Comparing two failure time distributions in the presence of dependent censoring

In a randomised clinical trial to compare two groups of patients, suppose that the time to disease occurrence, the major response variable, may be subject to dependent censoring by death or selective patient withdrawal, while the patients who have reached the disease endpoint are followed for their secondary endpoints or survival information. To adjust for the dependent censoring in assessing the group difference in disease occurrence, we assume that, on a logarithmic scale, the times to disease occurrence and dependent censoring for the two groups satisfy a bivariate location-shift model with a completely unspecified underlying distribution. Rank-based procedures are constructed for making inferences about the location-shift parameter. Model checking techniques are also developed. Numerical studies show that the proposed methods are appropriate for practical use. An illustration with data taken from a recent aids clinical trial is provided.