D-efficient Window Designs for Non-Linear Models

In many experiments various practical constraints make accurate timing for taking samples difficult or even impossible. It often happens in pharmacokinetic/pharmacodynamic studies in which patients have to come to a clinic for a blood sample to be taken. In chemical experiments a reaction is often run up to a point of time, then stopped and the concentration is measured. This can be done at any point of time and repeated as many times as required. Stopping a chemical reaction at a very exact time may be impractical. Some flexibility in timing the sample collection, whiles assuring that sufficient information is gathered from the experiment would be welcomed by practitioners. Also, efficient sampling windows give some degree of protection against model miss-specification. We present a method of calculating sampling windows based on the connection between the variance function of the model prediction and the D-optimum design criterion. The method is simple to apply, assures some minimum design efficiency and captures the importance of more accurate timing of sampling in some parts of the design region giving windows of unequal lengths.