Correlated bivariate continuous and binary outcomes: issues and applications

Hierarchical Bayesian modeling of heterogeneous cluster- and subject-level associations between continuous and binary outcomes in dairy production

The augmentation of categorical outcomes with underlying Gaussian variables in bivariate generalized mixed effects models has facilitated the joint modeling of continuous and binary response variables. These models typically assume that random effects and residual effects (co)variances are homogeneous across all clusters and subjects, respectively. Motivated by conflicting evidence about the association between performance outcomes in dairy production systems, we consider the situation where these (co)variance parameters may themselves be functions of systematic and/or random effects. We present a hierarchical Bayesian extension of bivariate generalized linear models whereby functions of the (co)variance matrices are specified as linear combinations of fixed and random effects following a square-root-free Cholesky reparameterization that ensures necessary positive semidefinite constraints. We test the proposed model by simulation and apply it to the analysis of a dairy cattle data set in which the random herd-level and residual cow-level effects (co)variances between a continuous production trait and binary reproduction trait are modeled as functions of fixed management effects and random cluster effects.

Simultaneous modeling of the impact of treatments on alcohol consumption and quality of life in the COMBINE study: a coupled hidden Markov analysis

BACKGROUND

Clinical trials for alcoholism have historically regarded alcohol consumption as the primary outcome. In a subset of trials, quality of life (QOL) has been considered as a secondary outcome. Joint latent-variable modeling techniques may provide a more accurate and powerful simultaneous analysis of primary and secondary outcomes in clinical trials. The goal of this study was to evaluate longitudinal associations between treatment status, alcohol consumption, and QOL in the Combined Pharmacotherapies and Behavioral Interventions for Alcohol Dependence (COMBINE) study.

METHODS

A total of 1,383 alcohol-dependent patients were randomized to 9 treatment groups. Percent heavy drinking days (PHDD) and health-related QOL from the 30 days preceding baseline, week 16, and week 52 were calculated using the Form 90 and the Medical Outcomes Study Health Survey Short Form-12 (SF-12), respectively. Latent profile analysis (LPA) was conducted to determine an appropriate number of latent states to represent PHDD and QOL. Subsequently, univariate and coupled hidden Markov models (for PHDD and SF-12 mental health, and PHDD and SF-12 physical) were fit to the data.

RESULTS

LPA suggested that PHDD should be represented by 3 latent states and that each SF-12 scale should be represented by 2 states. Joint modeling results suggested that (i) naltrexone significantly predicted decreased PHDD (p < 0.05), and marginally predicted improved mental health QOL via decreased PHDD (p < 0.10), and (ii) that the combinations of naltrexone and combined behavioral intervention (CBI), and acamprosate and CBI, each predicted significantly improved physical QOL (p < 0.05), and marginally predicted decreased PHDD via improved physical QOL (p < 0.10).

CONCLUSIONS

This study illustrates a powerful and novel statistical approach for simultaneously evaluating the impact of treatments on primary and secondary outcomes in clinical trials. This study also suggests that behavioral interventions may impact drinking behavior through their ameliorative effects on QOL.

Moving toward System Genetics through Multiple Trait Analysis in Genome-Wide Association Studies

Association studies are a staple of genotype–phenotype mapping studies, whether they are based on single markers, haplotypes, candidate genes, genome-wide genotypes, or whole genome sequences. Although genetic epidemiological studies typically contain data collected on multiple traits which themselves are often correlated, most analyses have been performed on single traits. Here, I review several methods that have been developed to perform multiple trait analysis. These methods range from traditional multivariate models for systems of equations to recently developed graphical approaches based on network theory. The application of network theory to genetics is termed systems genetics and has the potential to address long-standing questions in genetics about complex processes such as coordinate regulation, homeostasis, and pleiotropy.

Optimal dose-finding designs with correlated continuous and discrete responses

In dose-finding clinical studies, it is common that multiple endpoints are of interest. For instance, in phase I/II studies, efficacy and toxicity are often the primary endpoints, which are observed simultaneously and which need to be evaluated together. Motivated by this, we confine ourselves to bivariate responses and focus on the most analytically difficult case: a mixture of continuous and categorical responses. We adopt the bivariate probit dose-response model and quantify our goal by a utility function. We study locally optimal designs, two-stage optimal designs, and fully adaptive designs under different ethical and cost constraints in the experiments. We assess the performance of two-stage designs and fully adaptive designs via simulations. Our simulations suggest that the two-stage designs are as efficient as and may be more efficient than the fully adaptive designs if there is a moderate sample size in the initial stage. In addition, two-stage designs are easier to construct and implement and thus can be a useful approach in practice.

