Abstract for RR-19

Trend Test for Binary Data with Survivability and Clustering Adjustments

Report Date: November 2023

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This report introduces a trend test for binary data that accommodates both treatment-affected survivability and clustering within treatment groups. The test is motivated by chronic rodent carcinogenicity assays that begin exposure in utero and continue exposing postweaning siblings at the same dose level as their dams. The new test modifies the Poly-3 trend test introduced by Bailer and Portier [1] to include clustering by adjusting the variance estimate of the lifetime incidence rate of findings. The weighted least squares linear regression approach to the Cochran-Armitage test with weights equal to the inverse of the variance is used to determine the initial statistic. Since sparse findings are common in low-dose groups and may be present in higher dose groups, the variance estimate is pooled across dose groups following Bieler and Williams [2] to increase robustness. The new method was first evaluated with simulated data using distributional models for tumor onset and mortality [1] with sibling correlation added through copulas. The simulations show that in the absence of positive sibling correlation, the false positive rate and power are similar for the Poly-3 test and the Poly-3 test modified for sibling correlation. However, with positive sibling correlation, the false positive rate is lower using the modified Poly-3 test than with the Poly-3 test. The two methods are also compared using real data from a National Toxicology Program perinatal chronic study, and the results reinforce the conclusion that failing to account for sibling correlation sometimes leads to inflated statistical significance.

National Toxicology Program (NTP). 2023. NTP research report on the trend test for binary data with survivability and clustering adjustments. Research Triangle Park, NC: National Toxicology Program. Research Report 19.

1. Bailer AJ, Portier CJ. Effects of treatment-induced mortality and tumor-induced mortality on tests for carcinogenicity in small samples. Biometrics. 1988; 44(2):417-431.
2. Bieler GS, Williams RL. Ratio estimates, the delta method, and quantal response tests for increased carcinogenicity. Biometrics. 1993; 49(3):793-801.