An Application of Transformed Distribution: Length of Stay in Hospitals


Abstract


Length of stay in hospitals are mostly characterized as asymmetric, right skewed and leptokurtic in nature. Earlier studies have considered parametric distributions like gamma, Pareto, lognormal for studying length of stay of patients in hospitals. However, in this study we have proposed transformed distributions to be the best choice for characterizing the length of stay. For this study, we have considered paediatric asthma dataset and identified that transformed Weibull-Pareto as the best fit. For a comparative purpose we have also provided the results of gamma, lognormal, and Pareto distribution. Maximum likelihood approach is considered to estimate the unknown parameters of the Transformed distribution followed by goodness of fit tests to examine the suitability of the fitted distributions. The results provide a direction for modelling the length of stay in hospitals due to different medical problems which require hospitalization.

DOI Code: 10.1285/i20705948v12n3p691

References


Alshawarbeh E, Famoye F, & Lee C. (2013) Beta-Cauchy Distribution: Some Properties and Applications. Journal of Statistical Theory and Applications. 12(4). 378-391.

Alzaatreh A, Famoye F, & Lee C. Gamma-Pareto Distribution and its Applications. Journal of Modern Applied Statistical Methods. 11(1), 78-94.

Alzaatreh A, Famoye F, Lee C. (2013) Weibull-Pareto Distribution and its Applications. Communication in Statistics ? Theory and Methods. 42(9), 1673-1691.

Alzaatreh A, Lee C, & Famoye F. (2016) The Generalized Cauchy Family of Distributions with Applications. Journal of Statistical Distributions and Applications. 3(1):12.

Asmuseen S, & Lehtomaa J. (2017) Distinguishing Log-Concavity from Heavy Tails. Risks. 5(10).

Beata, S., Deshazo, J.P., Gennings, C., Olmo, J.L., Ventura, S., Cios, K.J., & Clore, J.N. (2011) ?Impact of HbA1c Measurement on Hospital Readmissions Rates: Analysis of 70,000 Clinical Database Patient Records.? BioMed Research International. 1-11.

Coles SG, Powell EA. (1996) Bayesian methods in extreme value modelling: a review and new developments. International Statistical Review. 64(1):119?136.

Cooke RM, Nieboer D, Misiewicz J. (2014) Fat-Tailed Distributions: Data, Diagnostics and Dependence.

Drees H. (2003) Extreme quantile estimation for dependent data, with applications to finance. Bernoulli. 9(4):617?657.

Embrechts P, & Schmidli H. (1994) Modelling of extremal events in insurance and finance. ZOR Zeitschrift für Operation Research Mathematical Methods. 39(1):1-34.

Faddy M, & Mcclean S. (1999) Analyzing Data on Lengths Of Stay Of Hospital Patients Using Phase-Type Distributions. Applications Of Stochastic Model In Business And Industry. 15(4):311-317.

Faddy M, Graves N, & Pettitt A. (2009)Modeling length of stay in hospital and other right skewed data: Comparison of phase-type, gamma and log-normal distributions. Value in Health. 12(2):309-314.

Gardiner JC (2014) Fitting Heavy-Tailed Distributions to Healthcare Data by Parametric and Bayesian Methods. Journal of Statistical Theory and Practice. 8(4): 619-652.

Gomes MI, & Guillou A. (2015) Extreme Value Theory and Statistics of Univariate Extremes: A Review. International Statistical Review. 83(2):263-292.

Gul M, Guneri AF (2015) Forecasting patient length of stay in an emergency department by artificial neural networks. Journal of Aeronautical and Space Technologies. 8(2):15.

------------- (2018) Fitting Length of Stay in Hospitals using Transformed Distributions. Communications in Statistics ? Case Studies, Data Analysis and Applications (Accepted).

Houchens R (1998) Comparison of Hospital Length of Stay between Two Insurers for Patients with Paediatric Asthma. Society for Industrial and Applied Mathematics 29-38.

Ickowicz A, & Sparks R (2017) Modelling Hospital Length of Stay using Convolutive Mixtures Distributions. Statistics in Medicine. 36(1).

Lin M, Lucas Jr HC, & Shmueli G (2013). Too Big to Fail: Large Samples and the p-Value Problem. Information System Research. 24(4): 906-917.

Luceno A (2006) Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators. Computation and Statistical Data Analysis. 51(2):904-917.

Marazzi A, Paccaud F, Ruffieux C, & Beguin C (1998) Fitting the Distributions of Length of Stay by Parametric Models. Medical Care. 36(6):915-927.

McClean S, & Millard P (1993) Patterns of Length of Stay after Admission in Geriatric Medicine: An Event History Approach. Journal of Royal Statistical Society. 42(D): 263-274.

More JJ, & Wild SM (2009) Benchmarking Derivative-Free Optimization Algorithms. SIAM Journal on Optimization, 20(1), 172-191.

Murdoch JD, Tsai YL, & Adcock J (2012) P-values are random variables. The American Statistician. 62: 242-245.

Nash JC (2014) Nonlinear Parameter Optimization Using R Tools. John Wiley & Sons, Chichester.

Nocedal J, Wright WJ (1999) Numerical Optimization. Springer Series in Operation Research. New York.

Papi M, Pontecorvi L, & Setola R (2016) A New Model for the Length of Stay of Hospital Patients. Health Care Management Science. 19(1):58-65.

Qualls M, Pallin DJ, & Schuur JD (2010) Parametric versus nonparametric statistical tests: The length of stay example. Academic Emergency Medicine. 17(10):1113-1121.

R Core Team. R - A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. 2015. URL https://www.R-project.org.

Sawilowsky S (2016) Rao-Lovric and the Triwizard Point Null Hypothesis Tournament. Journal of Modern Applied Statistical Methods. 15(2), 22-32.

Singh CH, & Ladusingh L (2010) Inpatient length of stay: A Finite Mixture Modelling Analysis. European Journal of Health Economics. 2010 ;11(2):119-126.

Smith, LR (1985) Maximum Likelihood Estimation in a Class of Non-regular Classes. Biometrika. 72(1): 67-90.

Thomas M, Lemaitre M, Wilson ML (2016) Applications of Extreme Value Theory in Public Health. PLoS One. 2016; 11(7).

Verburg IWM, De Keizer NF, De Jonge E, & Peek N (2014) Comparison of Regression Methods for Modelling Intensive Care Length of Stay. PLoS One. 9(10).


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