Direct estimation of latent time for radiation injury in late-responding normal tissues: gut, lung, and spinal cord

Mixture models are proposed for simultaneous analysis of the latency and fractionation characteristics of radiation injury in late-responding normal tissues. The method is an extension of the direct analysis for quantal response data. Conceptually, the application of the mixture model is based on the biological observation that over a wide range of doses a proportion of the irradiated subjects will never express damage. Mixture models allow the time of occurrence to be utilized in the analysis. Furthermore, this type of model takes time-censored observations into account in a natural way and provides an adequate framework for modelling and analysis of effect-dependent latency. Mixture models with complete and incomplete repair are applied to dose-incidence data for four late endpoints in rodents: death from radiation-induced pneumonitis, leg paralysis after spinal-cord irradiation, and radiation-induced rectal stenosis and anal discharge. Radiation-induced pneumonitis had an effect-dependent latency. The modelling of this phenomenon correlates well with the results of histologic studies. Interestingly, the ratio of hazard rates was not constant for this endpoint. The dominating feature in the latency of radiation injury to the spinal cord was a strong dependency on dose per fraction. After correction for this effect a tendency towards a longer latent time for lower effect levels was observed. For the rectal complications, there was no difference between latency with radiation only vs. radiation combined with cis-platin.