Linear Mixed-Effect Models Through the Lens of Hardy-Weinberg Disequilibrium

For genetic association studies with related individuals, the linear mixed-effect model is the most commonly used method. In this report, we show that contrary to the popular belief, this standard method can be sensitive to departure from Hardy-Weinberg equilibrium (i.e., Hardy-Weinberg disequilibrium) at the causal SNPs in two ways. First, when the trait heritability is treated as a nuisance parameter, although the association test has correct type I error control, the resulting heritability estimate can be biased, often upward, in the presence of Hardy-Weinberg disequilibrium. Second, if the true heritability is used in the linear mixed-effect model, then the corresponding association test can be biased in the presence of Hardy-Weinberg disequilibrium. We provide some analytical insights along with supporting empirical results from simulation and application studies.

Design and analysis of two-phase studies with multivariate longitudinal data

Two-phase studies are crucial when outcome and covariate data are available in a first phase sample (e.g., a cohort study), but costs associated with retrospective ascertainment of a novel exposure limit the size of the second phase sample, in whom the exposure is collected. For longitudinal outcomes, one class of two-phase studies stratifies subjects based on an outcome vector summary (e.g., an average or a slope over time) and oversamples subjects in the extreme value strata while undersampling subjects in the medium value stratum. Based on the choice of the summary, two-phase studies for longitudinal data can increase efficiency of time-varying and/or time-fixed exposure parameter estimates. In this manuscript, we extend efficient, two-phase study designs to multivariate longitudinal continuous outcomes, and we detail two analysis approaches. The first approach is a multiple imputation analysis that combines complete data from subjects selected for phase two with the incomplete data from those not selected. The second approach is a conditional maximum likelihood analysis that is intended for applications where only data from subjects selected for phase two are available. Importantly, we show that both approaches can be applied to secondary analyses of previously conducted two-phase studies. We examine finite sample operating characteristics of the two approaches and use the Lung Health Study (Connett et al., 1993) to examine genetic associations with lung function decline over time. This article is protected by copyright. All rights reserved.

A generalized robust allele-based genetic association test

The allele-based association test, comparing allele frequency difference between case and control groups, is locally most powerful. However, application of the classical allelic test is limited in practice, because the method is sensitive to the Hardy-Weinberg equilibrium (HWE) assumption, not applicable to continuous traits, and not easy to account for covariate effect or sample correlation. To develop a generalized robust allelic test, we propose a new allele-based regression model with individual allele as the response variable. We show that the score test statistic derived from this robust and unifying regression framework contains a correction factor that explicitly adjusts for potential departure from HWE and encompasses the classical allelic test as a special case. When the trait of interest is continuous, the corresponding allelic test evaluates a weighted difference between individual-level allele frequency estimate and sample estimate where the weight is proportional to an individual's trait value, and the test remains valid under Y-dependent sampling. Finally, the proposed allele-based method can analyze multiple (continuous or binary) phenotypes simultaneously and multiallelic genetic markers, while accounting for covariate effect, sample correlation, and population heterogeneity. To support our analytical findings, we provide empirical evidence from both simulation and application studies.

Optimal Designs of Two-Phase Studies

The two-phase design is a cost-effective sampling strategy to evaluate the effects of covariates on an outcome when certain covariates are too expensive to be measured on all study subjects. Under such a design, the outcome and inexpensive covariates are measured on all subjects in the first phase and the first-phase information is used to select subjects for measurements of expensive covariates in the second phase. Previous research on two-phase studies has focused largely on the inference procedures rather than the design aspects. We investigate the design efficiency of the two-phase study, as measured by the semiparametric efficiency bound for estimating the regression coefficients of expensive covariates. We consider general two-phase studies, where the outcome variable can be continuous, discrete, or censored, and the second-phase sampling can depend on the first-phase data in any manner. We develop optimal or approximately optimal two-phase designs, which can be substantially more efficient than the existing designs. We demonstrate the improvements of the new designs over the existing ones through extensive simulation studies and two large medical studies.

