMID: 23074525
23.  Optimal caliper widths for propensity-score matching when estimating differences in means and differences in proportions in observational studies 
Pharmaceutical Statistics  2010;10(2):150-161.
In a study comparing the effects of two treatments, the propensity score is the probability of assignment to one treatment conditional on a subject's measured baseline covariates. Propensity-score matching is increasingly being used to estimate the effects of exposures using observational data. In the most common implementation of propensity-score matching, pairs of treated and untreated subjects are formed whose propensity scores differ by at most a pre-specified amount (the caliper width). There has been a little research into the optimal caliper width. We conducted an extensive series of Monte Carlo simulations to determine the optimal caliper width for estimating differences in means (for continuous outcomes) and risk differences (for binary outcomes). When estimating differences in means or risk differences, we recommend that researchers match on the logit of the propensity score using calipers of width equal to 0.2 of the standard deviation of the logit of the propensity score. When at least some of the covariates were continuous, then either this value, or one close to it, minimized the mean square error of the resultant estimated treatment effect. It also eliminated at least 98% of the bias in the crude estimator, and it resulted in confidence intervals with approximately the correct coverage rates. Furthermore, the empirical type I error rate was approximately correct. When all of the covariates were binary, then the choice of caliper width had a much smaller impact on the performance of estimation of risk differences and differences in means. Copyright © 2010 John Wiley & Sons, Ltd.
doi:10.1002/pst.433
PMCID: PMC3120982  PMID: 20925139
propensity score; observational study; binary data; risk difference; propensity-score matching; Monte Carlo simulations; bias; matching
24.  Variable Importance and Prediction Methods for Longitudinal Problems with Missing Variables 
PLoS ONE  2015;10(3):e0120031.
We present prediction and variable importance (VIM) methods for longitudinal data sets containing continuous and binary exposures subject to missingness. We demonstrate the use of these methods for prognosis of medical outcomes of severe trauma patients, a field in which current medical practice involves rules of thumb and scoring methods that only use a few variables and ignore the dynamic and high-dimensional nature of trauma recovery. Well-principled prediction and VIM methods can provide a tool to make care decisions informed by the high-dimensional patient’s physiological and clinical history. Our VIM parameters are analogous to slope coefficients in adjusted regressions, but are not dependent on a specific statistical model, nor require a certain functional form of the prediction regression to be estimated. In addition, they can be causally interpreted under causal and statistical assumptions as the expected outcome under time-specific clinical interventions, related to changes in the mean of the outcome if each individual experiences a specified change in the variable (keeping other variables in the model fixed). Better yet, the targeted MLE used is doubly robust and locally efficient. Because the proposed VIM does not constrain the prediction model fit, we use a very flexible ensemble learner (the SuperLearner), which returns a linear combination of a list of user-given algorithms. Not only is such a prediction algorithm intuitive appealing, it has theoretical justification as being asymptotically equivalent to the oracle selector. The results of the analysis show effects whose size and significance would have been not been found using a parametric approach (such as stepwise regression or LASSO). In addition, the procedure is even more compelling as the predictor on which it is based showed significant improvements in cross-validated fit, for instance area under the curve (AUC) for a receiver-operator curve (ROC). Thus, given that 1) our VIM applies to any model fitting procedure, 2) under assumptions has meaningful clinical (causal) interpretations and 3) has asymptotic (influence-curve) based robust inference, it provides a compelling alternative to existing methods for estimating variable importance in high-dimensional clinical (or other) data.
doi:10.1371/journal.pone.0120031
PMCID: PMC4376910  PMID: 25815719
25.  On a Closed-Form Doubly Robust Estimator of the Adjusted Odds Ratio for a Binary Exposure 
American Journal of Epidemiology  2013;177(11):1314-1316.
Epidemiologic studies often aim to estimate the odds ratio for the association between a binary exposure and a binary disease outcome. Because confounding bias is of serious concern in observational studies, investigators typically estimate the adjusted odds ratio in a multivariate logistic regression which conditions on a large number of potential confounders. It is well known that modeling error in specification of the confounders can lead to substantial bias in the adjusted odds ratio for exposure. As a remedy, Tchetgen Tchetgen et al. (Biometrika. 2010;97(1):171–180) recently developed so-called doubly robust estimators of an adjusted odds ratio by carefully combining standard logistic regression with reverse regression analysis, in which exposure is the dependent variable and both the outcome and the confounders are the independent variables. Double robustness implies that only one of the 2 modeling strategies needs to be correct in order to make valid inferences about the odds ratio parameter. In this paper, I aim to introduce this recent methodology into the epidemiologic literature by presenting a simple closed-form doubly robust estimator of the adjusted odds ratio for a binary exposure. A SAS macro (SAS Institute Inc., Cary, North Carolina) is given in an online appendix to facilitate use of the approach in routine epidemiologic practice, and a simulated data example is also provided for the purpose of illustration.
doi:10.1093/aje/kws377
PMCID: PMC3664333  PMID: 23558352
case-control sampling; doubly robust estimator; logistic regression; odds ratio; SAS macro

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