A regression model for pooled data in a two-stage survey under informative sampling with application for detecting and estimating the presence of transgenic corn

Group-testing regression methods are effective for estimating and classifying binary responses and can substantially reduce the number of required diagnostic tests. However, there is no appropriate methodology when the sampling process is complex and informative. In these cases, researchers often ignore stratification and weights that can severely bias the estimates of the population parameters. In this paper, we develop group-testing regression models for analysing two-stage surveys with unequal selection probabilities and informative sampling. Weights are incorporated into the likelihood function using the pseudo-likelihood approach. A simulation study demonstrates that the proposed model reduces the bias in estimation considerably compared to other methods that ignore the weights. Finally, we apply the model for estimating the presence of transgenic corn in Mexico and we give the SAS code used for the analysis.