II. MATERIALS AND METHODS 



Suruiual Analyses: The probability of survival 

 was estimated by the product-limit procedure of 

 Kaplan and Meier (1958) and is presented in the 

 form of graphs. Animals were censored from the 

 survival analyses at the time they were found to 

 be missing or dead from other than natural 

 causes; animals dying from natural causes were 

 not censored. Statistical analyses for a possible 

 dose-related effect on survival used the method 

 of Cox (1972) for testing two groups for equality 

 and Tarone's (1975) life table test for a dose- 

 related trend. When significant survival differ- 

 ences were detected, additional analyses using 

 these procedures were carried out to determine 

 the time point at which significant differences in 

 the survival curves were first detected. All re- 

 ported P values for the survival analysis are 

 two-sided. 



Calculation of Incidence: The incidence of neo- 

 plastic or nonneoplastic lesions is given as the 

 ratio of the number of animals bearing such le- 

 sions at a specific anatomic site to the number of 

 animals in which that site was examined In 

 most instances, the denominators include only 

 those animals for which the site was examined 

 histologically. However, when macroscopic ex- 

 amination was required to detect lesions (e.g , 

 skin or mammary tumors) prior to histologic 

 sampling, or when lesions could have appeared 

 at multiple sites (e.g., lymphomas), the denomi- 

 nators consist of the number of animals on which 

 a necropsy was performed. 



Analysis of Tumor Incidence: Three statistical 

 methods are used to analyze tumor incidence 

 data: life table tests, logistic regression, and 

 Fisher exact/Cochran-Armitage trend analyses. 

 Tests of significance include pairwise compari- 

 sons of high dose and low dose groups with con- 

 trols and tests for overall dose-response trends. 

 For studies in which administration of the study 

 compound has little effect on survival, the re- 

 sults of the three alternative analyses will 

 generally be similar. When differing results are 

 obtained by the three methods, the final inter- 

 pretation of the data will depend on the extent to 

 which the tumor under consideration is regarded 

 as being the cause of death Continuity- 



corrected tests are used in the analysis of tumor 

 incidence, and reported P values are one-sided. 

 The procedures described below also were used 

 to evaluate selected nonneoplastic lesions. 



Life Table Analyses-This method of analysis as- 

 sumes that all tumors of a given type observed in 

 animals dying before the end of the study were 

 "fatal"; i.e , they either directly or indirectly 

 caused the death of the animal. According to 

 this approach, the proportions of tumor-bearing 

 animals in the dosed and control groups were 

 compared at each point in time at which an ani- 

 mal died with a tumor of interest. The denomi- 

 nators of these proportions were the total num- 

 ber of animals at risk in each group. These re- 

 sults, including the data from animals killed at 

 the end of the study, were then combined by the 

 Mantel-Haenszel method (1959) to obtain an 

 overall P value This method of adjusting for in- 

 tercurrent mortality is the life table method of 

 Cox (1972) and of Tarone (1975). The underly- 

 ing variable considered by this analysis is time 

 to death due to tumor If the tumor is rapidly 

 lethal, then time to death due to tumor closely 

 approximates time to tumor onset. In this case, 

 the life table test also provides a comparison of 

 the time-specific tumor incidences. 



Logistic Regression Analyses-This method of 

 analysis assumes that all tumors of a given type 

 observed in animals that died before the end of 

 the study were "incidental"; i e., they did not al- 

 ter the risk of death and were discovered merely 

 as the result of death from an unrelated cause. 

 According to this approach, tumor prevalence 

 was modeled as a logistic function of dose and 

 time. Both linear and quadratic terms in time 

 were incorporated initially, and the quadratic 

 term was eliminated if it did not significantly 

 enhance the fit of the model. The dosed and con- 

 trol groups were compared on the basis of the 

 likelihood score test for the regression coefficient 

 of dose. This method of adjusting for intercur- 

 rent mortality is the prevalence analysis of 

 Dinse and Lagakos (1983), further described and 

 illustrated by Dinse and Haseman (1986). If the 

 tumor type is nonlethal, prevalence analyses 

 and incidence analyses are equivalent. 



33 



Nitrofurantoin, NTP TR 341 



