The DES algorithm we've implemented for the CHD model is, in the terminology of a paper by Gillespie, a direct stochastic simulation model (SSM). This basically means that each individual is simulated in continuous time until the specified end point e.g. death. The downside with this is that, especially for small transition times and large number of states, the runtime is prohibitively sloooooow. One way of addressing this is to approxaimate the process. The approximation should improve the computational performance and we should still be able to obtain the output of interest, though perhaps in a more course form.
Simple alternative version include a Poisson count process over a specified time window or a "tau jump" model which uses a Binomial approximation to generate transition numbers. A refined version can be used to ensure there are no more jumps from a state than allowed. I've implementented a version of this latter algorithm for the CHD model but used a multivariate distribution rather than a simpel Binomial, to account for the competing risks.
This approach thus relies on specifying the discrete transition probabilities for the distributions. At present these values are produced via a model fitting step where data is combined in the form of both rates and discrete probabilities. To simplify the implementation further, I fitted a logistic regression through the age categories for given from and to states, e.g. from Healthy to CHD Death for 0-25, 26-35, 36-45, 46-55, 56-65, 66-75, 76-85, 85+. This reduces down the necessary storage.
Simple alternative version include a Poisson count process over a specified time window or a "tau jump" model which uses a Binomial approximation to generate transition numbers. A refined version can be used to ensure there are no more jumps from a state than allowed. I've implementented a version of this latter algorithm for the CHD model but used a multivariate distribution rather than a simpel Binomial, to account for the competing risks.
This approach thus relies on specifying the discrete transition probabilities for the distributions. At present these values are produced via a model fitting step where data is combined in the form of both rates and discrete probabilities. To simplify the implementation further, I fitted a logistic regression through the age categories for given from and to states, e.g. from Healthy to CHD Death for 0-25, 26-35, 36-45, 46-55, 56-65, 66-75, 76-85, 85+. This reduces down the necessary storage.
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