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

Unmatched spatially stratified controls: A simulation study examining efficiency and precision using spatially-diverse controls and generalized additive models

Unmatched spatially stratified random sampling (SSRS) of non-cases selects geographically balanced controls by dividing the study area into spatial strata and randomly selecting controls from all non-cases within each stratum. The performance of SSRS control selection was evaluated in a case study spatial analysis of preterm birth in Massachusetts. In a simulation study, we fit generalized additive models using controls selected by SSRS or simple random sample (SRS) designs. We compared mean squared error (MSE), bias, relative efficiency (RE), and statistically significant map results to the model results with all non-cases. SSRS designs had lower average MSE (0.0042-0.0044) and higher RE (77-80%) compared to SRS designs (MSE: 0.0072-0.0073; RE across designs: 71%). SSRS map results were more consistent across simulations, reliably identifying statistically significant areas. SSRS designs improved efficiency by selecting controls that are geographically distributed, particularly from low population density areas, and may be more appropriate for spatial analyses.

Practical strategies for operationalizing optimal allocation in stratified cluster-based outcome-dependent sampling designs

Cluster-based outcome-dependent sampling (ODS) has the potential to yield efficiency gains when the outcome of interest is relatively rare, and resource constraints allow only a certain number of clusters to be visited for data collection. Previous research has shown that when the intended analysis is inverse-probability weighted generalized estimating equations, and the number of clusters that can be sampled is fixed, optimal allocation of the (cluster-level) sample size across strata defined by auxiliary variables readily available at the design stage has the potential to increase efficiency in the estimation of the parameter(s) of interest. In such a setting, the optimal allocation formulae depend on quantities that are unknown in practice, currently making such designs difficult to implement. In this paper, we consider a two-wave adaptive sampling approach, in which data is collected from a first wave sample, and subsequently used to compute the optimal second wave stratum-specific sample sizes. We consider two strategies for estimating the necessary components using the first wave data: an inverse-probability weighting (IPW) approach and a multiple imputation (MI) approach. In a comprehensive simulation study, we show that the adaptive sampling approach performs well, and that the MI approach yields designs that are very near-optimal, regardless of the covariate type. The IPW approach, on the other hand, has mixed results. Finally, we illustrate the proposed adaptive sampling procedures with data on maternal characteristics and birth outcomes among women enrolled in the Safer Deliveries program in Zanzibar, Tanzania.

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.