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1.  Ensemble learning of inverse probability weights for marginal structural modeling in large observational datasets 
Statistics in medicine  2014;34(1):106-117.
Inverse probability weights used to fit marginal structural models are typically estimated using logistic regression. However a data-adaptive procedure may be able to better exploit information available in measured covariates. By combining predictions from multiple algorithms, ensemble learning offers an alternative to logistic regression modeling to further reduce bias in estimated marginal structural model parameters. We describe the application of two ensemble learning approaches to estimating stabilized weights: super learning (SL), an ensemble machine learning approach that relies on V -fold cross validation, and an ensemble learner (EL) that creates a single partition of the data into training and validation sets. Longitudinal data from two multicenter cohort studies in Spain (CoRIS and CoRIS-MD) were analyzed to estimate the mortality hazard ratio for initiation versus no initiation of combined antiretroviral therapy among HIV positive subjects. Both ensemble approaches produced hazard ratio estimates further away from the null, and with tighter confidence intervals, than logistic regression modeling. Computation time for EL was less than half that of SL. We conclude that ensemble learning using a library of diverse candidate algorithms offers an alternative to parametric modeling of inverse probability weights when fitting marginal structural models. With large datasets, EL provides a rich search over the solution space in less time than SL with comparable results.
PMCID: PMC4262745  PMID: 25316152
ensemble learning; super learning; marginal structural model; inverse probability weighting; data-adaptive; longitudinal data
2.  Evaluation of the duplication of staging CT scans for localized colon cancer in Medicare population 
Medical care  2014;52(11):963-968.
To quantify and characterize duplicated tests done during the staging of localized colon cancer in Medicare population.
We used the SEER-Medicare linked database to select patients diagnosed with localized colon cancer the years 1996–2009. We considered a patient as adequately staged after having received a colonoscopy, an abdominal CT scan, and a pelvic CT scan. Abdominal and pelvic CT scans performed between complete staging and first cancer-directed treatment, if not ordered due to an acute condition, were considered duplicates. We characterized the institutions providing the tests and evaluated the association with survival using a weighted pooled logistic regression adjusted by baseline and time-varying confounders.
Of 36,291 patients with a complete staging, 2,680 (7.4%) had at least one duplicated test. Patients receiving a duplicate had a higher comorbidity score, were more symptomatic, and had more visits to the emergency department and clinical evaluations. They also were treated with surgery less frequently and had worse survival (HR 1.22, 95% CI 1.16-1.28). The type of institution involved in the staging (non-profit/government centers, proprietary centers, free-standing facilities) was not associated with receiving duplicated tests.
We found a low frequency of duplicated abdominal or pelvic CT scans in the staging of colon cancer in Medicare population.
PMCID: PMC4197077  PMID: 25226545
colon cancer; CAT scan; SEER-Medicare; staging; prognosis
4.  Antiretroviral penetration into the CNS and incidence of AIDS-defining neurologic conditions 
Neurology  2014;83(2):134-141.
The link between CNS penetration of antiretrovirals and AIDS-defining neurologic disorders remains largely unknown.
HIV-infected, antiretroviral therapy–naive individuals in the HIV-CAUSAL Collaboration who started an antiretroviral regimen were classified according to the CNS Penetration Effectiveness (CPE) score of their initial regimen into low (<8), medium (8–9), or high (>9) CPE score. We estimated “intention-to-treat” hazard ratios of 4 neuroAIDS conditions for baseline regimens with high and medium CPE scores compared with regimens with a low score. We used inverse probability weighting to adjust for potential bias due to infrequent follow-up.
A total of 61,938 individuals were followed for a median (interquartile range) of 37 (18, 70) months. During follow-up, there were 235 cases of HIV dementia, 169 cases of toxoplasmosis, 128 cases of cryptococcal meningitis, and 141 cases of progressive multifocal leukoencephalopathy. The hazard ratio (95% confidence interval) for initiating a combined antiretroviral therapy regimen with a high vs low CPE score was 1.74 (1.15, 2.65) for HIV dementia, 0.90 (0.50, 1.62) for toxoplasmosis, 1.13 (0.61, 2.11) for cryptococcal meningitis, and 1.32 (0.71, 2.47) for progressive multifocal leukoencephalopathy. The respective hazard ratios (95% confidence intervals) for a medium vs low CPE score were 1.01 (0.73, 1.39), 0.80 (0.56, 1.15), 1.08 (0.73, 1.62), and 1.08 (0.73, 1.58).
We estimated that initiation of a combined antiretroviral therapy regimen with a high CPE score increases the risk of HIV dementia, but not of other neuroAIDS conditions.
