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Hospital length of stay (LOS) is often used as a reliable proxy for measuring the consumption of hospital resources because it exhibits a strong correlation with resource consumptions (Librero et al., 2004). LOS is also an easily available indicator of hospital activity and is used for various purposes such as management of hospital care, quality control, and hospital planning. Therefore, LOS is a key performance indicator for hospital management and a key measure of efficiency of the healthcare system currently implemented (Kulinskaya et al., 2005). According to Lee et al. (2005), “comprehensive and accurate information about inpatient LOS should be a high priority for health planners and administrators in the strategic planning and deployment of financial, human and physical resources.”
The mean of LOS is often used as a benchmark for the consumption of resources because of its readiness and good relation with raised costs. However, the common approach of averaging LOS is only a localization measure of the variable and it would be misleading if the underlying distribution is not symmetrical (Vasilakis & Marshall, 2005). The empirical distribution of LOS is established to be positively skewed with a heavy right tail. It is also well-known to contain many outliers and significantly vary between homogeneous groups of patients. This heterogeneity of LOS has posed serious problems for statistical analysis and has limited the use of inference techniques based on normality assumptions.
Previously, optimizing the use of LOS as an indicator of care has been attempted through various mathematical models. LOS data are conventionally analyzed using the non-parametric methods of survival analysis (Li, 1999). Survival analysis typically uses LOS data as a vehicle to study the effects of patient features on survival time (which is equivalent to length of stay in hospital), such as the differential effects of social attributes (Kwoh et al., 2009), or discharge destinations on LOS (Xie et al., 2006). Mixture models have been used by Atienza et al. (2008) to approximate the distributions of LOS of certain Diagnosis-Related Groups (DRG) . Abbi et al. (2008) further used mixture distributions to categorize patients into homogeneous groups . Compartmental models have also been applied to model LOS as flow of patients through various wards (Vasilakis & Marshall, 2005). Recently, the Coxian phase-type distributions, a special type of continuous-time Markov process, have been shown to be able to model LOS distributions accurately with many useful applications such as identifying patient groups and estimating associated costs (Faddy & McClean, 1999; Marshall & McClean, 2004; Marshall et al., 2007). See Fackrell (2009) for a thorough literature review of phase-type distributions and their applications to modeling LOS.
However, practical matters such as analyzing temporal tends of LOS have not yet been addressed using any of the above-mentioned methods. This paper proposes a novel method to analyze trends of LOS using the Coxian phase-type distributions and simple regression analyses. The distribution has the ability to stochastically model the transitions of patients through different progressive stages of stay. This allows for the comparison of the discharge probabilities from each stage over the periods of interest. A trend can be identified by inspecting any patterns of change in these probabilities over time. This can be done by regressing these probabilities on time as the sole explanatory variable.