"Analysis of Neoplasm and Non-neoplastic Lesion Incidences

Statistical analyses of neoplasm and non-neoplastic lesion incidences took into account two features of the data. Some animals did not survive the entire 2 years of the study, so survival differences between groups had to be taken into account. Also, up to three animals per sex were randomly selected from each litter to participate in the study. The statistical analysis of lesion incidences used the Poly-3 test to account for survival differences, with a Rao-Scott adjustment for litter effects, as described below.

The Poly-k test162-164 was used to assess neoplasm and non-neoplastic lesion prevalence. This test is a survival-adjusted quantal-response procedure that modifies the Cochran-Armitage linear trend test to take survival differences into account. More specifically, this method modifies the denominator in the quantal estimate of lesion incidence to approximate more closely the total number of animal years at risk. For analysis of a given site, each animal is assigned a risk weight. This value is one if the animal had a lesion at that site or if it survived until terminal euthanasia; if the animal died prior to terminal euthanasia and did not have a lesion at that site, its risk weight is the fraction of the entire study time that it survived, raised to the kth power.

This method yields a lesion prevalence rate that depends only upon the choice of a shape parameter for a Weibull hazard function describing cumulative lesion incidence over time162. Unless otherwise specified, a value of k = 3 was used in the analysis of site-specific lesions. This value was recommended by Bailer and Portier162 following an evaluation of neoplasm onset time distributions for a variety of site-specific neoplasms in control F344 rats and B6C3F1 mice165. Bailer and Portier162 showed that the Poly-3 test gave valid results if the true value of k was anywhere in the range from 1 to 5. A further advantage of the Poly-3 method is that it does not require lesion lethality assumptions. Variation introduced by the use of risk weights, which reflect differential mortality, was accommodated by adjusting the variance of the Poly-3 statistic as recommended by Bieler and Williams166. Poly-3 tests used the continuity correction described by Nam167.

Because up to three pups per sex per litter were in the core study and in the 28-day study, the Poly-3 test was modified to accommodate litter effects using the Rao-Scott approach168. Litter effects arise when littermates are more similar to each other than they are to animals from other litters. If intra-litter correlations are present but ignored in the statistical analysis, the variance of the data will be underestimated, leading to P values that are too small. The Rao-Scott approach accounts for litter effects by estimating the ratio of the variance in the presence of litter effects to the variance in the absence of litter effects. This ratio is then used to adjust the sample size downward to yield the estimated variance in the presence of litter effects. The Rao-Scott approach was implemented in the Poly-3 test as recommended by Fung et al.169, formula ₸RS2.

Tests of significance included pairwise comparisons of each dosed group with controls and a test for an overall dose-related trend. Continuity-corrected Rao-Scott-adjusted Poly-3 tests were used in the analysis of lesion incidence and reported P values are one sided. The significance of lower incidences or decreasing trends in lesions is represented as 1–P with the letter N added (e.g., P = 0.99 is presented as P = 0.01N). For neoplasms and non-neoplastic lesions observed without litter structure (e.g., at the interim evaluation), Poly-3 tests that included the continuity correction, but without adjustment for potential litter effects, was used for trend and pairwise comparisons to the control group.

To evaluate litter incidences, the proportions of litters affected by each lesion type were tested among groups. Cochran-Armitage trend tests and Fisher exact tests170 were used to test for trends and pairwise differences from the control group, respectively.

The statistical analysis of brain gliomas and heart schwannomas reported in the NTP’s Report of Partial Findings158 differed from those presented here. In the previously reported analyses, only gliomas of the brain and schwannomas of the heart were analyzed. Because these are rare tumors and did not occur in more than one animal per litter and because effective statistical methods for litter effect adjustments had not been programmed at that point, Poly-3 and Poly-6 tests were used without adjustment for potential litter effects. The rarity of the tumors and the fact that no litter had more than one animal with the tumors indicated that the adjustment for litter effects would be negligible."

F1, Sprague-Dawley rats, female

HAWC