PMCID: PMC4117168  PMID: 24907236
5.  Observational studies analyzed like randomized experiments: an application to postmenopausal hormone therapy and coronary heart disease 
Epidemiology (Cambridge, Mass.)  2008;19(6):766-779.
The Women’s Health Initiative randomized trial found greater coronary heart disease (CHD) risk in women assigned to estrogen/progestin therapy than in those assigned to placebo. Observational studies had previously suggested reduced CHD risk in hormone users.
Using data from the observational Nurses’ Health Study, we emulated the design and intention-to-treat (ITT) analysis of the randomized trial. The observational study was conceptualized as a sequence of “trials” in which eligible women were classified as initiators or noninitiators of estrogen/progestin therapy.
The ITT hazard ratios (95% confidence intervals) of CHD for initiators versus noninitiators were 1.42 (0.92 – 2.20) for the first 2 years, and 0.96 (0.78 – 1.18) for the entire follow-up. The ITT hazard ratios were 0.84 (0.61 – 1.14) in women within 10 years of menopause, and 1.12 (0.84 – 1.48) in the others (P value for interaction = 0.08). These ITT estimates are similar to those from the Women’s Health Initiative. Because the ITT approach causes severe treatment misclassification, we also estimated adherence-adjusted effects by inverse probability weighting. The hazard ratios were 1.61 (0.97 – 2.66) for the first 2 years, and 0.98 (0.66 – 1.49) for the entire follow-up. The hazard ratios were 0.54 (0.19 – 1.51) in women within 10 years after menopause, and 1.20 (0.78 – 1.84) in others (P value for interaction = 0.01). Finally, we also present comparisons between these estimates and previously reported NHS estimates.
Our findings suggest that the discrepancies between the Women’s Health Initiative and Nurses’ Health Study ITT estimates could be largely explained by differences in the distribution of time since menopause and length of follow-up.
PMCID: PMC3731075  PMID: 18854702
6.  Observational data for comparative effectiveness research: an emulation of randomised trials to estimate the effect of statins on primary prevention of coronary heart disease 
This article reviews methods to estimate treatment effectiveness research using observational data. The basic idea is using an observational study to emulate a hypothetical randomised trial by comparing initiators vs. non-initiators of treatment. After adjustment for baseline confounders, one can estimate the analogue of the intention-to-treat effect. We also explain two approaches to adjust for imperfect adherence using the per-protocol and as-treated analyses after adjusting for measured time-varying confounding and selection bias using inverse probability weighting of marginal structural models.
As an example, we implemented these methods to estimate the effect of statins for primary prevention of coronary heart disease (CHD) using data from electronic medical records in the United Kingdom. Despite strong confounding by indication, our approach detected a potential benefit of statin therapy. The analogue of the intention-to-treat hazard ratio of CHD was 0.89 (0.73, 1.09) for statin initiators vs. noninitiators. The hazard ratio of CHD was 0.84 (0.54, 1.30) in the per-protocol analysis and 0.79 (0.41, 1.41) in the as-treated analysis for 2-years of use vs. no use. In contrast, a conventional comparison of current users vs. never users of statin therapy resulted in a hazard ratio of 1.31 (1.04, 1.66). We provide a flexible and annotated SAS program to implement the proposed analyses.
PMCID: PMC3613145  PMID: 22016461
comparative effectiveness; confounding; intention-to-treat analysis; per-protocol analysis; as-treated analysis; selection bias; inverse-probability weighting
7.  Estimating absolute risks in the presence of nonadherence: An application to a follow-up study with baseline randomization 
Epidemiology (Cambridge, Mass.)  2010;21(4):528-539.
The intention-to-treat (ITT) analysis provides a valid test of the null hypothesis and naturally results in both absolute and relative measures of risk. However, this analytic approach may miss the occurrence of serious adverse effects that would have been detected under full adherence to the assigned treatment. Inverse probability weighting of marginal structural models has been used to adjust for nonadherence, but most studies have provided only relative measures of risk. In this study, we used inverse probability weighting to estimate both absolute and relative measures of risk of invasive breast cancer under full adherence to the assigned treatment in the Women’s Health Initiative estrogen-plus-progestin trial. In contrast to an ITT hazard ratio (HR) of 1.25 (95% confidence interval [CI] = 1.01 to 1.54), the HR for 8-year continuous estrogen-plus-progestin use versus no use was 1.68 (1.24 to 2.28). The estimated risk difference (cases/100 women) at year 8 was 0.83 (−0.03 to 1.69) in the ITT analysis, compared with 1.44 (0.52 to 2.37) in the adherence-adjusted analysis. Results were robust across various dose-response models. We also compared the dynamic treatment regime “take hormone therapy until certain adverse events become apparent, then stop taking hormone therapy” with no use (HR= 1.64; 95% CI = 1.24 to 2.18). The methods described here are also applicable to observational studies with time-varying treatments.
