Using Prior Information on Parameters to Eliminate Dependence on Initial Values in Fitting Coxian Phase Type Distributions to Length of Stay Data in Healthcare Settings - Xie, Bin (International Journal of Statistics in Medical Research, 2012)
Background: Modeling length of stay (LOS) data in healthcare settings using Coxian phase type (PH) distributions is becoming increasingly popular. However, dependence on initial values is a persistent difficulty in parameter estimations. This paper explores the utility of prior information on the parameters to address this difficulty. Methods: Maximum likelihood methods were used to estimate parameters of PH distributions that best fit simulated datasets with various sample sizes arising from PH distributions of various numbers of phases and parameters, using randomly generated initial values. Estimated values for the parameters resulting from different initial values were compared to the known values to assess the extent to which estimates depend on initial values; the impacts of sample sizes, existence of prior information, as well as the number of parameters with prior information were assessed. Results: Without prior information, parameter estimates depend on initial values for all PH distributions and all sample sizes. Prior information on one or more parameters led to more concentrated estimates, with higher number of parameters with prior information or larger sample sizes leading to more concentrated estimates. For example, with a sample size of 500, the estimates for a parameter with known value of 0.706 without prior information had a wide range of 1.523; using prior information for two parameters narrowed that range down to 0.156. For 3-phase PH distributions, prior information on 3 parameters appeared to be sufficient to eliminate dependence on initial values, even for small sample sizes. For 4-phase PH distributions, prior information on 5 parameters and a moderate sample size were needed to eliminate such dependence. Conclusions: Combination of prior information on parameters and sufficient sample sizes can eliminate dependence on initial values in fitting PH distributions to LOS data.