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1.  Varying-coefficient models for longitudinal processes with continuous-time informative dropout 
Biostatistics (Oxford, England)  2009;11(1):93-110.
Dropout is a common occurrence in longitudinal studies. Building upon the pattern-mixture modeling approach within the Bayesian paradigm, we propose a general framework of varying-coefficient models for longitudinal data with informative dropout, where measurement times can be irregular and dropout can occur at any point in continuous time (not just at observation times) together with administrative censoring. Specifically, we assume that the longitudinal outcome process depends on the dropout process through its model parameters. The unconditional distribution of the repeated measures is a mixture over the dropout (administrative censoring) time distribution, and the continuous dropout time distribution with administrative censoring is left completely unspecified. We use Markov chain Monte Carlo to sample from the posterior distribution of the repeated measures given the dropout (administrative censoring) times; Bayesian bootstrapping on the observed dropout (administrative censoring) times is carried out to obtain marginal covariate effects. We illustrate the proposed framework using data from a longitudinal study of depression in HIV-infected women; the strategy for sensitivity analysis on unverifiable assumption is also demonstrated.
doi:10.1093/biostatistics/kxp040
PMCID: PMC2800163  PMID: 19837655
HIV/AIDS; Missing data; Nonparametric regression; Penalized splines
2.  A varying-coefficient method for analyzing longitudinal clinical trials data with nonignorable dropout 
Contemporary clinical trials  2011;33(2):378-385.
Dropout is common in longitudinal clinical trials and when the probability of dropout depends on unobserved outcomes even after conditioning on available data, it is considered missing not at random and therefore nonignorable. To address this problem, mixture models can be used to account for the relationship between a longitudinal outcome and dropout. We propose a Natural Spline Varying-coefficient mixture model (NSV), which is a straightforward extension of the parametric Conditional Linear Model (CLM). We assume that the outcome follows a varying-coefficient model conditional on a continuous dropout distribution. Natural cubic B-splines are used to allow the regression coefficients to semiparametrically depend on dropout and inference is therefore more robust. Additionally, this method is computationally stable and relatively simple to implement. We conduct simulation studies to evaluate performance and compare methodologies in settings where the longitudinal trajectories are linear and dropout time is observed for all individuals. Performance is assessed under conditions where model assumptions are both met and violated. In addition, we compare the NSV to the CLM and a standard random-effects model using an HIV/AIDS clinical trial with probable nonignorable dropout. The simulation studies suggest that the NSV is an improvement over the CLM when dropout has a nonlinear dependence on the outcome.
doi:10.1016/j.cct.2011.11.009
PMCID: PMC3414213  PMID: 22101223
Dropout; Nonignorable Missing Data; Longitudinal data; Varying-coefficient model; B-spline; HIV/AIDS
3.  Bayesian Latent-class Mixed-effect Hybrid Models for Dyadic Longitudinal Data with Non-ignorable Dropouts 
Biometrics  2013;69(4):914-924.
SUMMARY
The analysis of longitudinal dyadic data is challenging due to the complicated correlations within and between dyads, as well as possibly non-ignorable dropouts. Based on a mixed-effects hybrid model, we propose an approach to analyze longitudinal dyadic data with non-ignorable dropouts. We factorize the joint distribution of the measurement and dropout processes into three components: the marginal distribution of random effects, the conditional distribution of the dropout process given the random effects, and the conditional distribution of the measurement process given the random effects and missing data patterns. We model the conditional dropout process using a discrete survival model, and the conditional measurement process using a latent-class pattern-mixture model. These models account for the dyadic interdependence using the “actor” and “partner” effects and dyad-specific random effects. We use the latent-dropout-class approach to address the problem of a large number of missing data patterns caused by the dyadic data structure. We evaluate the performance of the proposed method using a simulation study, and apply our method to a longitudinal dyadic data set that arose from a prostate cancer trial.
doi:10.1111/biom.12100
PMCID: PMC3970927  PMID: 24328715
dyadic; non-ignorable missingness; mixed-effect; longitudinal; latent class
4.  A marginalized conditional linear model for longitudinal binary data when informative dropout occurs in continuous time 
Biostatistics (Oxford, England)  2011;13(2):355-368.
Within the pattern-mixture modeling framework for informative dropout, conditional linear models (CLMs) are a useful approach to deal with dropout that can occur at any point in continuous time (not just at observation times). However, in contrast with selection models, inferences about marginal covariate effects in CLMs are not readily available if nonidentity links are used in the mean structures. In this article, we propose a CLM for long series of longitudinal binary data with marginal covariate effects directly specified. The association between the binary responses and the dropout time is taken into account by modeling the conditional mean of the binary response as well as the dependence between the binary responses given the dropout time. Specifically, parameters in both the conditional mean and dependence models are assumed to be linear or quadratic functions of the dropout time; and the continuous dropout time distribution is left completely unspecified. Inference is fully Bayesian. We illustrate the proposed model using data from a longitudinal study of depression in HIV-infected women, where the strategy of sensitivity analysis based on the extrapolation method is also demonstrated.
doi:10.1093/biostatistics/kxr041
PMCID: PMC3297830  PMID: 22133756
Bayesian analysis; HIV/AIDS; Marginal model; Missing data; Sensitivity analysis
5.  Accounting for dropout reason in longitudinal studies with nonignorable dropout 
Dropout is a common problem in longitudinal cohort studies and clinical trials, often raising concerns of nonignorable dropout. Selection, frailty, and mixture models have been proposed to account for potentially nonignorable missingness by relating the longitudinal outcome to time of dropout. In addition, many longitudinal studies encounter multiple types of missing data or reasons for dropout, such as loss to follow-up, disease progression, treatment modifications and death. When clinically distinct dropout reasons are present, it may be preferable to control for both dropout reason and time to gain additional clinical insights. This may be especially interesting when the dropout reason and dropout times differ by the primary exposure variable. We extend a semi-parametric varying-coefficient method for nonignorable dropout to accommodate dropout reason. We apply our method to untreated HIV-infected subjects recruited to the Acute Infection and Early Disease Research Program HIV cohort and compare longitudinal CD4+ T cell count in injection drug users to nonusers with two dropout reasons: anti-retroviral treatment initiation and loss to follow-up.
doi:10.1177/0962280215590432
PMCID: PMC4679750  PMID: 26078357
B-spline; dropout; HIV/AIDS; longitudinal data; nonignorable missing data; varying-coefficient model
6.  Growth Modeling with Non-Ignorable Dropout: Alternative Analyses of the STAR*D Antidepressant Trial 
Psychological methods  2011;16(1):17-33.
