[en] The temporal distribution of exposure-related cancers is relevant to the study of carcinogenic mechanisms. Statistical methods for extracting pertinent information from time-to-tumor data, however, are not well developed. Separation of incidence from 'latency' and the contamination of background cases are two problems. In this paper, we present methods for estimating both the conditional distribution given exposure-related cancers observed during the study period and the unconditional distribution. The methods adjust for confounding influences of background cases and the relationship between time to tumor and incidence. Two alternative methods are proposed. The first is based on a structured, theoretically derived model and produces direct inferences concerning the distribution of interest but often requires more-specialized software. The second relies on conventional modeling of incidence and is implemented through readily available, easily used computer software. Inferences concerning the effects of radiation dose and other covariates, however, are not always obtainable directly. We present three examples to illustrate the use of these two methods and suggest criteria for choosing between them. The first approach was used, with a log-logistic specification of the distribution of interest, to analyze times to bone sarcoma among a group of German patients injected with ²²⁴Ra. Similarly, a log-logistic specification was used in the analysis of time to chronic myelogenous leukemias among male atomic-bomb survivors. We used the alternative approach, involving conventional modeling, to estimate the conditional distribution of exposure-related acute myelogenous leukemias among male atomic-bomb survivors, given occurrence between 1 October 1950 and 31 December 1985. All analyses were performed using Poisson regression methods for analyzing grouped survival data. (J.P.N.)