The self-controlled case series method assumes that adverse outcomes arise according to a non-homogeneous Poisson process. This implies that it is applicable to independent recurrent outcomes. However, the self-controlled case series method may also be applied to unique, non-recurrent outcomes or first outcomes only, in the limit where these become rare. We investigate this rare outcome assumption when the self-controlled case series method is applied to non-recurrent outcomes. We study this requirement analytically and by simulation, and quantify what is meant by \'rare\' in this context. In simulations we also apply the self-controlled risk interval design, a special case of the self-controlled case series design. To illustrate, we extract data on the incidence rate of some recurrent and non-recurrent outcomes within a defined study population to check whether outcomes are sufficiently rare for the rare outcome assumption to hold when applying the self-controlled case series method to first or unique outcomes. The main findings are that the relative bias should be no more than 5% when the cumulative incidence over total time observed is less than 0.1 per individual. Inclusion of age (or calendar time) effects will further reduce bias. Designs that begin observation with exposure maximise bias, whereas little or no bias will be apparent when there is no time trend in the distribution of exposures, or when exposure is central within time observed.

We consider modeling case-patterns under a complex spatial and longitudinal sampling design as conducted via a serial case-control study of diarrheal disease in northwestern Ecuador. We build a two-stage space-time model to understand the role of spatially and temporally referenced covariates that reflect social and natural environments in the sampled region, after accounting for unmeasured residual heterogeneities. All diarrheal case events are collected from 21 sampled communities in Esmeraldes province in Ecuador, during seven sampling cycles from 2003 to 2008. The region of interest comprises 158 communities along a river basin. Prediction of case counts at unsampled communities at a future time is of interest along with estimation of risk-related parameters. We propose a computationally feasible two-stage Bayesian approach to estimate the risk-related parameters and conduct predictive inference. We first apply the log Gaussian Cox process (LGCP), commonly used to model spatial clustering of point patterns, to accommodate temporal variation within the sampled communities. Prediction of the number of cases at unsampled communities at a future time is obtained by a disease mapping model conditional on the expected case counts from Stage I.