Two-stage sampling is frequently used in the health and social sciences. Classical theory underlying the use of this sampling mechanism involves simple random sampling for each of the two stages or unequal probabilities of selection at one or more of the two stages. In such cases the relationship between the response variable and the covariates in the sample is the same as modeled for the population. When the selection probabilities are related to the values of the response variable, even after conditioning on concomitant variables included in the population model, the sample design is defined as informative. This may result in selection bias and, consequently, the relationship between the response variable and the covariates in the sample may differ from that in the population model. Thus, standard estimates of the population model parameters may be severely biased, leading possibly to false inference. This paper considers the effects of informative sampling at the first stage of sampling and nonignorable missing response at the second stage of sampling, on estimation and prediction of general parameter when dealing with small area estimation. The analytical framework developed to understand the inferential problems raised by informative sampling and nonignorable nonresponse is also fruitful in understanding the problem of selection bias.
