Regression analysis under non-standard situations: a pairwise pseudolikelihood approach

Regression analysis is one of the most used statistical methods for data analysis. There are, however, many situations in which one cannot base inference solely on f(y \ x; beta), the conditional probability (density) function for the response variable Y, given x, the covariates. Examples include missing data where the missingness is non-ignorable, sampling surveys in which subjects are selected on the basis of the Y-values and meta-analysis where published studies are subject to 'selection bias'. The conventional approaches require the correct specification of the missingness mechanism, sampling probability and probability for being published respectively. In this paper, we propose an alternative estimating procedure for beta based on an idea originated by Kalbfleisch. The novelty of this method is that no assumption on the missingness probability mechanisms etc. mentioned above is required to be specified. Asymptotic efficiency calculations and simulation studies were conducted to compare the method proposed with the two existing methods: the conditional likelihood and the weighted estimating function approaches.