This paper uses a general latent variable framework to study a series of models for non-ignorable missingness due to dropout. Non-ignorable missing data modeling acknowledges that missingness may depend on not only covariates and observed outcomes at previous time points as with the standard missing at random (MAR) assumption, but also on latent variables such as values that would have been observed (missing outcomes), developmental trends (growth factors), and qualitatively different types of development (latent trajectory classes). These alternative predictors of missing data can be explored in a general latent variable framework using the Mplus program. A flexible new model uses an extended pattern-mixture approach where missingness is a function of latent dropout classes in combination with growth mixture modeling using latent trajectory classes. A new selection model allows not only an influence of the outcomes on missingness, but allows this influence to vary across latent trajectory classes. Recommendations are given for choosing models. The missing data models are applied to longitudinal data from STAR*D, the largest antidepressant clinical trial in the U.S. to date. Despite the importance of this trial, STAR*D growth model analyses using non-ignorable missing data techniques have not been explored until now. The STAR*D data are shown to feature distinct trajectory classes, including a low class corresponding to substantial improvement in depression, a minority class with a U-shaped curve corresponding to transient improvement, and a high class corresponding to no improvement. The analyses provide a new way to assess drug efficiency in the presence of dropout.
doi:10.1037/a0022634
PMCID: PMC3060937  PMID: 21381817
Latent trajectory classes; random effects; survival analysis; not missing at random
7.  A Flexible Bayesian Approach to Monotone Missing Data in Longitudinal Studies with Nonignorable Missingness with Application to an Acute Schizophrenia Clinical Trial 
We develop a Bayesian nonparametric model for a longitudinal response in the presence of nonignorable missing data. Our general approach is to first specify a working model that flexibly models the missingness and full outcome processes jointly. We specify a Dirichlet process mixture of missing at random (MAR) models as a prior on the joint distribution of the working model. This aspect of the model governs the fit of the observed data by modeling the observed data distribution as the marginalization over the missing data in the working model. We then separately specify the conditional distribution of the missing data given the observed data and dropout. This approach allows us to identify the distribution of the missing data using identifying restrictions as a starting point. We propose a framework for introducing sensitivity parameters, allowing us to vary the untestable assumptions about the missing data mechanism smoothly. Informative priors on the space of missing data assumptions can be specified to combine inferences under many different assumptions into a final inference and accurately characterize uncertainty. These methods are motivated by, and applied to, data from a clinical trial assessing the efficacy of a new treatment for acute Schizophrenia.
doi:10.1080/01621459.2014.969424
PMCID: PMC4517693  PMID: 26236060
Dirichlet process mixture; Identifiability; Identifying restrictions; Sensitivity analysis
8.  Bayesian Inference for Growth Mixture Models with Latent Class Dependent Missing Data 
Multivariate behavioral research  2011;46(4):567-597.
Growth mixture models (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class probabilities depend on some observed explanatory variables and data missingness depends on both the explanatory variables and a latent class variable. A full Bayesian method is then proposed to estimate the model. Through the data augmentation method, conditional posterior distributions for all model parameters and missing data are obtained. A Gibbs sampling procedure is then used to generate Markov chains of model parameters for statistical inference. The application of the model and the method is first demonstrated through the analysis of mathematical ability growth data from the National Longitudinal Survey of Youth 1997 (Bureau of Labor Statistics, U.S. Department of Labor, 1997). A simulation study considering 3 main factors (the sample size, the class probability, and the missing data mechanism) is then conducted and the results show that the proposed Bayesian estimation approach performs very well under the studied conditions. Finally, some implications of this study, including the misspecified missingness mechanism, the sample size, the sensitivity of the model, the number of latent classes, the model comparison, and the future directions of the approach, are discussed.
doi:10.1080/00273171.2011.589261
PMCID: PMC4002129  PMID: 24790248
9.  A comparison of parametric models for the investigation of the shape of cognitive change in the older population 
BMC Neurology  2008;8:16.
Background
Cognitive decline is a major threat to well being in later life. Change scores and regression based models have often been used for its investigation. Most methods used to describe cognitive decline assume individuals lose their cognitive abilities at a constant rate with time. The investigation of the parametric curve that best describes the process has been prevented by restrictions imposed by study design limitations and methodological considerations. We propose a comparison of parametric shapes that could be considered to describe the process of cognitive decline in late life.
Attrition plays a key role in the generation of missing observations in longitudinal studies of older persons. As ignoring missing observations will produce biased results and previous studies point to the important effect of the last observed cognitive score on the probability of dropout, we propose modelling both mechanisms jointly to account for these two considerations in the model likelihood.
Methods
Data from four interview waves of a population based longitudinal study of the older population, the Cambridge City over 75 Cohort Study were used. Within a selection model process, latent growth models combined with a logistic regression model for the missing data mechanism were fitted. To illustrate advantages of the model proposed, a sensitivity analysis of the missing data assumptions was conducted.
Results
Results showed that a quadratic curve describes cognitive decline best. Significant heterogeneity between individuals about mean curve parameters was identified. At all interviews, MMSE scores before dropout were significantly lower than those who remained in the study. Individuals with good functional ability were found to be less likely to dropout, as were women and younger persons in later stages of the study.
Conclusion
The combination of a latent growth model with a model for the missing data has permitted to make use of all available data and quantify the effect of significant predictors of dropout on the dropout and observational processes. Cognitive decline over time in older persons is often modelled as a linear process, though we have presented other parametric curves that may be considered.
doi:10.1186/1471-2377-8-16
PMCID: PMC2412911  PMID: 18485192
10.  A Random Pattern Mixture Model for Ordinal Outcomes with Informative Dropouts 
Statistics in medicine  2015;34(16):2391-2402.
We extend a random pattern mixture joint model for longitudinal ordinal outcomes and informative dropouts. The patients are generalized to ”pattern” groups based on known covariates that are potential surrogated for the severity of the underlying condition. The random pattern effects are defined as the latent effects linking the dropout process and the ordinal longitudinal outcome. Conditional on the random pattern effects, the longitudinal outcome and the dropout times are assumed independent. Estimates are obtained via the EM algorithm. We applied the model to the end-stage renal disease (ESRD) data. Anemia was found to be significantly affected by baseline iron treatment when the dropout information was adjusted via the study model; as opposed to an independent or shared parameter model. Simulations were performed to evaluate the performance of the random pattern mixture model under various assumptions.
doi:10.1002/sim.6514
PMCID: PMC4935089  PMID: 25894456
Adaptive gaussian quadrature; EM algorithm; Newton-Raphson algorithm; Pattern mixture model; Ordinal outcome
11.  Mixtures of Varying Coefficient Models for Longitudinal Data with Discrete or Continuous Nonignorable Dropout 
Biometrics  2004;60(4):854-864.
