gms | German Medical Science

In recurrent-events the subjects experience multiple occurrences of the event of interest. An example is the study of chronic diseases such as migraine headaches or epilepsy. In transplant studies, the recurrent events are graft rejection episodes. For recurrent events model, there are theoretically no limits to the number of events. Competing risks is a term which covers cause of death (failure) data, corresponding to the various causes of death “ competing” to end the life of a given person. Concurrent multiple event on the other hand, is an event which embraces both single failure and simultaneous failures. It is neither competing risk nor recurrent event. Examples includes two dental implant lifetimes, two infection times of the left and the right kidneys of patients, and similar concurrencies in total hip replacement studies. It also addresses multiple adverse events.

Parametric models are only occasionally used in the analysis of clinical studies of survival although they may offer some advantages. In some cases, parametric models lead to more efficient parameter estimates than other models, eg. Cox model.

Parametric models e.g Bivariate exponential (BVE) of Marshall and Olkin [Ref. 4] and Freund's [Ref. 2] are of great importance. Marshall-Olkin is relevant in analyzing the joint distribution of two event times arising from “ systems of two components” and their simultaneous failures. It has the appealing properties of having exponential, but dependent, marginals and a memoryless property similar to the univariate exponential distribution. It was also shown that the BVE distribution could arise from non-fatal shock models. Thus it is useful in modelling lifetimes of dependent components in reliability and biometry. Freund's on his part, is frequently used for parallel systems of two components. It permits different hazards before and after a first failure in either of the two components. It exhibits some features of the Prentice-Williams-Peterson's conditional hazards with the Wei-Lin-Weisfeld competing hazards marginal models.These models are also relevant for safety data analysis or multiple concurrent events.

We fit the exponential and Weibull distributions and their special case, the Hanagal bivariate Weibull [Ref. 3] in those models to data from multiple concurrent events. These would be compared with nonparametric estimators obtained from the statistical theory for counting processes Aalen [Ref. 1] in models of multi-state survival as described in Mau [Ref. 5], [Ref. 6].

It came out that hazards are normally affected by first failures. It is appropriate to assume nonexponential for hazards. Marshall-Olkin's Bivariate Exponential model is preferred to Freund since it accomodates simultaneous joint failures.