Selection models for efficient two-phase design of family studies

Optimal sampling allocation for outcome-dependent designs in cluster-correlated data settings

In clinical and public health studies, it is often the case that some variables relevant to the analysis are too difficult or costly to measure for all individuals in the population of interest. Rather, a subsample of these individuals must be identified for additional data collection. A sampling scheme that incorporates readily-available information for the entire target population at the design stage can increase the statistical efficiency of the intended analysis. While there is no universally optimal sampling design, under certain principles and restrictions, a well-designed and efficient sampling strategy can be implemented. In two-phase designs, efficiency can be gained by stratifying on the outcome and/or auxiliary information that is known at phase I. Additional gains in efficiency can be obtained by determining the optimal allocation of the sample sizes across the strata, which depends on the quantity that is being estimated. In this paper, the inference is concerned with one or multiple regression parameter(s) where the study units are naturally clustered and, thus, exhibit correlation in outcomes. We propose several allocation strategies within the framework of two-phase designs for the estimation of the regression parameter(s) obtained from weighted generalized estimating equations. The proposed methods extend existing theory to address the objective of the estimating regression parameters in cluster-correlated data settings by minimizing the asymptotic variance of the estimator subject to a fixed sample size. Through a comprehensive simulation study, we show that the proposed allocation schemes have the potential to yield substantial efficiency gains over alternative strategies.

Optimal allocation in stratified cluster-based outcome-dependent sampling designs

In public health research, finite resources often require that decisions be made at the study design stage regarding which individuals to sample for detailed data collection. At the same time, when study units are naturally clustered, as patients are in clinics, it may be preferable to sample clusters rather than the study units, especially when the costs associated with travel between clusters are high. In this setting, aggregated data on the outcome and select covariates are sometimes routinely available through, for example, a country's Health Management Information System. If used wisely, this information can be used to guide decisions regarding which clusters to sample, and potentially obtain gains in efficiency over simple random sampling. In this article, we derive a series of formulas for optimal allocation of resources when a single-stage stratified cluster-based outcome-dependent sampling design is to be used and a marginal mean model is specified to answer the question of interest. Specifically, we consider two settings: (i) when a particular parameter in the mean model is of primary interest; and, (ii) when multiple parameters are of interest. We investigate the finite population performance of the optimal allocation framework through a comprehensive simulation study. Our results show that there are trade-offs that must be considered at the design stage: optimizing for one parameter yields efficiency gains over balanced and simple random sampling, while resulting in losses for the other parameters in the model. Optimizing for all parameters simultaneously yields smaller gains in efficiency, but mitigates the losses for the other parameters in the model.