Estimating cost-offsets of new medications: use of new antipsychotics and mental health costs for schizophrenia

Estimation of the effect of one treatment compared to another in the absence of randomization is a common problem in biostatistics. An increasingly popular approach involves instrumental variables—variables that are predictive of who received a treatment yet not directly predictive of the outcome. When treatment is binary, many estimators have been proposed: method-of-moments estimators using a two-stage least-squares procedure, generalized-method-of-moments estimators using two-stage predictor substitution or two-stage residual inclusion procedures, and likelihood-based latent variable approaches. The critical assumptions to the consistency of two-stage procedures and of the likelihood-based procedures differ. Because neither set of assumptions can be completely tested from the observed data alone, comparing the results from the different approaches is an important sensitivity analysis. We provide a general statistical framework for estimation of the casual effect of a binary treatment on a continuous outcome using simultaneous equations to specify models. A comparison of health care costs for adults with schizophrenia treated with newer atypical antipsychotics and those treated with conventional antipsychotic medications illustrates our methods. Surprisingly large differences in the results among the methods are investigated using a simulation study. Several new findings concerning the performance in terms of precision and robustness of each approach in different situations are obtained. We illustrate that in general supplemental information is needed to determine which analysis, if any, is trustworthy and reaffirm that comparing results from different approaches is a valuable sensitivity analysis. Copyright © 2011 John Wiley & Sons, Ltd.

MISSING DATA IN REGRESSION MODELS FOR NON-COMMENSURATE MULTIPLE OUTCOMES

Biomedical research often involves the measurement of multiple outcomes in different scales (continuous, binary and ordinal). A common approach for the analysis of such data is to ignore the potential correlation among the outcomes and model each outcome separately. This can lead not only to loss of efficiency but also to biased estimates in the presence of missing data. We address the problem of missing data in the context of multiple non-commensurate outcomes. The consequences of missing data when using likelihood and quasi-likelihood methods are described, and an extension of these methods to the situation of missing observations in the outcomes is proposed. Two real data examples illustrate the methodology.

What is evidence?

The assumption that comparative effectiveness research will provide timely, relevant evidence rests on changing the current framework for assembling evidence. In this commentary, we provide the background of how coverage decisions for new medical technologies are currently made in the United States. We focus on the statistical issues regarding how to use the ensemble of information for inferring comparative effectiveness. It is clear a paradigm shift in how clinical information is integrated in real-world settings to establish effectiveness is required.

Statistical Approaches to Modeling Multiple Outcomes In Psychiatric Studies

Increasingly, multiple outcomes are collected in order to characterize treatment effectiveness or to evaluate risk factors. These outcomes tend to be correlated because they are measuring related quantities in the same individuals. While the analysis of outcomes measured in the same scale (commensurate outcomes) can be undertaken with standard statistical methods, outcomes measured in different scales (non-commensurate outcomes), such as mixed binary and continuous outcomes, present more difficult challenges.In this paper we contrast some statistical approaches to analyze non-commensurate multiple outcomes. We discuss the advantages of a multivariate method for the analysis of non-commensurate outcomes including situations of missing data. A real data example from a clinical trial, comparing different treatments for depression in low-income women, is used to illustrate the differences between the statistical approaches.

Statistical methodology for classifying units on the basis of multiple-related measures

Both the private and public sectors have begun giving financial incentives to healthcare providers, such as hospitals, delivering superior 'quality of care'. Quality of care is assessed through a set of disease-specific measures that characterize the performance of healthcare providers. These measures are then combined into a unidimensional composite score. Most of the programs that reward superior performance use raw averages of the measures as the composite score. The scores based on raw averages fail to take into account typical characteristics of data used for performance evaluation, such as within-patient and within-hospital correlations, variable number of measures available in different hospitals, and missing data. In this paper, we contrast two different versions of composites based on raw average scores with a model-based score constructed using a latent variable model. We also present two methods to identify hospitals with superior performance. The methods are illustrated using national data collected to evaluate quality of care delivered by the U.S. acute care hospitals.