Scheduling optimal examination times in a simple illness–death model

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Simple illness-death model arises in many medical and animal experiments as well as industrial applications. In a typical simple illness–death model, two types of events are of interest: the event of occurrence of disease or illness ( D) which is assumed to be unobservable, and the event of failure or death ( F) which is observable with or without disease. With the development of methodologies for making inference on the distribution of D, the design issue has also attracted some attention although not so greatly. In this work, the objective is to find an optimal design to safeguard the event of failure with illness before it is detected at an examination time. The standard likelihood-based criteria are difficult to apply since calculation of the expected information matrix is not straightforward. Here, we consider finding K(⩾1) optimal intermediate examination times during the span of a study involving simple illness–death model, using some new criteria. The performance of these criteria are investigated through a number of characteristics and comparisons are made. Some of the criteria can be suitably adjusted to make them adaptive in the sense that the subsequent examination time depends on the past and current data.