SUMMARY
The analysis of longitudinal repeated measures data is frequently complicated by missing data due to informative dropout. We describe a mixture model for joint distribution for longitudinal repeated measures, where the dropout distribution may be continuous and the dependence between response and dropout is semiparametric. Specifically, we assume that responses follow a varying coefficient random effects model conditional on dropout time, where the regression coefficients depend on dropout time through unspecified nonparametric functions that are estimated using step functions when dropout time is discrete (e.g., for panel data) and using smoothing splines when dropout time is continuous. Inference under the proposed semiparametric model is hence more robust than the parametric conditional linear model. The unconditional distribution of the repeated measures is a mixture over the dropout distribution. We show that estimation in the semiparametric varying coefficient mixture model can proceed by fitting a parametric mixed effects model and can be carried out on standard software platforms such as SAS. The model is used to analyze data from a recent AIDS clinical trial and its performance is evaluated using simulations.
doi:10.1111/j.0006-341X.2004.00240.x
PMCID: PMC2677904  PMID: 15606405
Clinical trials; Equivalence trial; Linear mixed model; Missing data; Nonignorable dropout; Pattern-mixture model; Pediatric AIDS; Selection bias; Smoothing splines
12.  BAYESIAN MODELING LONGITUDINAL DYADIC DATA WITH NONIGNORABLE DROPOUT, WITH APPLICATION TO A BREAST CANCER STUDY 
The annals of applied statistics  2012;6(2):753-771.
Dyadic data are common in the social and behavioral sciences, in which members of dyads are correlated due to the interdependence structure within dyads. The analysis of longitudinal dyadic data becomes complex when nonignorable dropouts occur. We propose a fully Bayesian selection-model-based approach to analyze longitudinal dyadic data with nonignorable dropouts. We model repeated measures on subjects by a transition model and account for within-dyad correlations by random effects. In the model, we allow subject’s outcome to depend on his/her own characteristics and measure history, as well as those of the other member in the dyad. We further account for the nonignorable missing data mechanism using a selection model in which the probability of dropout depends on the missing outcome. We propose a Gibbs sampler algorithm to fit the model. Simulation studies show that the proposed method effectively addresses the problem of nonignorable dropouts. We illustrate our methodology using a longitudinal breast cancer study.
doi:10.1214/11-AOAS515
PMCID: PMC3693094  PMID: 23814631
Dyadic Data; Missing Data; Nonignorable Dropout; Selection Model
13.  Identification of Multivariate Responders/Non-Responders Using Bayesian Growth Curve Latent Class Models 
Summary
In this paper, we propose a multivariate growth curve mixture model that groups subjects based on multiple symptoms measured repeatedly over time. Our model synthesizes features of two models. First, we follow Roy and Lin (2000) in relating the multiple symptoms at each time point to a single latent variable. Second, we use the growth mixture model of Muthén and Shedden (1999) to group subjects based on distinctive longitudinal profiles of this latent variable. The mean growth curve for the latent variable in each class defines that class’s features. For example, a class of “responders” would have a decline in the latent symptom summary variable over time. A Bayesian approach to estimation is employed where the methods of Elliott et al (2005) are extended to simultaneously estimate the posterior distributions of the parameters from the latent variable and growth curve mixture portions of the model. We apply our model to data from a randomized clinical trial evaluating the efficacy of Bacillus Calmette-Guerin (BCG) in treating symptoms of Interstitial Cystitis. In contrast to conventional approaches using a single subjective Global Response Assessment, we use the multivariate symptom data to identify a class of subjects where treatment demonstrates effectiveness. Simulations are used to confirm identifiability results and evaluate the performance of our algorithm. The definitive version of this paper is available at onlinelibrary.wiley.com.
doi:10.1111/j.1467-9876.2009.00663.x
PMCID: PMC3104279  PMID: 21637724
14.  Gastric Electrical Stimulation 
Executive Summary
Objective
The objective of this analysis was to assess the effectiveness, safety and cost-effectiveness of gastric electrical stimulation (GES) for the treatment of chronic, symptomatic refractory gastroparesis and morbid obesity.
Background
Gastroparesis - Epidemiology
Gastroparesis (GP) broadly refers to impaired gastric emptying in the absence of obstruction. Clinically, this can range from the incidental detection of delayed gastric emptying in an asymptomatic person to patients with severe nausea, vomiting and malnutrition. Symptoms of GP are nonspecific and may mimic structural disorders such as ulcer disease, partial gastric or small bowel obstruction, gastric cancer, and pancreaticobiliary disorders.
Gastroparesis may occur in association with diabetes, gastric surgery (consequence of peptic ulcer surgery and vagotomy) or for unknown reasons (idiopathic gastroparesis). Symptoms include early satiety, nausea, vomiting, abdominal pain and weight loss. The majority of patients with GP are women.
The relationship between upper gastrointestinal symptoms and the rate of gastric emptying is considered to be weak. Some patients with markedly delayed gastric emptying are asymptomatic and sometimes, severe symptoms may remit spontaneously.
Idiopathic GP may represent the most common form of GP. In one tertiary referral retrospective series, the etiologies in 146 GP patients were 36% idiopathic, 29% diabetic, 13% postgastric surgery, 7.5% Parkinson’s disease, 4.8% collagen vascular disorders, 4.1% intestinal pseudoobstruction and 6% miscellaneous causes.
The true prevalence of digestive symptoms in patients with diabetes and the relationship of these symptoms to delayed gastric emptying are unknown. Delayed gastric emptying is present in 27% to 58% of patients with type 1 diabetes and 30% with type 2 diabetes. However, highly variable rates of gastric emptying have been reported in type 1 and 2 diabetes, suggesting that development of GP in patients with diabetes is neither universal nor inevitable. In a review of studies examining gastric emptying in patients with diabetes compared to control patients, investigators noted that in many cases the magnitude of the delay in gastric emptying is modest.
GP may occur as a complication of a number of different surgical procedures. For example, vagal nerve injury may occur in 4% to 40% of patients who undergo laparoscopic fundoplication1 for gastroesophageal reflux disease.
The prevalence of severe, refractory GP is scantily reported in the literature. Using data from a past study, it has been estimated that the prevalence of severe, symptomatic and refractory GP in the United States population is 0.017%. Assuming an Ontario population of 13 million, this would correspond to approximately 2,000 people in Ontario having severe, symptomatic, refractory GP.
The incidence of severe refractory GP estimated by the United States Food and Drug Administration (FDA) is approximately 4,000 per year in the United States. This corresponds to about 150 patients in Ontario. Using expert opinion and FDA data, the incidence of severe refractory GP in Ontario is estimated to be about 20 to 150 per year.
Treatment for Gastroparesis
To date, there have been no long-term studies confirming the beneficial effects of maintaining euglycemia on GP symptoms. However, it has been suggested that consistent findings of physiologic studies in healthy volunteers and diabetes patients provides an argument to strive for near-normal blood glucose levels in affected diabetes patients.
