A two-phase Poisson process model and its application to analysis of cancer mortality among A-bomb survivors

• We considered a Poisson process model where only early transitions are sensitive to exposure.
• We gave an approximate formula for the excess hazard ratio (EHR) due to a single point exposure.
• Since the formula for EHR has a few unknown parameters, it is applicable easily in data analysis.
• An analysis for cancer mortality among A-bomb survivors using the proposed model was illustrated.

We consider a two-phase Poisson process model where only early successive transitions are assumed to be sensitive to exposure. In the case where intensity transitions are low, we derive analytically an approximate formula for the distribution of time to event for the excess hazard ratio (EHR) due to a single point exposure. The formula for EHR is a polynomial in exposure dose. Since the formula for EHR contains no unknown parameters except for the number of total stages, number of exposure-sensitive stages, and a coefficient of exposure effect, it is applicable easily under a variety of situations where there exists a possible latency time from a single point exposure to occurrence of event. Based on the multistage hypothesis of cancer, we formulate a radiation carcinogenesis model in which only some early consecutive stages of the process are sensitive to exposure, whereas later stages are not affected. An illustrative analysis using the proposed model is given for cancer mortality among A-bomb survivors.