On the relevance of prognostic information for clinical trials: A theoretical quantification

The question of how individual patient data from cohort studies or historical clinical trials can be leveraged for designing more powerful, or smaller yet equally powerful, clinical trials becomes increasingly important in the era of digitalisation. Today, the traditional statistical analyses approaches may seem questionable to practitioners in light of ubiquitous historical covariate information. Several methodological developments aim at incorporating historical information in the design and analysis of future clinical trials, most importantly Bayesian information borrowing, propensity score methods, stratification, and covariate adjustment. Recently, adjusting the analysis with respect to a prognostic score, which was obtained from some machine learning procedure applied to historical data, has been suggested and we study the potential of this approach for randomised clinical trials. In an idealised situation of a normal outcome in a two-arm trial with 1:1 allocation, we derive a simple sample size reduction formula as a function of two criteria characterising the prognostic score: (1) The coefficient of determination $R^2$ on historical data and (2) the correlation $\rho$ between the estimated and the true unknown prognostic scores. While maintaining the same power, the original total sample size $n$ planned for the unadjusted analysis reduces to $(1 - R^2 \rho^2) \times n$ in an adjusted analysis. Robustness in less ideal situations was assessed empirically. We conclude that there is potential for substantially more powerful or smaller trials, but only when prognostic scores can be accurately estimated.