Biometrics

Vine copula mixed models for meta-analysis of diagnostic accuracy studies without a gold standard

ABSTRACT Numerous statistical models have been proposed for conducting meta-analysis of diagnostic accuracy studies when a gold standard is available. However, in real-world scenarios, the gold standard test may not be perfect due to several factors such as measurement error, non-availability, invasiveness, or high cost. A generalized linear mixed model (GLMM) is currently recommended to account for an imperfect reference test. We propose vine copula mixed models for meta-analysis of diagnostic test accuracy studies with an imperfect reference standard. Our general models include the GLMM as a special case, can have arbitrary univariate distributions for the random effects, and can provide tail dependencies and asymmetries. Our general methodology is demonstrated with an extensive simulation study and illustrated by insightfully re-analyzing the data of a meta-analysis of the Papanicolaou test that diagnoses cervical neoplasia. Our study suggests that there can be an improvement on GLMM and makes the argument for moving to vine copula random effects models.

Integration of survival data from multiple studies

AbstractWe introduce a statistical procedure that integrates datasets from multiple biomedical studies to predict patients' survival, based on individual clinical and genomic profiles. The proposed procedure accounts for potential differences in the relation between predictors and outcomes across studies, due to distinct patient populations, treatments and technologies to measure outcomes and biomarkers. These differences are modeled explicitly with study‐specific parameters. We use hierarchical regularization to shrink the study‐specific parameters towards each other and to borrow information across studies. The estimation of the study‐specific parameters utilizes a similarity matrix, which summarizes differences and similarities of the relations between covariates and outcomes across studies. We illustrate the method in a simulation study and using a collection of gene expression datasets in ovarian cancer. We show that the proposed model increases the accuracy of survival predictions compared to alternative meta‐analytic methods.

Robust Bayesian graphical regression models for assessing tumor heterogeneity in proteomic networks

ABSTRACT Graphical models are powerful tools to investigate complex dependency structures in high-throughput datasets. However, most existing graphical models make one of two canonical assumptions: (i) a homogeneous graph with a common network for all subjects or (ii) an assumption of normality, especially in the context of Gaussian graphical models. Both assumptions are restrictive and can fail to hold in certain applications such as proteomic networks in cancer. To this end, we propose an approach termed robust Bayesian graphical regression (rBGR) to estimate heterogeneous graphs for non-normally distributed data. rBGR is a flexible framework that accommodates non-normality through random marginal transformations and constructs covariate-dependent graphs to accommodate heterogeneity through graphical regression techniques. We formulate a new characterization of edge dependencies in such models called conditional sign independence with covariates, along with an efficient posterior sampling algorithm. In simulation studies, we demonstrate that rBGR outperforms existing graphical regression models for data generated under various levels of non-normality in both edge and covariate selection. We use rBGR to assess proteomic networks in lung and ovarian cancers to systematically investigate the effects of immunogenic heterogeneity within tumors. Our analyses reveal several important protein–protein interactions that are differentially associated with the immune cell abundance; some corroborate existing biological knowledge, whereas others are novel findings.

Absolute risk from double nested case-control designs: cause-specific proportional hazards models with and without augmented estimating equations

ABSTRACT We estimate relative hazards and absolute risks (or cumulative incidence or crude risk) under cause-specific proportional hazards models for competing risks from double nested case-control (DNCC) data. In the DNCC design, controls are time-matched not only to cases from the cause of primary interest, but also to cases from competing risks (the phase-two sample). Complete covariate data are available in the phase-two sample, but other cohort members only have information on survival outcomes and some covariates. Design-weighted estimators use inverse sampling probabilities computed from Samuelsen-type calculations for DNCC. To take advantage of additional information available on all cohort members, we augment the estimating equations with a term that is unbiased for zero but improves the efficiency of estimates from the cause-specific proportional hazards model. We establish the asymptotic properties of the proposed estimators, including the estimator of absolute risk, and derive consistent variance estimators. We show that augmented design-weighted estimators are more efficient than design-weighted estimators. Through simulations, we show that the proposed asymptotic methods yield nominal operating characteristics in practical sample sizes. We illustrate the methods using prostate cancer mortality data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial Study of the National Cancer Institute.