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BMC Medical Research Methodology

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Open Access 01-12-2022 | Research

A comparison of statistical methods for modeling count data with an application to hospital length of stay

Authors: Gustavo A. Fernandez, Kristina P. Vatcheva

Published in: BMC Medical Research Methodology | Issue 1/2022

Abstract

Background

Hospital length of stay (LOS) is a key indicator of hospital care management efficiency, cost of care, and hospital planning. Hospital LOS is often used as a measure of a post-medical procedure outcome, as a guide to the benefit of a treatment of interest, or as an important risk factor for adverse events. Therefore, understanding hospital LOS variability is always an important healthcare focus. Hospital LOS data can be treated as count data, with discrete and non-negative values, typically right skewed, and often exhibiting excessive zeros. In this study, we compared the performance of the Poisson, negative binomial (NB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB) regression models using simulated and empirical data.

Methods

Data were generated under different simulation scenarios with varying sample sizes, proportions of zeros, and levels of overdispersion. Analysis of hospital LOS was conducted using empirical data from the Medical Information Mart for Intensive Care database.

Results

Results showed that Poisson and ZIP models performed poorly in overdispersed data. ZIP outperformed the rest of the regression models when the overdispersion is due to zero-inflation only. NB and ZINB regression models faced substantial convergence issues when incorrectly used to model equidispersed data. NB model provided the best fit in overdispersed data and outperformed the ZINB model in many simulation scenarios with combinations of zero-inflation and overdispersion, regardless of the sample size. In the empirical data analysis, we demonstrated that fitting incorrect models to overdispersed data leaded to incorrect regression coefficients estimates and overstated significance of some of the predictors.

Conclusions

Based on this study, we recommend to the researchers that they consider the ZIP models for count data with zero-inflation only and NB models for overdispersed data or data with combinations of zero-inflation and overdispersion. If the researcher believes there are two different data generating mechanisms producing zeros, then the ZINB regression model may provide greater flexibility when modeling the zero-inflation and overdispersion.

Thomas JW, Guire KE, Horvat GG. Is patient length of stay related to quality of care? United States. 1997;42:489–507.

Taheri PA, Butz DA, Greenfield LJ. Length of stay has minimal impact on the cost of hospital admission. United States. 2000;191:123–30.

Kossovsky MP, Sarasin FP, Chopard P, Louis-Simonet M, Sigaud P, Perneger TV, et al. Relationship between hospital length of stay and quality of care in patients with congestive heart failure. England. 2002;11:219–23.

Khalifa M. Reducing Length of Stay by Enhancing Patients’ Discharge: A Practical Approach to Improve Hospital Efficiency. Netherlands. 2017;238:157–60.

Baek H, Cho M, Kim S, Hwang H, Song M, Yoo S. Analysis of length of hospital stay using electronic health records: A statistical and data mining approach. PLoS One. 2018;13(4):e0195901. Available from: https://doi.org/10.1371/journal.pone.0195901.

Giraldi G, Montesano M, Sandorfi F, Iachini M, Orsi GB. Excess length of hospital stay due to healthcare acquired infections: methodologies evaluation. Italy. 2019;31:507–16.

Rees EM, Nightingale ES, Jafari Y, Waterlow NR, Clifford S, Pearson CAB, et al. COVID-19 length of hospital stay: a systematic review and data synthesis. BMC Med. 2020;18:270. Available from: https://doi.org/10.1186/s12916-020-01726-3.CrossRefPubMedPubMedCentral

Systematic, data-driven approach lowers length of stay and improves care coordination [Internet]. 2018. Available from: https://www.healthcatalyst.com/success_stories/reducing-length-of-stay-memorial-hospital-at-gulfport. Accessed 16 Feb 2022.

Freeman WJ, Weiss AJ, Heslin KC. Overview of U.S. Hospital Stays in 2016: Variation by Geographic Region. 2018. In: Healthcare Cost and Utilization Project (HCUP) Statistical Briefs [Internet]. Rockville: Agency for Healthcare Research and Quality (US); 2006. Statistical Brief #246.

10.

Pickering BW, Dong Y, Ahmed A, Giri J, Kilickaya O, Gupta A, et al. The implementation of clinician designed, human-centered electronic medical record viewer in the intensive care unit: a pilot step-wedge cluster randomized trial. Int J Med Inform. 2015;84:299–307 Ireland: Elsevier Ireland Ltd.CrossRef

11.

