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A new interesting class of multivariate probability distributions is constructed and applied in a biomedical framework. The practical objective is to determine a stochastic model that is expected to improve (in the sense of accuracy) predictions regarding patients' times from one attack of illness to the next (or death). These times are by nature random. Measures of predictions can be expressed as either the considered time's expected values or, whenever possible, approximations of the whole conditional probability distribution function of these times. The basic mathematical tool is the use of a conditional hazard rate of the considered time (given as numerical values) which characterizes some essential factors that may influence the health of a patient. For example, it may be the amount and intensity of consumed harmful substances. Also, one may consider amounts of specific medication administered during the process of treatment. The combined effect of these factors is discussed as well.
The formal description of the stochastic dependences between the considered times to event and measurable random stresses is established.