Dietary measures (e.g., low fibre, low fat food), prokinetic drugs (e.g., domperidone, metoclopramide and erythromycin) and antiemetic or antinausea drugs (e.g, phenothiazines, diphenhydramine) are generally effective for symptomatic relief in the majority of patients with GP.
For patients with chronic, symptomatic GP who are refractory to drug treatment, surgical options may include jejunostomy tube for feeding, gastrotomy tube for stomach decompression and pyloroplasty for gastric emptying.
Few small studies examined the use of botulinum toxin injections into the pyloric sphincter. However, the contribution of excessive pyloric contraction to GP has been insufficiently defined and there have been no controlled studies of this therapy.
Treatment with GES is reversible and may be a less invasive option compared to stomach surgery for the treatment of patients with chronic, drug-refractory nausea and vomiting secondary to GP. In theory, GES represents an intermediate step between treatment directed at the underlying pathophysiology, and the treatment of symptoms. It is based on studies of gastric electrical patterns in GP that have identified the presence of a variety of gastric arrhythmias. Similar to a cardiac pacemaker, it was hypothesized that GES could override the abnormal rhythms, stimulate gastric emptying and eliminate symptoms.
Morbid Obesity Epidemiology
Obesity is defined as a body mass index (BMI) of at last 30 kg/m2. Morbid obesity is defined as a BMI of at least 40 kg/m2 or at least 35 kg/m2 with comorbid conditions. Comorbid conditions associated with obesity include diabetes, hypertension, dyslipidemias, obstructive sleep apnea, weight-related arthropathies, and stress urinary incontinence.
In the United States, the age-adjusted prevalence of extreme obesity (BMI ≥ 40 kg/m2) for adults aged 20 years and older has increased significantly in the population, from 2.9% (1988–1994) to 4.7% (1999–2000). An expert estimated that about 160,000 to 180,000 people are morbidly obese in Ontario.
Treatment for Morbid Obesity
Diet, exercise, and behavioural therapy are used to help people lose weight.
Bariatric surgery for morbid obesity is considered an intervention of last resort for patients who have attempted first-line forms of medical management.
Gastric stimulation has been investigated for the treatment of morbid obesity; the intention being to reduce appetite and induce early satiety possibly due to inhibitory effects on gastric motility and effects on the central nervous system (CNS) and hormones related to satiety and/or appetite.
Possible advantages to GES for the treatment of morbid obesity include reversibility of the procedure, less invasiveness than some bariatric procedures, e.g., gastric bypass, and less side effects (e.g., dumping syndrome).
The Device
Electrical stimulation is delivered via an implanted system that consists of a neurostimulator and 2 leads. The surgical procedure can be performed via either an open or laparoscopic approach. An external programmer used by the physician can deliver instructions to the GES, i.e., adjust the rate and amplitude of stimulation (Figure 1). GES may be turned off by the physician at any time or may be removed. The battery life is approximately 4-5 years
For treatment of GP, the GES leads are secured in the muscle of the lower stomach, 10 cm proximal to the pylorus (the opening from the stomach to the intestine), 1 cm apart and connected to an implantable battery-powered neurostimulator which is placed in a small pocket in the abdominal wall
For treatment of morbid obesity, GES leads are implanted along the lesser curvature of the stomach where the vagal nerve branches spread, approximately 8 cm proximal to the pylorus. However, the implant positioning of the leads has been variably reported in the literature.
Regulatory Status
The Enterra Therapy System and the Transcend II Implantable Gastric Stimulation System (Medtronic Inc.) are both licensed as class 3 devices by Health Canada (license numbers 60264 and 66948 respectively). The Health Canada indications for use are:
Enterra Therapy System
“For use in the treatment of chronic intractable (drug-refractory) nausea and vomiting.”
Transcend II Implantable Gastric Stimulation System
“For use in weight reduction for obese adults with a body mass index greater than 35.”
The GES device that is licensed by Health Canada for treatment of GP, produces high-frequency GES. Most clinical studies examining GES for GP have used high-frequency (4 times the intrinsic slow wave frequency, i.e., 12 cycles per minute), low energy, short duration pulses. This type of stimulation does not alter gastric muscular contraction and has no effect on slow wave dysrhythmias. The mechanism of action is unclear but it is hypothesized that high-frequency GES may act on sensory fibers directed to the CNS.
The GES device licensed by Health Canada for treatment of morbid obesity produces low-frequency GES, which is close to or just above the normal/native gastric slow wave cycle (approximately 3 cycles/min.). This pacing uses low-frequency, high-energy, long-duration pulses to induce propagated slow waves that replace the spontaneous ones. Low-frequency pacing does not invoke muscular contractions.
Most studies examining the use of GES for the treatment of morbid obesity use low-frequency GES. Under normal circumstances, the gastric slow wave propagates distally and determines the frequency and propagation direction of gastric peristalsis. Low-frequency GES aims to produce abnormal gastric slow waves that can induce gastric dysrhythmia, disrupt regular propagation of slow waves, cause hypomotility of the stomach, delay gastric emptying, reduce food intake, prolong satiety, and produce weight loss.
In the United States, the Enterra Therapy System is a Humanitarian Use Device (HUD), meaning it is a medical device designated by the FDA for use in the treatment of medical conditions that affect fewer than 4,000 individuals per year.2 The Enterra Therapy System is indicated for “the treatment of chronic, drug- refractory nausea and vomiting secondary to GP of diabetes or idiopathic etiology” (not postsurgical etiologies).
GES for morbid obesity has not been approved by the FDA and is for investigational use only in the United States.
Review Strategy
The Medical Advisory Secretariat systematically reviewed the literature to assess the effectiveness, safety, and cost-effectiveness of GES to treat patients who have: a) chronic refractory symptomatic GP; or b) morbid obesity.
The Medical Advisory Secretariat used its standard search strategy to retrieve international health technology assessments and English-language journal articles from selected databases.
The GRADE approach was used to systematically and explicitly make judgments about the quality of evidence and strength of recommendations.
Findings
As stated by the GRADE Working Group, the following definitions were used in grading the quality of the evidence in Tables 1 and 2.
GRADE Quality of Studies – Gastroparesis
Confounders related to diabetes.
Possible Type 2 error for subgroup analyses.
Subjective self-reported end point.
Posthoc change in primary end point analysis.
No sample size justification.
Concomitant prokinetic/antiemetic therapy.
Only 1 RCT (with different results for FDA and publication).
GES originally hypothesized to correct gastric rhythms, stimulate gastric emptying and therefore eliminate symptoms.
Now hypothesized to directly act on neurons to the CNS to control symptoms.
Weak correlation between symptoms and gastric emptying.
Unclear whether gastric emptying is still considered an end point to investigate.
GRADE Quality of Studies – Morbid Obesity
No sample size calculation.
Small sample size.
No ITT analysis.
Lack of detail regarding dropouts.
