Analysis of responses in migraine modelling using hidden Markov models

Markov-type models have been used in the analysis of disease progression. Although standard errors of model parameters are usually estimated, available software often does not permit the construction of confidence intervals around predictions of the dependent or response variable. A method is presented to calculate means and confidence intervals of model-predicted responses in time governed by a non-homogeneous hidden Markov model in continuous time. The Kolmogorov equations serve as the basis for the calculations. The method is realised in S-Plus and is applied to the prediction of headache responses in clinical studies of anti-migraine treatment. Means and confidence intervals are calculated by numerically solving differential equations that are non-linear in the explanatory variable. Results indicate that uncertainty on predicted drug responses is larger than that on predicted placebo responses and that pain-free responses are less precisely predicted than pain-relief responses. This is due to the uncertainty in the drug-specific parameters which is not present in predicted placebo responses.