  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.
