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

Abstract

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.

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

“…This again confirms that allocation to any of the influence functions will generally result in efficiency gains for all of the parameters, though this may not hold true when the covariate of interest is negatively associated with the stratification variable(s), as discussed in Sauer et al. 20 The choice of weights ν q should be done according to the relevance of each variable in the study. For example, if interest lies in making inference about a treatment, where the analysis model adjusts for some confounders, the investigators may want to choose a higher weight for the treatment effect variable.…”

“…Han et al 17 proposed optimal allocation for survival models using an extension of Reilly’s mean score method, and McIsaac and Cook 18 , also building on the work of Reilly 14 developed optimal two-phase designs in the independent data setting with Bernoulli sampling, for a variety of analysis methods. 17 McIsaac and Cook 19 evaluated a proposed framework for optimal allocation in the clustered data setting where clusters are sampled via Bernoulli sampling, and Sauer et al 20 developed optimal allocation formulae in the context of stratified cluster-based outcome-dependent sampling. Finally, Chen and Lumley 21 presented practical strategies for operationalizing optimal allocation designs for regression models.…”

“…Finally, Chen and Lumley 21 presented practical strategies for operationalizing optimal allocation designs for regression models. 19–21…”

“…Finally, Chen and Lumley 21 presented practical strategies for operationalizing optimal allocation designs for regression models. [19][20][21] While McIsaac and Cook 19 and Sauer et al 20 considered optimal allocation in the cluster-correlated data setting, both of these involved sampling at the level of the cluster, and both evaluated the proposed allocation schemes under settings with a binary outcome only. To date, optimal allocation in the context of two-phase stratified sampling designs (as opposed to Bernoulli sampling designs) where sampling occurs at the level of the individual, and where the outcomes across study units in the population, which may be continuous, exhibit correlation, has not been formally presented or evaluated.…”

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

“…Data that has been collected in such a way can be analyzed using inverse‐probability weighted generalized estimating equations (IPW‐GEE), 1,2 where the weights are the inverse of the cluster‐specific probabilities of selection. The number of clusters sampled from each of the defined strata can influence the efficiency gain or loss for a particular parameter in the analysis model, and Sauer et al 3 derived formulae for the optimal allocation of the (cluster‐level) sample size across the strata, when the intended analysis is IPW‐GEE. The authors showed that such an optimal allocation strategy yields efficiency gains for the parameter of interest relative to simple random sampling of clusters or balanced sampling of clusters across strata.…”