Model misspecification and robust analysis for outcome-dependent sampling designs under generalized linear models

Outcome-dependent sampling (ODS) is a commonly used class of sampling designs to increase estimation efficiency in settings where response information (and possibly adjuster covariates) is available, but the exposure is expensive and/or cumbersome to collect. We focus on ODS within the context of a two-phase study, where in Phase One the response and adjuster covariate information is collected on a large cohort that is representative of the target population, but the expensive exposure variable is not yet measured. In Phase Two, using response information from Phase One, we selectively oversample a subset of informative subjects in whom we collect expensive exposure information. Importantly, the Phase Two sample is no longer representative, and we must use ascertainment-correcting analysis procedures for valid inferences. In this paper, we focus on likelihood-based analysis procedures, particularly a conditional-likelihood approach and a full-likelihood approach. Whereas the full-likelihood retains incomplete Phase One data for subjects not selected into Phase Two, the conditional-likelihood explicitly conditions on Phase Two sample selection (ie, it is a "complete case" analysis procedure). These designs and analysis procedures are typically implemented assuming a known, parametric model for the response distribution. However, in this paper, we approach analyses implementing a novel semi-parametric extension to generalized linear models (SPGLM) to develop likelihood-based procedures with improved robustness to misspecification of distributional assumptions. We specifically focus on the common setting where standard GLM distributional assumptions are not satisfied (eg, misspecified mean/variance relationship). We aim to provide practical design guidance and flexible tools for practitioners in these settings.

Interpretable, predictive spatio-temporal models via enhanced pairwise directions estimation

This article concerns predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. We develop a novel approach based on supervised dimension reduction for such data in order to capture nonlinear mean structures without requiring a prespecified parametric model. In addition to prediction as a common interest, this approach emphasizes the exploration of geometric information from the data. The method of Pairwise Directions Estimation (PDE) is implemented in our approach as a data-driven function searching for spatial patterns and temporal trends. The benefit of using geometric information from the method of PDE is highlighted, which aids effectively in exploring data structures. We further enhance PDE, referring to it as PDE+, by incorporating kriging to estimate the random effects not explained in the mean functions. Our proposal can not only increase prediction accuracy but also improve the interpretation for modeling. Two simulation examples are conducted and comparisons are made with several existing methods. The results demonstrate that the proposed PDE+ method is very useful for exploring and interpreting the patterns and trends for spatio-temporal data. Illustrative applications to two real datasets are also presented.

Clustered longitudinal data subject to irregular observation

Data collected longitudinally as part of usual health care is becoming increasingly available for research, and is often available across several centres. Because the frequency of follow-up is typically determined by the patient's health, the timing of measurements may be related to the outcome of interest. Failure to account for the informative nature of the observation process can result in biased inferences. While methods for accounting for the association between observation frequency and outcome are available, they do not currently account for clustering within centres. We formulate a semi-parametric joint model to include random effects for centres as well as subjects. We also show how inverse-intensity weighted GEEs can be adapted to account for clustering, comparing stratification, frailty models, and covariate adjustment to account for clustering in the observation process. The finite-sample performance of the proposed methods is evaluated through simulation and the methods illustrated using a study of the relationship between outdoor play and air quality in children aged 2-9 living in the Greater Toronto Area.

Obtaining optimal cutoff values for tree classifiers using multiple biomarkers

In biomedical practices, multiple biomarkers are often combined using a prespecified classification rule with tree structure for diagnostic decisions. The classification structure and cutoff point at each node of a tree are usually chosen on an ad hoc basis, depending on decision makers' experience. There is a lack of analytical approaches that lead to optimal prediction performance, and that guide the choice of optimal cutoff points in a pre-specified classification tree. In this paper, we propose to search for and estimate the optimal decision rule through an approach of rank correlation maximization. The proposed method is flexible, theoretically sound, and computationally feasible when many biomarkers are available for classification or prediction. Using the proposed approach, for a prespecified tree-structured classification rule, we can guide the choice of optimal cutoff points at tree nodes and estimate optimal prediction performance from multiple biomarkers combined.

A Semi-parametric Transformation Frailty Model for Semi-competing Risks Survival Data

In the analysis of semi-competing risks data interest lies in estimation and inference with respect to a so-called non-terminal event, the observation of which is subject to a terminal event. Multi-state models are commonly used to analyse such data, with covariate effects on the transition/intensity functions typically specified via the Cox model and dependence between the non-terminal and terminal events specified, in part, by a unit-specific shared frailty term. To ensure identifiability, the frailties are typically assumed to arise from a parametric distribution, specifically a Gamma distribution with mean 1.0 and variance, say, σ². When the frailty distribution is misspecified, however, the resulting estimator is not guaranteed to be consistent, with the extent of asymptotic bias depending on the discrepancy between the assumed and true frailty distributions. In this paper, we propose a novel class of transformation models for semi-competing risks analysis that permit the non-parametric specification of the frailty distribution. To ensure identifiability, the class restricts to parametric specifications of the transformation and the error distribution; the latter are flexible, however, and cover a broad range of possible specifications. We also derive the semi-parametric efficient score under the complete data setting and propose a non-parametric score imputation method to handle right censoring; consistency and asymptotic normality of the resulting estimators is derived and small-sample operating characteristics evaluated via simulation. Although the proposed semi-parametric transformation model and non-parametric score imputation method are motivated by the analysis of semi-competing risks data, they are broadly applicable to any analysis of multivariate time-to-event outcomes in which a unit-specific shared frailty is used to account for correlation. Finally, the proposed model and estimation procedures are applied to a study of hospital readmission among patients diagnosed with pancreatic cancer.

Neuropsychological function in school-age children with low mercury exposures

The EPA reference dose for methylmercury (MeHg) was established using data from populations with greater exposures than those typical of the US. Few data are available on potential adverse health effects at lower levels. We examined relationships between hair mercury (Hg) levels and neuropsychological outcomes in a population of US children. This study included data from 355 children ages 6-10 enrolled in the New England Children's Amalgam Trial. Data on total hair Hg levels, sociodemographic information and neuropsychological function were collected. We evaluated associations between hair Hg and neuropsychological test scores with linear regression methods and used generalized additive models to determine the shape of associations that departed from linearity. Models controlled for relevant covariates, including the potential beneficial effects of consuming fish. In adjusted models, we observed no significant linear relationships between hair Hg level and any test score. Significant departures from linearity were identified for WIAT Math Reasoning and WRAMVA Visual-Motor Composite scores. The association was positive for hair Hg levels below 0.5 microg/g and negative for levels between 0.5 and 1.0 microg/g. Overall, test scores of children with hair Hg levels 1.0 microg/g appeared to be lower than those of children with levels < 1.0 microg/g, but few children had levels in this upper range and these differences did not reach statistical significance. Hair Hg levels below 1.0 microg/g in US school-age children were not adversely related to neuropsychological function.