Abstract:
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As renal colic pain from kidney stones becomes more intense, individuals seek medical attention and are often admitted into the emergency room (ER). Previous studies have shown that environmental effects, such as extreme heat, can cause dehydration and increased risk of kidney stone development. This analysis hypothesized that renal colic admission counts in the summer months could be best described by a two-state Markov mixture model in which days transition between high and low risk levels, with differing Poisson parameters, according to an unobserved transition probability matrix. A modified version of the expectation-maximization (EM) algorithm was used to obtain maximum likelihood estimates for the two Poisson parameters and the two unique parameters of the transition probability matrix. The two-state Markov mixture model based on ER admissions in Houston, Texas from May through September 2010 showed a significant difference between the Poisson parameters of high and low risk days and exhibited accurate prediction characteristics when compared to traditional methods such as a single parameter Poisson distribution or a generalized linear model accounting for over-dispersion.
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