352. Note: Conservatism of the Approximation Σ(O - E) 2 /E in the Logrank Test for Survival Data or Tumor Incidence Data

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Abstract
The logrank test has been widely recommended for the statistical comparison of groups of observations of event times in which some observations may be censored. It is the rank test of greatest local power for detecting multiplicative differences in failure rates, and has many applications in clinical trials and carcinogenesis experiments. This note provides a "cook-book" account of how to do it, and proves the conservatism of a certain easily calculated chi-squared approximation to the conditional logrank test for group heterogeneity. An immediate consequence of this proof is that if several r by 2 contingency tables are being summed (as, for example, in the indirect standardization technique), then the Poisson approximation to the usual conditional x$^2_{r-1}$ heterogeneity test is strictly conservative.

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