Likelihood-based analysis of longitudinal data from outcome-related sampling designs

Small-sample inference for cluster-based outcome-dependent sampling schemes in resource-limited settings: Investigating low birthweight in Rwanda

The neonatal mortality rate in Rwanda remains above the United Nations Sustainable Development Goal 3 target of 12 deaths per 1000 live births. As part of a larger effort to reduce preventable neonatal deaths in the country, we conducted a study to examine risk factors for low birthweight. The data were collected via a cost-efficient cluster-based outcome-dependent sampling (ODS) scheme wherein clusters of individuals (health centers) were selected on the basis of, in part, the outcome rate of the individuals. For a given data set collected via a cluster-based ODS scheme, estimation for a marginal model may proceed via inverse-probability-weighted generalized estimating equations, where the cluster-specific weights are the inverse probability of the health center's inclusion in the sample. In this paper, we provide a detailed treatment of the asymptotic properties of this estimator, together with an explicit expression for the asymptotic variance and a corresponding estimator. Furthermore, motivated by the study we conducted in Rwanda, we propose a number of small-sample bias corrections to both the point estimates and the standard error estimates. Through simulation, we show that applying these corrections when the number of clusters is small generally reduces the bias in the point estimates, and results in closer to nominal coverage. The proposed methods are applied to data from 18 health centers and 1 district hospital in Rwanda.

Outcome-dependent sampling in cluster-correlated data settings with application to hospital profiling

Hospital readmission is a key marker of quality of healthcare and an important policy measure, used by the Centers for Medicare and Medicaid Services to determine, in part, reimbursement rates. Currently, analyses of readmissions are based on a logistic-normal generalized linear mixed model that permits estimation of hospital-specific measures while adjusting for case mix differences. Recent moves to identify and address healthcare disparities call for expanding case mix adjustment to include measures of socio-economic status while minimizing additional burden to hospitals associated with collecting data on such measures. Towards resolving this dilemma, we propose that detailed socio-economic data be collected on a subsample of patients via an outcome-dependent sampling scheme, specifically the cluster-stratified case-control design. Estimation and inference, for both the fixed and the random-effects components, are performed via pseudo-maximum-likelihood wherein inverse probability weights are incorporated in the usual integrated likelihood to account for the design. In comprehensive simulations, cluster-stratified case-control sampling proves to be an efficient design whenever interest lies in fixed or random effects of a generalized linear mixed model and covariates are unobserved or expensive to collect. The methods are motivated by and illustrated with an analysis of N = 889661 Medicare beneficiaries hospitalized between 2011 and 2013 with congestive heart failure at one of K = 3116 hospitals. Results highlight that the framework proposed provides a means of mitigating disparities in terms of which hospitals are indicated as being poor performers, relative to a naive analysis that fails to adjust for missing case mix variables.

Biomarker combinations for diagnosis and prognosis in multicenter studies: Principles and methods

Many investigators are interested in combining biomarkers to predict a binary outcome or detect underlying disease. This endeavor is complicated by the fact that many biomarker studies involve data from multiple centers. Depending upon the relationship between center, the biomarkers, and the target of prediction, care must be taken when constructing and evaluating combinations of biomarkers. We introduce a taxonomy to describe the role of center and consider how a biomarker combination should be constructed and evaluated. We show that ignoring center, which is frequently done by clinical researchers, is often not appropriate. The limited statistical literature proposes using random intercept logistic regression models, an approach that we demonstrate is generally inadequate and may be misleading. We instead propose using fixed intercept logistic regression, which appropriately accounts for center without relying on untenable assumptions. After constructing the biomarker combination, we recommend using performance measures that account for the multicenter nature of the data, namely the center-adjusted area under the receiver operating characteristic curve. We apply these methods to data from a multicenter study of acute kidney injury after cardiac surgery. Appropriately accounting for center, both in construction and evaluation, may increase the likelihood of identifying clinically useful biomarker combinations.

BIASED SAMPLING DESIGNS TO IMPROVE RESEARCH EFFICIENCY: FACTORS INFLUENCING PULMONARY FUNCTION OVER TIME IN CHILDREN WITH ASTHMA

Substudies of the Childhood Asthma Management Program (CAMP Research Group, 1999, 2000) seek to identify patient characteristics associated with asthma symptoms and lung function. To determine if genetic measures are associated with trajectories of lung function as measured by forced vital capacity (FVC), children in the primary cohort study retrospectively had candidate loci evaluated. Given participant burden and constraints on financial resources, it is often desirable to target a sub-sample for ascertainment of costly measures. Methods that can leverage the longitudinal outcome on the full cohort to selectively measure informative individuals have been promising, but have been restricted in their use to analysis of the targeted sub-sample. In this paper we detail two multiple imputation analysis strategies that exploit outcome and partially observed covariate data on the non-sampled subjects, and we characterize alternative design and analysis combinations that could be used for future studies of pulmonary function and other outcomes. Candidate predictor (e.g. IL10 cytokine polymorphisms) associations obtained from targeted sampling designs can be estimated with very high efficiency compared to standard designs. Further, even though multiple imputation can dramatically improve estimation efficiency for covariates available on all subjects (e.g., gender and baseline age), only modest efficiency gains were observed in parameters associated with predictors that are exclusive to the targeted sample. Our results suggest that future studies of longitudinal trajectories can be efficiently conducted by use of outcome-dependent designs and associated full cohort analysis.