Remarks on the conservatism of sigma(0 -- E)2/E in survival data

This note presents theoretical and numerical calculations which investigate the adequacy of the sigma(0 -- E)2/E approximation (Peto and Pike [1973]) when applying the Mantel/Haenszel summary chisquare statistic to the comparison of r life tables in the manner suggested by Mantel [1966], Peto and Peto [1972], and Cox [1972]. These indicate that conservatism is mild unless there are marked differences in the withdrawal patterns in the r tables. Such differences may, however, be anticipated in the case of a generalization of the life table procedure suggested by Crowley [1973], Mantel and Byar [1974], and Turnbull, Brown, and Hu [1974], wherein individuals are moved from one life table to another according to changes in their treatment (or other) statuses.