Treatment effect estimators for count data models

In this paper, we consider a switching regression model with count data outcomes, where the possible outcome differs across two alternate states and individuals endogenously select one of the states. We assume lognormal latent heterogeneity. Building on the switching regression model, we derive estimators of various treatment effects: the average treatment effect, the average treatment effect on the treated, the local average treatment effect, and the marginal treatment effect. We illustrate an application that examines the effects of public insurance on the number of doctor visits using the data employed by previous studies.     

Hierarchical Archimedean copula models for the analysis of binary familial data

Archimedean copulas are commonly used in a wide range of statistical models due to their simplicity, manageable analytical expressions, rich choices of generator functions, and other workable properties. However, the exchangeable dependence structure inherent to Archimedean copulas limits its application to familial data, where the dependence among family members is often different. When response variables are binary, modeling the familial associations becomes more challenging due to the stringent constraints imposed on the dependence parameters. This paper proposes hierarchical Archimedean copulas to account for the natural hierarchical dependence structure in familial data and addresses the details in the modeling of binary familial data and the inference based on maximum likelihood estimate. An example showing the flexibility of this powerful tool is also presented with possible extension to other similar studies.     

Secondary outcome analysis for data from an outcome‐dependent sampling design

Outcome‐dependent sampling (ODS) scheme is a cost‐effective way to conduct a study. For a study with continuous primary outcome, an ODS scheme can be implemented where the expensive exposure is only measured on a simple random sample and supplemental samples selected from 2 tails of the primary outcome variable. With the tremendous cost invested in collecting the primary exposure information, investigators often would like to use the available data to study the relationship between a secondary outcome and the obtained exposure variable. This is referred as secondary analysis. Secondary analysis in ODS designs can be tricky, as the ODS sample is not a random sample from the general population. In this article, we use the inverse probability weighted and augmented inverse probability weighted estimating equations to analyze the secondary outcome for data obtained from the ODS design. We do not make any parametric assumptions on the primary and secondary outcome and only specify the form of the regression mean models, thus allow an arbitrary error distribution. Our approach is robust to second‐ and higher‐order moment misspecification. It also leads to more precise estimates of the parameters by effectively using all the available participants. Through simulation studies, we show that the proposed estimator is consistent and asymptotically normal. Data from the Collaborative Perinatal Project are analyzed to illustrate our method.     

Likelihood‐based analysis of outcome‐dependent sampling designs with longitudinal data

The use of outcome‐dependent sampling with longitudinal data analysis has previously been shown to improve efficiency in the estimation of regression parameters. The motivating scenario is when outcome data exist for all cohort members but key exposure variables will be gathered only on a subset. Inference with outcome‐dependent sampling designs that also incorporates incomplete information from those individuals who did not have their exposure ascertained has been investigated for univariate but not longitudinal outcomes. Therefore, with a continuous longitudinal outcome, we explore the relative contributions of various sources of information toward the estimation of key regression parameters using a likelihood framework. We evaluate the efficiency gains that alternative estimators might offer over random sampling, and we offer insight into their relative merits in select practical scenarios. Finally, we illustrate the potential impact of design and analysis choices using data from the Cystic Fibrosis Foundation Patient Registry.     

Evaluation of biomarkers for treatment selection using individual participant data from multiple clinical trials

Biomarkers that predict treatment effects may be used to guide treatment decisions, thus improving patient outcomes. A meta‐analysis of individual participant data (IPD) is potentially more powerful than a single‐study data analysis in evaluating markers for treatment selection. Our study was motivated by the IPD that were collected from 2 randomized controlled trials of hypertension and preeclampsia among pregnant women to evaluate the effect of labor induction over expectant management of the pregnancy in preventing progression to severe maternal disease. The existing literature on statistical methods for biomarker evaluation in IPD meta‐analysis have evaluated a marker's performance in terms of its ability to predict risk of disease outcome, which do not directly apply to the treatment selection problem. In this study, we propose a statistical framework for evaluating a marker for treatment selection given IPD from a small number of individual clinical trials. We derive marker‐based treatment rules by minimizing the average expected outcome across studies. The application of the proposed methods to the IPD from 2 studies in women with hypertension in pregnancy is presented.     

Regression analysis of interval‐censored failure time data with possibly crossing hazards

Interval‐censored failure time data occur in many areas, especially in medical follow‐up studies such as clinical trials, and in consequence, many methods have been developed for the problem. However, most of the existing approaches cannot deal with the situations where the hazard functions may cross each other. To address this, we develop a sieve maximum likelihood estimation procedure with the application of the short‐term and long‐term hazard ratio model. In the method, the I‐splines are used to approximate the underlying unknown function. An extensive simulation study was conducted for the assessment of the finite sample properties of the presented procedure and suggests that the method seems to work well for practical situations. The analysis of an motivated example is also provided.     

