Estimating the duration of latency and survival time of snails with schistosomiasis

By means of techniques of analyses of survival data developed for cancer trials it is possible to study aspects of the natural history of the infection of schistosomiasis on the intermediate host of transmission, the snail. The simultaneous study of three response variables is largely based on a model of Lagakos (1976). When using this approach in the schistosomiasis setting it seems inappropriate to assume that one process, the duration of latency, follows an exponential distribution. Thus this stage is modified to follow a normal distribution and the derivatives required to obtain maximum-likelihood estimates and approximate variances of all parameters are provided. Simple graphical tools for assessing the validity of distributional assumptions in survival data are available from industrial research. The reader's attention is drawn to a paper by Nelson (1972). The relevance and application of these methods to the current problem are described in Section 4. In the event that the times to death of prepatent and patent snails do not follow exponential distributions as assumed in the primary model, a further modification is introduced to enable either or both to follow Weibull densities. Lastly it is possible to adapt both the primary model of Section Three and the modified model of Section Five to allow for the inclusion of auxiliary variables or covariates. Again the required derivatives to obtain maximum likelihood estimates and approximate variances are provided.