In medical research individuals are often sampled subject to certain conditions on an event time of interest. For example, subjects are required to have survived long enough or to be adverse event free to be recruited. These conditions yield response-biased samples featuring left-truncated event times. Moreover, data often arise from different geographic locations or can be classified into distinct groups within a study. The failure times of the individuals within clusters can be correlated due to natural common features or shared environmental factors. Incomplete covariate data are widely encountered in these settings. The fact that the covariate distribution is affected by the left truncation selection criterion and the clustering is often ignored in standard methods leading to biased estimates. An algorithm is developed to deal with these complications when the distribution of survival time and the effects of explanatory variables are of interest.