Lingsma HF, Bottle A, Middleton S, Kievit J, Steyerberg EW, Marang-van de Mheen PJ. Evaluation of hospital outcomes: the relation between length-of-stay, readmission, and mortality in a large international administrative database. BMC Health Serv Res. 2018;18(1):116. Available from: https://doi.org/10.1186/s12913-018-2916-1.

12.

Betancourt-Garcia MM, Vatcheva K, Gupta PK, Martinez RD, McCormick JB, Fisher-Hoch SP, et al. The effect of Hispanic ethnicity on surgical outcomes: An analysis of the NSQIP database. Am J Surg. 2019;217:618–33 United States: Elsevier Inc.CrossRef

13.

Almashrafi A, Elmontsri M, Aylin P. Systematic review of factors influencing length of stay in ICU after adult cardiac surgery. BMC Health Serv Res. 2016;16:318. Available from: https://doi.org/10.1186/s12913-016-1591-3.

14.

Rosenthal MJ, Fajardo M, Gilmore S, Morley JE, Naliboff BD. Hospitalization and Mortality of Diabetes in Older Adults: A 3-year prospective study. Diabetes Care. 1998;21:231–5. Available from: https://doi.org/10.2337/diacare.21.2.231.CrossRefPubMed

15.

Aro S, Kangas T, Reunanen A, Salinto M, Koivisto V. Hospital use among diabetic patients and the general population. United States. 1994;17:1320–9.

16.

Bo S, Ciccone G, Grassi G, Gancia R, Rosato R, Merletti F, et al. Patients with type 2 diabetes had higher rates of hospitalization than the general population. United States. 2004;57:1196–201.

17.

Carter EM, Potts HW. Predicting length of stay from an electronic patient record system: a primary total knee replacement example. BMC Med Inform Decis Mak. 2014;14:26. Available from: https://doi.org/10.1186/1472-6947-14-26.

18.

Comino EJ, Harris MF, Islam MD, Tran DT, Jalaludin B, Jorm L, Flack J, Haas M. Impact of diabetes on hospital admission and length of stay among a general population aged 45 year or more: a record linkage study. BMC Health Serv Res. 2015;15:12. Available from: https://doi.org/10.1186/s12913-014-0666-2.

19.

Feng CX, Li L. Modeling Zero Inflation and Overdispersion in the Length of Hospital Stay for Patients with Ischaemic Heart Disease. In: Chen D-G, Chen J, Lu X, Yi GY, Yu H, editors. Singapore: Springer Singapore; 2016. p. 35–53. Available from: https://doi.org/10.1007/978-981-10-2594-5_3.

20.

Cheng SW, Wang CY, Ko Y. Costs and Length of Stay of Hospitalizations due to Diabetes-Related Complications. J Diabetes Res. 2019;2019:2363292. Available from: https://doi.org/10.1155/2019/2363292.

21.

Donnan PT, Leese GP, Morris AD. Diabetes Audit and Research in Tayside SMUC. Hospitalizations for people with type 1 and type 2 diabetes compared with the nondiabetic population of Tayside, Scotland: a retrospective cohort study of resource use. Diabetes Care. 2000;23:1774–9 United States.CrossRef

22.

Priyadi A, Permana H, Muhtadi A, Sumiwi SA, Sinuraya RK, Suwantika AA. Cost-Effectiveness Analysis of Type 2 Diabetes Mellitus (T2DM) Treatment in Patients with Complications of Kidney and Peripheral Vascular Diseases in Indonesia. Healthcare (Basel). 2021;9(2):211. Available from: https://doi.org/10.3390/healthcare9020211.CrossRef

23.

Dictionary SM. length of stay. (n.d.) [Internet]. 2011. Available from: https://www.who.int/data/gho/indicatormetadata-registry/imr-details/2541. Accessed 16 Feb 2022.

24.

Shaaban AN, Peleteiro B, Martins MRO. Statistical models for analyzing count data: predictors of length of stay among HIV patients in Portugal using a multilevel model. BMC Health Serv Res. 2021;21:372. Available from: https://doi.org/10.1186/s12913-021-06389-1.CrossRefPubMedPubMedCentral

25.

World Health Organization. The Global Health Observatory. Explore a world of health data. Length of stay for inpatient short-term treatment, days [Internet]. Available from: https://www.who.int/data/gho/indicator-metadata-registry/imr-details/2541. Accessed 16 Feb 2022.

26.

Bert F, Kakaa O, Corradi A, Mascaro A, Roggero S, Corsi D, Scarmozzino A, Siliquini R. Predicting Length of Stay and Discharge Destination for Surgical Patients: A Cohort Study. Int J Environ Res Public Health. 2020;17(24):9490. Available from: https://doi.org/10.3390/ijerph17249490.

