Bias, efficiency, and agreement for group-testing regression models

Abstract

Group testing involves pooling individual items together and testing them simultaneously for a rare binary trait. Whether the goal is to estimate the prevalence of the trait or to identify those individuals that possess it, group testing can provide substantial benefits when compared to testing subjects individually. Recently, group-testing regression models have been proposed as a way to incorporate covariates when estimating trait prevalence. In this paper, we examine these models by comparing fits obtained from individual and group testing samples. Relative bias and efficiency measures are used to assess the accuracy and precision of the resulting estimates using different grouping strategies. We also investigate the agreement of individual and group-testing regression estimates for various grouping strategies and the effects of group size selection. Depending on how groups are formed, our results show that group-testing regression models can perform very well when compared to the analogous models based on individual observations. However, different grouping strategies can provide very different results in finite samples.

Figure 1

Model fits for individual and group testing for one simulated data set using different pooling strategies. The covariate is age. Corresponding model estimates are in Table 1.

Figure 2

Values of the slope estimate β̂₁ in model (3) for individual and group testing using 100 simulated data sets with different pooling strategies.