# Statistical Procedures

The content on this page is a summary. For detailed information, please see the expanded overview or the Related Links.

NTP uses a variety of statistical procedures to:

- Analyze data produced by two-year toxicology/carcinogenicity studies
- Develop estimates of chemical properties
- Predict the toxicological effects of certain chemicals
- Reduce or replace the use of animals for toxicity testing

## Survival

We use the Kaplan and Meier product-limit procedure, presented in graphical form, to estimate the probability of survival. Dose-related trends are identified with Tarone's life table test, and dose-related effects on survival are assessed using a Cox proportional hazards model.

## Neoplasm and Nonneoplastic Lesion Incidences

We determine incidence rates based on the numbers of animals bearing neoplasms or nonneoplastic lesions at a specific anatomic site, as well as the numbers of animals with that site examined microscopically. The Poly-k test, a survival-adjusted procedure that takes survival differences into account, is used to assess the effect of dose on the prevalence of neoplasms and nonneoplastic lesions. Other tests of significance include pairwise comparisons of each exposed group with controls, and a test for overall exposure-related trends.

## Continuous Variables

We employ two approaches to assess the significance of pairwise comparisons between exposed and control groups in the analysis of continuous variables. Organ and body-weight data are analyzed with parametric multiple comparison procedures. Hematology, clinical chemistry, urinalysis, urine- concentrating ability, cell proliferation, tissue concentrations, litter size, estrous cycle counts and durations, sperm counts, and concentration are analyzed using nonparametric multiple comparison methods.

## Litter Effects

Incorporating litter effects into statistical analyses, when there are multiple pups per sex per litter, is one example of how NTP is committed to implementing new statistical procedures to produce more accurate data analyses. Littermates tend to be more like one another than fetuses/pups in other litters, sharing such common features as:

- Genetics
- Maternal environments during gestation
- Shared environments during lactation
- Possibly shared environments into adulthood

If litter effects are ignored, within-litter correlation leads to underestimates of variance in statistical tests, resulting in higher probabilities of Type I errors ("false positives"). We use various statistical approaches, including a modified version of the Poly-k test that incorporates the within-litter correlation and the effective sample size, as well as mixed-effects logistic regression, to account for between-litter variability.