The Mantel–Haenszel test provides a straightforward method to combine results from several clinical trials when only summary information, such as the proportion of deaths, is available for each trial. More efficient tests, such as the stratified logrank test, should be used if the survival and censoring times are known for all individuals, but in practice, the cost and effort of obtaining this information may be prohibitive. The purpose of this paper is to derive a general expression for the asymptotic relative efficiency (ARE) of the Mantel–Haenszel test with respect to the stratified logrank test, and to compute the ARE in situations which are likely to be of practical interest. The results show that under realistic assumptions about the survival distribution, losses to follow-up and duration of accrual, the ARE frequently exceeds 80 per cent. An example is given to show the usefulness of the approach when combining proportions of deaths from several cancer clinical trials.