Possible Type 2 error.
Sparse details about randomization/blinding.
Full, final results not published.
Only 1 RCT (technically grey literature).
Economic Analysis
No formal economic analysis was identified in the literature search.
The Alberta Heritage Foundation for Medical Research reported that the cost of implanting a GES in the United States for the treatment of GP is estimated to be $30,000 US. In Canada, the device costs approximately $10,700 Cdn; this does not include costs associated with the physician’s training, the implantation procedure, or device programming and maintenance.
Ontario Context
There is no Schedule of Benefits code for GES.
There is no Canadian Classification of Health Interventions Index (CCI) procedure code for GES.
Since the ICD-10 diagnosis code for gastroparesis falls under K31.8 “Other specified diseases of the stomach and duodenum”, it is impossible to determine how many patients in Ontario had discharge abstracts because of gastroparesis.
In 2005, there were less than 5 out-of-country requests for GES (for either consultation only or for surgery).
Gastroparesis
The prevalence of severe, refractory GP is variably reported in the literature.
The Alberta Heritage Foundation for Medical Research estimated that the prevalence of severe, symptomatic and medically refractory GP in the United States population was 0.017%. Assuming a total Ontario population of 13 million, this would correspond to a budget impact of approximately $23.6 M
Cdn ($10,700 Cdn x 2,210 patients) for the device cost alone.
The incidence of severe refractory GP estimated by the FDA is approximately 4,000 per year in the United States. This corresponds to about 150 patients in Ontario. Using expert opinion and FDA data, the incidence of severe refractory GP in Ontario is estimated to be about 20 to 150 per year. This corresponds to a budget impact of approximately $107,000 Cdn to $1.6M Cdn per year for the device cost alone.
Morbid Obesity
An expert in the field estimated that there are 160,000 to 180,000 people in Ontario who are morbidly obese. This would correspond to a budget impact of approximately $1.7B Cdn to $1.9B Cdn for the device cost alone (assuming 100% uptake). However, the true uptake of GES for morbid obesity is unknown in relation to other types of bariatric surgery (which are more effective).
Conclusion
As per the GRADE Working Group, overall recommendations consider 4 main factors.
The tradeoffs, taking into account the estimated size of the effect for the main outcome, the confidence limits around those estimates and the relative value placed on the outcome.
The quality of the evidence.
Translation of the evidence into practice in a specific setting, taking into consideration important factors that could be expected to modify the size of the expected effects such as proximity to a hospital or availability of necessary expertise.
Uncertainty about the baseline risk for the population of interest.
The GRADE Working Group also recommends that incremental costs of healthcare alternatives should be considered explicitly alongside the expected health benefits and harms. Recommendations rely on judgments about the value of the incremental health benefits in relation to the incremental costs. The last column in Table 3 shows the overall trade-off between benefits and harms and incorporates any risk/uncertainty.
For GP, the overall GRADE and strength of the recommendation is “weak” – the quality of the evidence is “low” (uncertainties due to methodological limitations in the study design in terms of study quality, consistency and directness), and the corresponding risk/uncertainty is increased due to a budget impact of approximately $107,000 Cdn to $1.6M Cdn for the device cost alone, while the cost-effectiveness of GES is unknown and difficult to estimate considering that there are no high-quality studies of effectiveness. Further evidence of effectiveness should be available in the future since there is a RCT underway that is examining the use of GES in patients with severe refractory GP associated with diabetes and idiopathic etiologies (ClinicalTrials.gov identifier NCT00157755).
For morbid obesity, the overall GRADE and strength of the recommendation is “weak” – the quality of the evidence is “low” (uncertainties due to methodological limitations in the study design in terms of study quality and consistency), and the corresponding risk/uncertainty is increased due to a budget impact of approximately $1.7B Cdn to $1.9B Cdn for the device cost alone (assuming 100% uptake) while the cost-effectiveness of GES is unknown and difficult to estimate considering that there are no high quality studies of effectiveness. However, the true uptake of GES for morbid obesity is unknown in relation to other types of bariatric surgery (which are more effective).
Overall GRADE and Strength of Recommendation (Including Uncertainty)
PMCID: PMC3413096  PMID: 23074486
15.  Joint modeling of multivariate longitudinal data and the dropout process in a competing risk setting: application to ICU data 
Background
Joint modeling of longitudinal and survival data has been increasingly considered in clinical trials, notably in cancer and AIDS. In critically ill patients admitted to an intensive care unit (ICU), such models also appear to be of interest in the investigation of the effect of treatment on severity scores due to the likely association between the longitudinal score and the dropout process, either caused by deaths or live discharges from the ICU. However, in this competing risk setting, only cause-specific hazard sub-models for the multiple failure types data have been used.
Methods
We propose a joint model that consists of a linear mixed effects submodel for the longitudinal outcome, and a proportional subdistribution hazards submodel for the competing risks survival data, linked together by latent random effects. We use Markov chain Monte Carlo technique of Gibbs sampling to estimate the joint posterior distribution of the unknown parameters of the model. The proposed method is studied and compared to joint model with cause-specific hazards submodel in simulations and applied to a data set that consisted of repeated measurements of severity score and time of discharge and death for 1,401 ICU patients.
Results
Time by treatment interaction was observed on the evolution of the mean SOFA score when ignoring potentially informative dropouts due to ICU deaths and live discharges from the ICU. In contrast, this was no longer significant when modeling the cause-specific hazards of informative dropouts. Such a time by treatment interaction persisted together with an evidence of treatment effect on the hazard of death when modeling dropout processes through the use of the Fine and Gray model for sub-distribution hazards.
Conclusions
In the joint modeling of competing risks with longitudinal response, differences in the handling of competing risk outcomes appear to translate into the estimated difference in treatment effect on the longitudinal outcome. Such a modeling strategy should be carefully defined prior to analysis.
doi:10.1186/1471-2288-10-69
PMCID: PMC2923158  PMID: 20670425
16.  Developmental Profiles of Eczema, Wheeze, and Rhinitis: Two Population-Based Birth Cohort Studies 
PLoS Medicine  2014;11(10):e1001748.
Using data from two population-based birth cohorts, Danielle Belgrave and colleagues examine the evidence for atopic march in developmental profiles for allergic disorders.
Please see later in the article for the Editors' Summary
Background
The term “atopic march” has been used to imply a natural progression of a cascade of symptoms from eczema to asthma and rhinitis through childhood. We hypothesize that this expression does not adequately describe the natural history of eczema, wheeze, and rhinitis during childhood. We propose that this paradigm arose from cross-sectional analyses of longitudinal studies, and may reflect a population pattern that may not predominate at the individual level.