Robust Score Tests With Missing Data in Genomics Studies

Analysis of genomic data is often complicated by the presence of missing values, which may arise due to cost or other reasons. The prevailing approach of single imputation is generally invalid if the imputation model is misspecified. In this paper, we propose a robust score statistic based on imputed data for testing the association between a phenotype and a genomic variable with (partially) missing values. We fit a semiparametric regression model for the genomic variable against an arbitrary function of the linear predictor in the phenotype model and impute each missing value by its estimated posterior expectation. We show that the score statistic with such imputed values is asymptotically unbiased under general missing-data mechanisms, even when the imputation model is misspecified. We develop a spline-based method to estimate the semiparametric imputation model and derive the asymptotic distribution of the corresponding score statistic with a consistent variance estimator using sieve approximation theory and empirical process theory. The proposed test is computationally feasible regardless of the number of independent variables in the imputation model. We demonstrate the advantages of the proposed method over existing methods through extensive simulation studies and provide an application to a major cancer genomics study.

Powerful extreme phenotype sampling designs and score tests for genetic association studies

We consider cross-sectional genetic association studies (common and rare variants) where non-genetic information is available or feasible to obtain for N individuals, but where it is infeasible to genotype all N individuals. We consider continuously measurable Gaussian traits (phenotypes). Genotyping n < N extreme phenotype individuals can yield better power to detect phenotype-genotype associations, as compared to randomly selecting n individuals. We define a person as having an extreme phenotype if the observed phenotype is above a specified threshold or below a specified threshold. We consider a model where these thresholds can be tailored to each individual. The classical extreme sampling design is to set equal thresholds for all individuals. We introduce a design (z-extreme sampling) where personalized thresholds are defined based on the residuals of a regression model including only non-genetic (fully available) information. We derive score tests for the situation where only n extremes are analyzed (complete case analysis) and for the situation where the non-genetic information on N - n non-extremes is included in the analysis (all case analysis). For the classical design, all case analysis is generally more powerful than complete case analysis. For the z-extreme sample, we show that all case and complete case tests are equally powerful. Simulations and data analysis also show that z-extreme sampling is at least as powerful as the classical extreme sampling design and the classical design is shown to be at times less powerful than random sampling. The method of dichotomizing extreme phenotypes is also discussed.

Variable selection and prediction in biased samples with censored outcomes

With the increasing availability of large prospective disease registries, scientists studying the course of chronic conditions often have access to multiple data sources, with each source generated based on its own entry conditions. The different entry conditions of the various registries may be explicitly based on the response process of interest, in which case the statistical analysis must recognize the unique truncation schemes. Moreover, intermittent assessment of individuals in the registries can lead to interval-censored times of interest. We consider the problem of selecting important prognostic biomarkers from a large set of candidates when the event times of interest are truncated and right- or interval-censored. Methods for penalized regression are adapted to handle truncation via a Turnbull-type complete data likelihood. An expectation-maximization algorithm is described which is empirically shown to perform well. Inverse probability weights are used to adjust for the selection bias when assessing predictive accuracy based on individuals whose event status is known at a time of interest. Application to the motivating study of the development of psoriatic arthritis in patients with psoriasis in both the psoriasis cohort and the psoriatic arthritis cohort illustrates the procedure.

Two-phase outcome-dependent studies for failure times and testing for effects of expensive covariates

Two- or multi-phase study designs are often used in settings involving failure times. In most studies, whether or not certain covariates are measured on an individual depends on their failure time and status. For example, when failures are rare, case-cohort or case-control designs are used to increase the number of failures relative to a random sample of the same size. Another scenario is where certain covariates are expensive to measure, so they are obtained only for selected individuals in a cohort. This paper considers such situations and focuses on cases where we wish to test hypotheses of no association between failure time and expensive covariates. Efficient score tests based on maximum likelihood are developed and shown to have a simple form for a wide class of models and sampling designs. Some numerical comparisons of study designs are presented.