Inferences are made concerning population proportions when data are not missing at random.Both one sample and two sample situations are considered with examples in clinical trials.The one samplesituation involves the existence of response related incomplete data in a study conducted to make inferences involving the proportion. The two sample problem involves comparing two treatments in clinical trials when there exists dropouts due to both the treatment and the response to the treatment.Bayes procedures are used in estimating parameters of interest and testing hypotheses of interest in these two situations. An ad-hoc approach to the classical inference is presented for each ofthe two situations and compared with the Bayesian approach discussed. To illustrate the theory developed, data from clinical trials of severe head trauma patients at the Medical College of Virginia Head Injury Center from 1984 to 1987 is considered