A stochastic model for the occurrence of transient ischemic attacks

This paper presents the development, application and evaluation of a stochastic model of the frequency of occurrence of transient ischemic attacks (TIAs). TIAs occur during periods of abnormal arterial activity. The TIAs which occur during a single period of abnormal activity are called a cluster of TIAs. Thus, the number of TIAs occurring in a time interval is determined by the number of clusters of TIAs occurring and the number of TIAs per cluster. The distribution of the number of clusters, which is a modification of the Poisson distribution, is obtained through the use of infinitesimal probabilities and the method of generating function. The number of TIAs per cluster follows the logarithmic series distribution. The distribution of the number of TIAs is then a modification of the negative binomial distribution, which allows for censoring of the data that may be related to the occurrence of the clusters of TIAs. Estimates for the parameters, based on observed frequencies, are obtained, which allow the model to be applied to data from the Aspirin in Transient Ischemic Attacks Study.