The correlated Weibull regression model for the analysis of correlated binary data is presented. This regression model is based on Bonney’s disposition model for the regression analysis of correlated binary outcomes. Parameter estimation was done through the maximum likelihood method. The correlated Weibull regression model was contrasted with the correlated logistic regression model. The results showed that both regression models were useful in explaining the familial aggregation of oesophageal cancer. The correlated logistic regression model fitted the oesophageal cancer data better than the correlated Weibull regression model for both the non-nested and nested cases. Furthermore, the correlated logistic regression model was computationally more attractive than the correlated Weibull regression model.