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Clinical trials can be lengthy and costly, with new treatments taking more than a decade to become available to the patients who need them. It is therefore of great interest to improve efficiency in this process, such as replacing the primary endpoint of a clinical trial with an alternative endpoint that can be measured with greater ease, reduced cost or reduced observation periods. Such replacement endpoints are called surrogate endpoints, and there has been a vast amount of research conducted to establish statistical methodology that can reliably assess whether such endpoints are appropriate for future use. The aims of this research are therefore threefold; to identify appropriate methodology that can be used in the assessment of time-to-event surrogate and true endpoints; to examine the identified methods via simulation studies for the setting of small sample sizes, across a variety of scenarios, and in particular for surrogate endpoints that capture information on both an intermediate disease status and the long-term clinical outcome of interest; and finally to develop improved methodology that can advance the surrogacy evaluation process for these settings. The findings of the research build on the existing surrogate endpoint literature by demonstrating that the most commonly used approaches for evaluation of time-to-event surrogate and true endpoints can have potential limitations. As a result of this finding, and based on the identified strengths and weaknesses of the examined statistical approaches under the settings of interest, a novel methodology for the evaluation of time-to-event surrogate and true endpoints is proposed and evaluated. This method provides an alternative option for the evaluation of surrogate endpoints, and is recommended for further use.