Modeling multivariate discrete failure time data

A bivariate discrete survival distribution that allows flexible modeling of the marginal distributions and yields a constant odds ratio at any grid point is proposed. The distribution can be extended to a multivariate distribution and is readily generalized to accommodate covariates in the marginal distributions and pairwise odds ratios. In addition, a pseudo-likelihood estimation procedure for estimating the regression coefficients in the marginal models and the association parameters in the pairwise odds ratios is presented. We evaluate the performance of the proposed estimation procedure through simulations. For bivariate data, pseudo-likelihood estimation of the association parameter has high efficiency. Loss of efficiency in the marginal regression coefficient estimates is small when the association is not strong. For both the marginal regression coefficients and the association parameter, coverage probabilities are close to the 95% nominal level. For multivariate data, the simulation results show that the parameter estimates are consistent. Coverage probability for the regression coefficient in the marginal model is close to the 95% nominal level but is slightly less than the nominal level for the association parameter. We illustrate the proposed methods using a subset of the Framingham Heart Study data where a significant positive association was found between the failure times of siblings.