Use of Logrank Scores in the Analysis of Litter-matched Data on Time to Tumor Appearance

Biostatistics Center, George Washington University, Bethesda, Maryland 20014 [N. M.], and Biometrics Research, Merck Sharp and Dohme Research Laboratories, West Point, Pennsylvania 19486 [J. L. C.] Previously, Mantel, Bohidar, and Ciminera (Mantel-Haenszel analyses of litter-matched time-to-response data, with modifications for recovery of interlitter information. Cancer Res., 37: 3863–3868, 1977) described how the Mantel-Haenszel method could be applied to litter-matched time-to-tumor data. Each litter would be treated as a separate stratum but only for as long as there remained contrastingly treated animals in that litter. Various devices were described for recovering interlitter information from remaining animals when that condition no longer obtained. An alternative procedure for the assessment of such data is now provided. Data from all litters are merged, and the merged data are used to assign a score to each treated or control animal, such score depending on when or whether the animal developed a tumor. The set of scores for the members of each litter now define a finite population, and those finite populations are then considered in the analysis made. Correspondences are brought out between the Mantel-Haenszel procedure, the logrank scoring procedure of Peto and Peto, and Savage's use of expectations of order statistics for the exponential distribution. Where incoming data are continuously analyzed, the logrank scores have to be changed, a difficulty that does not arise with the Mantel-Bohidar-Ciminera analyses. As in the Mantel-Bohidar-Ciminera report, it is recommended that results for tumors discovered only through autopsy of dying animals be integrated with results for observable tumors in a manner suggested by Peto. The scoring procedure used has implications for the interpretation of individual animal results. For a study of limited duration, i.e. , limited to a time at which the cumulative tumor rate is low, the primary distinction in scores is as between animals developing tumor and those not developing tumor. However, for a study in which the cumulative tumor rate is high, an animal with a late-appearing tumor could be assigned a score which is not suggestive of stimulated tumor formation. This is contrary to the frequent practice of counting all tumors, however late in appearance, as indicative of the tumorigenic effect of an agent. 1 This work was partially supported by USPHS Grant CA-15686 from the National Cancer Institute. 2 To whom requests for reprints should be addressed, at Biostatistics Center, George Washington University, 7979 Old Georgetown Road, Bethesda, Md. 20014. Received 1/12/79. Accepted 8/13/79.