Methods and Findings
Data from 9,801 children in two population-based birth cohorts were used to determine individual profiles of eczema, wheeze, and rhinitis and whether the manifestations of these symptoms followed an atopic march pattern. Children were assessed at ages 1, 3, 5, 8, and 11 y. We used Bayesian machine learning methods to identify distinct latent classes based on individual profiles of eczema, wheeze, and rhinitis. This approach allowed us to identify groups of children with similar patterns of eczema, wheeze, and rhinitis over time.
Using a latent disease profile model, the data were best described by eight latent classes: no disease (51.3%), atopic march (3.1%), persistent eczema and wheeze (2.7%), persistent eczema with later-onset rhinitis (4.7%), persistent wheeze with later-onset rhinitis (5.7%), transient wheeze (7.7%), eczema only (15.3%), and rhinitis only (9.6%). When latent variable modelling was carried out separately for the two cohorts, similar results were obtained. Highly concordant patterns of sensitisation were associated with different profiles of eczema, rhinitis, and wheeze. The main limitation of this study was the difference in wording of the questions used to ascertain the presence of eczema, wheeze, and rhinitis in the two cohorts.
Conclusions
The developmental profiles of eczema, wheeze, and rhinitis are heterogeneous; only a small proportion of children (∼7% of those with symptoms) follow trajectory profiles resembling the atopic march.
Please see later in the article for the Editors' Summary
Editors' Summary
Background
Our immune system protects us from viruses, bacteria, and other pathogens by recognizing specific molecules on the invader's surface and initiating a sequence of events that culminates in the death of the pathogen. Sometimes, however, our immune system responds to harmless materials (allergens such as pollen) and triggers allergic, or atopic, symptoms. Common atopic symptoms include eczema (transient dry itchy patches on the skin), wheeze (high pitched whistling in the chest, a symptom of asthma), and rhinitis (sneezing or a runny nose in the absence of a cold or influenza). All these symptoms are very common during childhood, but recent epidemiological studies (examinations of the patterns and causes of diseases in a population) have revealed age-related changes in the proportions of children affected by each symptom. So, for example, eczema is more common in infants than in school-age children. These findings have led to the idea of “atopic march,” a natural progression of symptoms within individual children that starts with eczema, then progresses to wheeze and finally rhinitis.
Why Was This Study Done?
The concept of atopic march has led to the initiation of studies that aim to prevent the development of asthma in children who are thought to be at risk of asthma because they have eczema. Moreover, some guidelines recommend that clinicians tell parents that children with eczema may later develop asthma or rhinitis. However, because of the design of the epidemiological studies that support the concept of atopic march, children with eczema who later develop wheeze and rhinitis may actually belong to a distinct subgroup of children, rather than representing the typical progression of atopic diseases. It is important to know whether atopic march adequately describes the natural history of atopic diseases during childhood to avoid the imposition of unnecessary strategies on children with eczema to prevent asthma. Here, the researchers use machine learning techniques to model the developmental profiles of eczema, wheeze, and rhinitis during childhood in two large population-based birth cohorts by taking into account time-related (longitudinal) changes in symptoms within individuals. Machine learning is a data-driven approach that identifies structure within the data (for example, a typical progression of symptoms) using unsupervised learning of latent variables (variables that are not directly measured but are inferred from other observable characteristics).
What Did the Researchers Do and Find?
The researchers used data from two UK birth cohorts—the Avon Longitudinal Study of Parents and Children (ALSPAC) and the Manchester Asthma and Allergy Study (MAAS)—for their study (9,801 children in total). Both studies enrolled children at birth and monitored their subsequent health at regular review clinics. At each review clinic, information about eczema, wheeze, and rhinitis was collected from the parents using validated questionnaires. The researchers then used these data and machine learning methods to identify groups of children with similar patterns of onset of eczema, wheeze, and rhinitis over the first 11 years of life. Using a type of statistical model called a latent disease profile model, the researchers found that the data were best described by eight latent classes—no disease (51.3% of the children), atopic march (3.1%), persistent eczema and wheeze (2.7%), persistent eczema with later-onset rhinitis (4.7%), persistent wheeze with later-onset rhinitis (5.7%), transient wheeze (7.7%), eczema only (15.3%), and rhinitis only (9.6%).
What Do These Findings Mean?
These findings show that, in two large UK birth cohorts, the developmental profiles of eczema, wheeze, and rhinitis were heterogeneous. Most notably, the progression of symptoms fitted the profile of atopic march in fewer than 7% of children with symptoms. The researchers acknowledge that their study has some limitations. For example, small differences in the wording of the questions used to gather information from parents about their children's symptoms in the two cohorts may have slightly affected the findings. However, based on their findings, the researchers propose that, because eczema, wheeze, and rhinitis are common, these symptoms often coexist in individuals, but as independent entities rather than as a linked progression of symptoms. Thus, using eczema as an indicator of subsequent asthma risk and assigning “preventative” measures to children with eczema is flawed. Importantly, clinicians need to understand the heterogeneity of patterns of atopic diseases in children and to communicate this variability to parents when advising them about the development and resolution of atopic symptoms in their children.
Additional Information
Please access these websites via the online version of this summary at http://dx.doi.org/10.1371/journal.pmed.1001748.
The UK National Health Service Choices website provides information about eczema (including personal stories), asthma (including personal stories), and rhinitis
The US National Institute of Allergy and Infectious Diseases provides information about atopic diseases
The UK not-for-profit organization Allergy UK provides information about atopic diseases and a description of the atopic march
MedlinePlus encyclopedia has pages on eczema, wheezing, and rhinitis (in English and Spanish)
MedlinePlus provides links to further resources about allergies, eczema, and asthma (in English and Spanish)
Information about ALSPAC and MAAS is available
Wikipedia has pages on machine learning and latent disease profile models (note that Wikipedia is a free online encyclopedia that anyone can edit; available in several languages)
doi:10.1371/journal.pmed.1001748
PMCID: PMC4204810  PMID: 25335105
17.  Modelling variable dropout in randomised controlled trials with longitudinal outcomes: application to the MAGNETIC study 
Trials  2016;17:222.
Background
Clinical trials with longitudinally measured outcomes are often plagued by missing data due to patients withdrawing or dropping out from the trial before completing the measurement schedule. The reasons for dropout are sometimes clearly known and recorded during the trial, but in many instances these reasons are unknown or unclear. Often such reasons for dropout are non-ignorable. However, the standard methods for analysing longitudinal outcome data assume that missingness is non-informative and ignore the reasons for dropout, which could result in a biased comparison between the treatment groups.
Methods
In this article, as a post hoc analysis, we explore the impact of informative dropout due to competing reasons on the evaluation of treatment effect in the MAGNETIC trial, the largest randomised placebo-controlled study to date comparing the addition of nebulised magnesium sulphate to standard treatment in acute severe asthma in children. We jointly model longitudinal outcome and informative dropout process to incorporate the information regarding the reasons for dropout by treatment group.