A novel case‐control subsampling approach for rapid model exploration of large clustered binary data

In many settings, an analysis goal is the identification of a factor, or set of factors associated with an event or outcome. Often, these associations are then used for inference and prediction. Unfortunately, in the big data era, the model building and exploration phases of analysis can be time‐consuming, especially if constrained by computing power (ie, a typical corporate workstation). To speed up this model development, we propose a novel subsampling scheme to enable rapid model exploration of clustered binary data using flexible yet complex model set‐ups (GLMMs with additive smoothing splines). By reframing the binary response prospective cohort study into a case‐control–type design, and using our knowledge of sampling fractions, we show one can approximate the model estimates as would be calculated from a full cohort analysis. This idea is extended to derive cluster‐specific sampling fractions and thereby incorporate cluster variation into an analysis. Importantly, we demonstrate that previously computationally prohibitive analyses can be conducted in a timely manner on a typical workstation. The approach is applied to analysing risk factors associated with adverse reactions relating to blood donation.     

Modeling individualized coefficient alpha to measure quality of test score data

Individualized coefficient alpha is defined. It is item and subject specific and is used to measure the quality of test score data with heterogenicity among the subjects and items. A regression model is developed based on 3 sets of generalized estimating equations. The first set of generalized estimating equation models the expectation of the responses, the second set models the response's variance, and the third set is proposed to estimate the individualized coefficient alpha, defined and used to measure individualized internal consistency of the responses. We also use different techniques to extend our method to handle missing data. Asymptotic property of the estimators is discussed, based on which inference on the coefficient alpha is derived. Performance of our method is evaluated through simulation study and real data analysis. The real data application is from a health literacy study in Hunan province of China.     

A unified partial likelihood approach for X‐chromosome association on time‐to‐event outcomes

The expression of X‐chromosome undergoes three possible biological processes: X‐chromosome inactivation (XCI), escape of the X‐chromosome inactivation (XCI‐E), and skewed X‐chromosome inactivation (XCI‐S). Although these expressions are included in various predesigned genetic variation chip platforms, the X‐chromosome has generally been excluded from the majority of genome‐wide association studies analyses; this is most likely due to the lack of a standardized method in handling X‐chromosomal genotype data. To analyze the X‐linked genetic association for time‐to‐event outcomes with the actual process unknown, we propose a unified approach of maximizing the partial likelihood over all of the potential biological processes. The proposed method can be used to infer the true biological process and derive unbiased estimates of the genetic association parameters. A partial likelihood ratio test statistic that has been proved asymptotically chi‐square distributed can be used to assess the X‐chromosome genetic association. Furthermore, if the X‐chromosome expression pertains to the XCI‐S process, we can infer the correct skewed direction and magnitude of inactivation, which can elucidate significant findings regarding the genetic mechanism. A population‐level model and a more general subject‐level model have been developed to model the XCI‐S process. Finite sample performance of this novel method is examined via extensive simulation studies. An application is illustrated with implementation of the method on a cancer genetic study with survival outcome.     

Analysis of pedigree data in populations with multiple ancestries: Strategies for dealing with admixture in Caribbean Hispanic families from the ADSP

Multipoint linkage analysis is an important approach for localizing disease‐associated loci in pedigrees. Linkage analysis, however, is sensitive to misspecification of marker allele frequencies. Pedigrees from recently admixed populations are particularly susceptible to this problem because of the challenge of accurately accounting for population structure. Therefore, increasing emphasis on use of multiethnic samples in genetic studies requires reevaluation of best practices, given data currently available. Typical strategies have been to compute allele frequencies from the sample, or to use marker allele frequencies determined by admixture proportions averaged over the entire sample. However, admixture proportions vary among pedigrees and throughout the genome in a family‐specific manner. Here, we evaluate several approaches to model admixture in linkage analysis, providing different levels of detail about ancestral origin. To perform our evaluations, for specification of marker allele frequencies, we used data on 67 Caribbean Hispanic admixed families from the Alzheimer's Disease Sequencing Project. Our results show that choice of admixture model has an effect on the linkage analysis results. Variant‐specific admixture proportions, computed for individual families, provide the most detailed regional admixture estimates, and, as such, are the most appropriate allele frequencies for linkage analysis. This likely decreases the number of false‐positive results, and is straightforward to implement.