Probabilistic Models with Random Hazard Rates

1 Probabilistic Models with Random Hazard Rates 

The solution of the probabilistic transfer equations leads to the exponential model (9.3). The presence of negative exponentials in the model may simplify somewhat the choice of distribution associated with the random hazard rate. In fact, the elements p(t,h) of the state probability matrix exp(Ht) in (9.3) are exponentials, and integrating (9.27) over the random variable h, we obtain 

For the one-compartment model with n0 initial conditions, the distribution of the random hazard rate h can be simply mixed with the state probability p t,h) = exp (—/it), and relations (9.27) become 

By using the moment generating functions of Table 9.2, one directly obtains the following cases (the variance expressions were omitted for simplicity)  

This model is an analogue to the previous model with multiple rates in that the m specified fractions are replaced by a continuous rectangular rate distribution [375,376]. 

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In the following, we show how to apply probabilistic transfer models with random hazard rates associated with the administration and elimination processes in a single-compartment configuration. 

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