The aim of this thesis is to develop methodology for combining multiple endpoints within a single statistical analysis that compares the responses of patients treated with a novel treatment with those of control patients treated conventionally. The focus is on interval-censored bivariate survival data, and five real data sets from previous studies concerning multiple responses are used to illustrate the techniques developed. The background to survival analysis is introduced by a general description of survival data, and an overview of existing methods and underlying models is included. A review is given of two of the most popular survival analysis methods, namely the logrank test and Cox's proportional hazards model. The global score test methodology for combining multiple endpoints is described in detail, and application to real data demonstrates its benefits. The correlation between two score statistics arising from bivariate interval-censored survival data is the core of this research. The global score test methodology is extended to the case of bivariate interval-censored survival data and a complementary log-log link is applied to derive the covariance and the correlation between the two score statistics. A number of common scenarios are considered in this investigation and the accuracy of the estimator is evaluated by means of extensive simulations. An established method, namely the approach of Wei, Lin and Weissfeld, is examined and compared with the proposed method using both real and simulated data. It is concluded that our method is accurate, consistent and comparable to the competitor. This study marked the first successful development of the global score test methodology for bivariate survival data, employing a new approach to the derivation of the covariance between two score statistics on the basis of an interval-censored model. Additionally, the relationship between the jackknife technique and the Wei, Lin and Weissfeld method has been clarified.