Results
The effect of nebulised magnesium sulphate compared with standard treatment is evaluated more accurately using a joint longitudinal-competing risk model by taking account of such complexities. The corresponding estimates indicate that the rate of dropout due to good prognosis is about twice as high in the magnesium group compared with standard treatment.
Conclusions
We emphasise the importance of identifying reasons for dropout and undertaking an appropriate statistical analysis accounting for such dropout. The joint modelling approach accounting for competing reasons for dropout is proposed as a general approach for evaluating the sensitivity of conclusions to assumptions regarding missing data in clinical trials with longitudinal outcomes.
Trial registration
EudraCT number 2007-006227-12. Registration date 18 Mar 2008.
Electronic supplementary material
The online version of this article (doi:10.1186/s13063-016-1342-0) contains supplementary material, which is available to authorized users.
doi:10.1186/s13063-016-1342-0
PMCID: PMC4849065  PMID: 27125779
Longitudinal outcome; Dropout process; Joint modelling; Competing risks
18.  A Repeated Trajectory Class Model for Intensive Longitudinal Categorical Outcome 
Statistics in medicine  2014;33(15):2645-2664.
This paper presents a novel repeated latent class model for a longitudinal response that is frequently measured as in our prospective study of older adults with monthly data on activities of daily living (ADL) for more than ten years. The proposed method is especially useful when the longitudinal response is measured much more frequently than other relevant covariates. The repeated trajectory classes represent distinct temporal patterns of the longitudinal response wherein an individual’s membership in the trajectory classes may renew or change over time. Within a trajectory class, the longitudinal response is modeled by a class-specific generalized linear mixed model. Effectively, an individual may remain in a trajectory class or switch to another as the class membership predictors are updated periodically over time. The identification of a common set of trajectory classes allows changes among the temporal patterns to be distinguished from local fluctuations in the response. An informative event such as death is jointly modeled by class-specific probability of the event through shared random effects. We do not impose the conditional independence assumption given the classes. The method is illustrated by analyzing the change over time in ADL trajectory class among 754 older adults with 70500 person-months of follow-up in the Precipitating Events Project. We also investigate the impact of jointly modeling the class-specific probability of the event on the parameter estimates in a simulation study. The primary contribution of our paper is the periodic updating of trajectory classes for a longitudinal categorical response without assuming conditional independence.
doi:10.1002/sim.6109
PMCID: PMC4145078  PMID: 24519416
joint model; intensive longitudinal data; longitudinal categorical data; shared random effects; repeated latent class; trajectory class
19.  Bayesian estimation of associations between identified longitudinal hormone subgroups and age at final menstrual period 
Background
Although follicle stimulating hormone (FSH) is known to be predictive of age at final menstrual period (FMP), previous methods use FSH levels measured at time points that are defined relative to the age at FMP, and hence are not useful for prospective prediction purposes in clinical settings where age at FMP is an unknown outcome. This study is aimed at assessing whether FSH trajectory feature subgroups identified relative to chronological age can be used to improve the prediction of age at FMP.
Methods
We develop a Bayesian model to identify latent subgroups in longitudinal FSH trajectories, and study the relationship between subgroup membership and age at FMP. Data for our study is taken from the Penn Ovarian Aging study, 1996–2010. The proposed model utilizes mixture modeling and nonparametric smoothing methods to capture hypothesized latent subgroup features of the FSH longitudinal trajectory; and simultaneously studies the prognostic value of these latent subgroup features to predict age at FMP.
Results
The analysis identified two FSH trajectory subgroups that were significantly associated with FMP age: 1) early FSH class (15 %), which displayed initial increases in FSH shortly after age 40; and 2) late FSH class (85 %), which did not have a rise in FSH until after age 45. The use of FSH subgroup memberships, along with class-specific characteristics, i.e., level and rate of FSH change at class-specific pre-specified ages, improved prediction of FMP age by 20–22 % in comparison to the prediction based on previously identified risk factors (BMI, smoking and pre-menopausal levels of anti-mullerian hormone (AMH)).
Conclusions
To the best of our knowledge, this work is the first in the area to demonstrate the existence of subgroups in FSH trajectory patterns relative to chronological age and the fact that such a subgroup membership possesses prediction power for age at FMP. Earlier ages at FMP were found in a subgroup of women with rise in FSH levels commencing shortly after age 40, in comparison to women who did not exhibit an increase in FSH until after 45 years of age. Periodic evaluations of FSH in these age ranges are potentially useful for predicting age at FMP.
Electronic supplementary material
The online version of this article (doi:10.1186/s12874-015-0101-3) contains supplementary material, which is available to authorized users.
doi:10.1186/s12874-015-0101-3
PMCID: PMC4683774  PMID: 26677844
Menopause; Reproductive aging; Reproductive hormones; Joint modeling of longitudinal and time-to-event data; Mixture modeling; Penalized splines
20.  An exploration of fixed and random effects selection for longitudinal binary outcomes in the presence of nonignorable dropout 
Biometrical journal. Biometrische Zeitschrift  2012;55(1):10.1002/bimj.201100107.
We explore a Bayesian approach to selection of variables that represent fixed and random effects in modeling of longitudinal binary outcomes with missing data caused by dropouts. We show via analytic results for a simple example that nonignorable missing data lead to biased parameter estimates. This bias results in selection of wrong effects asymptotically, which we can confirm via simulations for more complex settings. By jointly modeling the longitudinal binary data with the dropout process that possibly leads to nonignorable missing data, we are able to correct the bias in estimation and selection. Mixture priors with a point mass at zero are used to facilitate variable selection. We illustrate the proposed approach using a clinical trial for acute ischemic stroke.
doi:10.1002/bimj.201100107
PMCID: PMC3855104  PMID: 23124889
Bayesian variable selection; Bias; Dropout; Missing data; Model selection
21.  A Marginal Mixture Model for Selecting Differentially Expressed Genes across Two Types of Tissue Samples 
Bayesian hierarchical models that characterize the distributions of (transformed) gene profiles have been proven very useful and flexible in selecting differentially expressed genes across different types of tissue samples (e.g. Lo and Gottardo, 2007). However, the marginal mean and variance of these models are assumed to be the same for different gene clusters and for different tissue types. Moreover, it is not easy to determine which of the many competing Bayesian hierarchical models provides the best fit for a specific microarray data set. To address these two issues, we propose a marginal mixture model that directly models the marginal distribution of transformed gene profiles. Specifically, we approximate the marginal distributions of transformed gene profiles via a mixture of three-component multivariate Normal distributions, each component of which has the same structures of marginal mean vector and covariance matrix as those for Bayesian hierarchical models, but the values can differ. Based on the proposed model, a method is derived to select genes differentially expressed across two types of tissue samples. The derived gene selection method performs well on a real microarray data set and consistently has the best performance (based on class agreement indices) compared with several other gene selection methods on simulated microarray data sets generated from three different mixture models.
doi:10.2202/1557-4679.1093
PMCID: PMC2835454  PMID: 20231912
22.  Bayesian Inference in Semiparametric Mixed Models for Longitudinal Data 
Biometrics  2009;66(1):70-78.