PMCID: PMC3315056  PMID: 20526200
8.  Regression Calibration with Heteroscedastic Error Variance 
The problem of covariate measurement error with heteroscedastic measurement error variance is considered. Standard regression calibration assumes that the measurement error has a homoscedastic measurement error variance. An estimator is proposed to correct regression coefficients for covariate measurement error with heteroscedastic variance. Point and interval estimates are derived. Validation data containing the gold standard must be available. This estimator is a closed-form correction of the uncorrected primary regression coefficients, which may be of logistic or Cox proportional hazards model form, and is closely related to the version of regression calibration developed by Rosner et al. (1990). The primary regression model can include multiple covariates measured without error. The use of these estimators is illustrated in two data sets, one taken from occupational epidemiology (the ACE study) and one taken from nutritional epidemiology (the Nurses’ Health Study). In both cases, although there was evidence of moderate heteroscedasticity, there was little difference in estimation or inference using this new procedure compared to standard regression calibration. It is shown theoretically that unless the relative risk is large or measurement error severe, standard regression calibration approximations will typically be adequate, even with moderate heteroscedasticity in the measurement error model variance. In a detailed simulation study, standard regression calibration performed either as well as or better than the new estimator. When the disease is rare and the errors normally distributed, or when measurement error is moderate, standard regression calibration remains the method of choice.
PMCID: PMC3404553  PMID: 22848187
measurement error; logistic regression; heteroscedasticity; regression calibration
9.  When to Start Treatment? A Systematic Approach to the Comparison of Dynamic Regimes Using Observational Data* 
Dynamic treatment regimes are the type of regime most commonly used in clinical practice. For example, physicians may initiate combined antiretroviral therapy the first time an individual’s recorded CD4 cell count drops below either 500 cells/mm3 or 350 cells/mm3. This paper describes an approach for using observational data to emulate randomized clinical trials that compare dynamic regimes of the form “initiate treatment within a certain time period of some time-varying covariate first crossing a particular threshold.” We applied this method to data from the French Hospital database on HIV (FHDH-ANRS CO4), an observational study of HIV-infected patients, in order to compare dynamic regimes of the form “initiate treatment within m months after the recorded CD4 cell count first drops below x cells/mm3” where x takes values from 200 to 500 in increments of 10 and m takes values 0 or 3. We describe the method in the context of this example and discuss some complications that arise in emulating a randomized experiment using observational data.
PMCID: PMC3406513  PMID: 21972433
dynamic treatment regimes; marginal structural models; HIV infection; antiretroviral therapy
10.  Coronary heart disease in postmenopausal recipients of estrogen plus progestin therapy: Does the increased risk ever disappear? A randomized trial 
Annals of internal medicine  2010;152(4):211-217.
Estrogen-plus-progestin therapy increases the risk of coronary heart disease (CHD) in postmenopausal women. However, this increased risk might be limited to the first years of use and to women who start therapy late in menopause.
To estimate the effect of continuous estrogen-plus-progestin therapy on CHD risk over time and stratified by years since menopause, i.e., to estimate an adherence-adjusted effect.
The Women's Health Initiative randomized, double-blinded, placebo-controlled trial.
40 US clinical centers.
16,608 postmenopausal women with an intact uterus at baseline in 1993-1998
Conjugated equine estrogens, 0.625 mg/d, plus medroxyprogesterone acetate, 2.5 mg/d or placebo.
Adherence-adjusted hazard ratios (HRs) estimated via inverse probability weighting and CHD-free survival curves.
Compared with no use of hormone therapy, the HR (95% confidence interval [CI]) for continuous use of estrogen-plus-progestin was 2.36 (1.55-3.62) for the first 2 years and 1.69 (0.98-2.89) for the first 8 years. For women within 10 years after menopause, the HRs (95% CI) were 1.29 (0.52-3.18) for the first 2 years and 0.64 (0.21-1.99) for the first 8 years, and the CHD-free survival curves for continuous use and no use of estrogen-plus-progestin crossed at about 6 (95% CI: 2-10) years.
The analysis may have not fully adjusted for joint determinants of adherence and CHD risk. Sample sizes for some subgroup analyses were small.
There was no suggestion of a decreased risk of CHD from estrogen-plus-progestin within the first 2 years after randomization, including women who initiated therapy within 10 years after menopause, and a cardioprotective effect became apparent only after 6 years of use.
PMCID: PMC2936769  PMID: 20157135

Results 1-10 (10)