Exact versus Asymptotic Tests of Trend of Tumor Prevalence in Tumorigenicity Experiments: A Comparison of P-Values for Small Frequency of Tumors *

In the statistical evaluation of a tumorigenicity experiment, it is frequently of interest to test for dose-response trend in the incidence of a tumor type. A commonly used test is the prevalence test of Hoel and Walburg. This test is based on an extension of the Mantel-Haenszel (MH) statistic for combining s(≥ 2) 2 × k tables where k ≥ 2. The conditional null distribution (given marginal totals) of this statistic (MH) is discrete, and normal approximation is usually applied to obtain P-values. However, there is growing concern about the adequacy of the normal approximation when the number of animals bearing the tumor type (n_T) is “small.” For small n_T, it is suggested that the exact permutational distribution of MH be used for obtaining P-values. Another issue (which has attracted less attention) is related to the assignment of scores to the treatment groups when computing the test statistic. Various scoring systems are in use without quite realizing how they might affect the exact P-values in case of small n_T. This paper presents the results of a simulation study whereby the P-values obtained by the usual normal approximation and a continuity corrected normal approximation to MH are compared with the exact P-values (ie, P-values obtained from the exact permutational distribution of MH) using four different score sets. The normal approximation (without continuity correction) was found to be severely underestimating the exact P-values. The continuity correction, on the other hand, approximated the exact P-values with a high degree of accuracy when the (exact) distribution was fairly symmetric and n_T ≥ 3. As n_T increased, the exact P-values tended to decrease with an increase in the dispersion of the upper (medium and high) scores.