A new proportion measure of the treatment effect captured by candidate surrogate endpoints

The use of surrogate endpoints is expected to play an important role in the development of new drugs, as they can be used to reduce the sample size and/or duration of randomized clinical trials. Biostatistical researchers and practitioners have proposed various surrogacy measures; however, (i) most of these surrogacy measures often fall outside the range [0,1] without any assumptions, (ii) these surrogacy measures do not provide a cut-off value for judging a surrogacy level of candidate surrogate endpoints, and (iii) most surrogacy measures are highly variable; thus, the confidence intervals are often unacceptably wide. In order to solve problems (i) and (ii), we propose a new surrogacy measure, a proportion of the treatment effect captured by candidate surrogate endpoints (PCS), on the basis of the decomposition of the treatment effect into parts captured and non-captured by the candidate surrogate endpoints. In order to solve problem (iii), we propose an estimation method based on the half-range mode method with the bootstrap distribution of the estimated surrogacy measures. Finally, through numerical experiments and two empirical examples, we show that the PCS with the proposed estimation method overcomes these difficulties. The results of this paper contribute to the reliable evaluation of how much of the treatment effect is captured by candidate surrogate endpoints.