SUMMARY
We consider Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. SPMMs are a class of models that use a nonparametric function to model a time effect, a parametric function to model other covariate effects, and parametric or nonparametric random effects to account for the within-subject correlation. We model the nonparametric function using a Bayesian formulation of a cubic smoothing spline, and the random effect distribution using a normal distribution and alternatively a nonparametric Dirichlet process (DP) prior. When the random effect distribution is assumed to be normal, we propose a uniform shrinkage prior (USP) for the variance components and the smoothing parameter. When the random effect distribution is modeled nonparametrically, we use a DP prior with a normal base measure and propose a USP for the hyperparameters of the DP base measure. We argue that the commonly assumed DP prior implies a nonzero mean of the random effect distribution, even when a base measure with mean zero is specified. This implies weak identifiability for the fixed effects, and can therefore lead to biased estimators and poor inference for the regression coefficients and the spline estimator of the nonparametric function. We propose an adjustment using a postprocessing technique. We show that under mild conditions the posterior is proper under the proposed USP, a flat prior for the fixed effect parameters, and an improper prior for the residual variance. We illustrate the proposed approach using a longitudinal hormone dataset, and carry out extensive simulation studies to compare its finite sample performance with existing methods.
doi:10.1111/j.1541-0420.2009.01227.x
PMCID: PMC3081790  PMID: 19432777
Dirichlet process prior; Identifiability; Postprocessing; Random effects; Smoothing spline; Uniform shrinkage prior; Variance components
23.  A Bayesian Two-Part Latent Class Model for Longitudinal Medical Expenditure Data: Assessing the Impact of Mental Health and Substance Abuse Parity 
Biometrics  2011;67(1):280-289.
Summary
In 2001, the U.S. Office of Personnel Management required all health plans participating in the Federal Employees Health Benefits Program to offer mental health and substance abuse benefits on par with general medical benefits. The initial evaluation found that, on average, parity did not result in either large spending increases or increased service use over the four-year observational period. However, some groups of enrollees may have benefited from parity more than others. To address this question, we propose a Bayesian two-part latent class model to characterize the effect of parity on mental health use and expenditures. Within each class, we fit a two-part random effects model to separately model the probability of mental health or substance abuse use and mean spending trajectories among those having used services. The regression coefficients and random effect covariances vary across classes, thus permitting class-varying correlation structures between the two components of the model. Our analysis identified three classes of subjects: a group of low spenders that tended to be male, had relatively rare use of services, and decreased their spending pattern over time; a group of moderate spenders, primarily female, that had an increase in both use and mean spending after the introduction of parity; and a group of high spenders that tended to have chronic service use and constant spending patterns. By examining the joint 95% highest probability density regions of expected changes in use and spending for each class, we confirmed that parity had an impact only on the moderate spender class.
doi:10.1111/j.1541-0420.2010.01439.x
PMCID: PMC4445417  PMID: 20528856
Bayesian analysis; Growth mixture model; Latent class model; Mental health parity; Semi-continuous data; Two-part model
24.  Estimating the cumulative risk of false positive cancer screenings 
Background
When evaluating cancer screening it is important to estimate the cumulative risk of false positives from periodic screening. Because the data typically come from studies in which the number of screenings varies by subject, estimation must take into account dropouts. A previous approach to estimate the probability of at least one false positive in n screenings unrealistically assumed that the probability of dropout does not depend on prior false positives.
Method
By redefining the random variables, we obviate the unrealistic dropout assumption. We also propose a relatively simple logistic regression and extend estimation to the expected number of false positives in n screenings.
Results
We illustrate our methodology using data from women ages 40 to 64 who received up to four annual breast cancer screenings in the Health Insurance Program of Greater New York study, which began in 1963. Covariates were age, time since previous screening, screening number, and whether or not a previous false positive occurred. Defining a false positive as an unnecessary biopsy, the only statistically significant covariate was whether or not a previous false positive occurred. Because the effect of screening number was not statistically significant, extrapolation beyond 4 screenings was reasonable. The estimated mean number of unnecessary biopsies in 10 years per woman screened is .11 with 95% confidence interval of (.10, .12). Defining a false positive as an unnecessary work-up, all the covariates were statistically significant and the estimated mean number of unnecessary work-ups in 4 years per woman screened is .34 with 95% confidence interval (.32, .36).
Conclusion
Using data from multiple cancer screenings with dropouts, and allowing dropout to depend on previous history of false positives, we propose a logistic regression model to estimate both the probability of at least one false positive and the expected number of false positives associated with n cancer screenings. The methodology can be used for both informed decision making at the individual level, as well as planning of health services.
doi:10.1186/1471-2288-3-11
PMCID: PMC166156  PMID: 12841854
25.  Bayesian modeling of ChIP-chip data using latent variables 
BMC Bioinformatics  2009;10:352.
Background
The ChIP-chip technology has been used in a wide range of biomedical studies, such as identification of human transcription factor binding sites, investigation of DNA methylation, and investigation of histone modifications in animals and plants. Various methods have been proposed in the literature for analyzing the ChIP-chip data, such as the sliding window methods, the hidden Markov model-based methods, and Bayesian methods. Although, due to the integrated consideration of uncertainty of the models and model parameters, Bayesian methods can potentially work better than the other two classes of methods, the existing Bayesian methods do not perform satisfactorily. They usually require multiple replicates or some extra experimental information to parametrize the model, and long CPU time due to involving of MCMC simulations.
Results
In this paper, we propose a Bayesian latent model for the ChIP-chip data. The new model mainly differs from the existing Bayesian models, such as the joint deconvolution model, the hierarchical gamma mixture model, and the Bayesian hierarchical model, in two respects. Firstly, it works on the difference between the averaged treatment and control samples. This enables the use of a simple model for the data, which avoids the probe-specific effect and the sample (control/treatment) effect. As a consequence, this enables an efficient MCMC simulation of the posterior distribution of the model, and also makes the model more robust to the outliers. Secondly, it models the neighboring dependence of probes by introducing a latent indicator vector. A truncated Poisson prior distribution is assumed for the latent indicator variable, with the rationale being justified at length.
Conclusion
The Bayesian latent method is successfully applied to real and ten simulated datasets, with comparisons with some of the existing Bayesian methods, hidden Markov model methods, and sliding window methods. The numerical results indicate that the Bayesian latent method can outperform other methods, especially when the data contain outliers.
doi:10.1186/1471-2105-10-352
PMCID: PMC2779819  PMID: 19857265

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