27.

Garrison SR, Schneider KE, Singh M, Pogodzinski J. Preoperative physical therapy results in shorter length of stay and discharge disposition following total knee arthroplasty: a retrospective study. J Rehabil Med Clin Commun. 2019;2:1000017. Available from: https://doi.org/10.2340/20030711-1000017.

28.

Lim ATP. Methods for analyzing hospital length of stay with application to inpatients dying in Southern Thailand. Glob J Health Sci. 2009;1(1):27. Available from: https://doi.org/10.5539/gjhs.v1n1p27.CrossRef

29.

Mullahy J. Much ado about two: reconsidering retransformation and the two-part model in health econometrics. Netherlands. 1998;17:247–81.

30.

Manning WG. The logged dependent variable, heteroscedasticity, and the retransformation problem. Netherlands. 1998;17:283–95.

31.

Gardner W, Mulvey EP, Shaw EC. Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models. Psychol Bull. 1995;118:392–404 US: American Psychological Association.CrossRef

32.

O’Hara RB, Kotze DJ. Do not log-transform count data. Methods Ecol Evol. 2010;1:118–22. Available from: https://doi.org/10.1111/j.2041-210X.2010.00021.x.

33.

Martín-Fernández JA, Hron K, Templ M, Filzmoser P, Palarea-Albaladejo J. Model-based replacement of rounded zeros in compositional data: Classical and robust approaches. Computational Statistics & Data Analysis. 2012;56:2688–704. Available from: https://www.sciencedirect.com/science/article/pii/S0167947312000941.

34.

Bryk AS, Raudenbush SW, Congdon RT. HLM: hierarchical linear and nonlinear modeling with the HLM2L and HLM3L programs. Chicago: Scientific Software International; 1996.

35.

Huang JQ, Hooper PM, Marrie TJ. Factors associated with length of stay in hospital for suspected community-acquired pneumonia. Egypt. 2006;13:317–24.

36.

Sroka CJ, Nagaraja HN. Odds ratios from logistic, geometric, Poisson, and negative binomial regression models. BMC Med Res Methodol. 2018;18:112. Available from: https://doi.org/10.1186/s12874-018-0568-9.

37.

Lambert D. Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing. Technometrics. 1992;34:1–14. Available from: https://www.tandfonline.com/doi/abs/10.1080/00401706.1992.10485228.

38.

Cameron AC, Trivedi P. Regression Analysis of Count Data, 2nd edition, 2013. Econometric Society Monograph No.53. Cambridge University Press; 1998.

39.

Hilbe JM. Modeling Count Data [Internet]. Cambridge: Cambridge University Press; 2014. Available from: https://www.cambridge.org/core/books/modeling-count-data/BFEB3985905CA70523D9F98DA8E64D08.

40.

Agresti A. Foundations of linear and generalized linear models. Wiley; 2015.

41.

Greene W. Accounting for excess zeros and sample selection in poisson and negative binomial regression models [Internet]. In: Leonard N. Stern School of Business, Department of Economics. New York University; 1994.

42.

Slymen DJ, Ayala GX, Arredondo EM, Elder JP. A demonstration of modeling count data with an application to physical activity. Epidemiol Perspect Innov. 2006;3:3. Available from: https://doi.org/10.1186/1742-5573-3-3.

43.

Lee JH, Han G, Fulp WJ, Giuliano AR. Analysis of overdispersed count data: application to the Human Papillomavirus Infection in Men (HIM) Study. Epidemiol Infect. 2012;140(6):1087-94. Available from: https://doi.org/10.1017/S095026881100166X.

44.

Tüzen F, Erbaş S, Olmuş H. A simulation study for count data models under varying degrees of outliers and zeros. Communications in Statistics - Simulation and Computation. 2020;49:1078–88. Available from: https://doi.org/10.1080/03610918.2018.1498886.

45.

Tlhaloganyang BP TK. Are zero inflated distributions compulsory in the presence of zero-inflation? Int J Innov Sci Res Tech. 2020;5:1274–7.

46.

Poisson SD. Recherches sur la probabilité des jugements en matière criminelle et en matière civile, précédées des règles générales du calcul des probabilités. Imprimeur-Libraire pour les Mathématiques, Paris: Bachelier; 1837.

47.

Yang Z, Hardin JW, Addy CL. Score Tests for Zero-Inflation in Overdispersed Count Data. Communications in Statistics - Theory and Methods. 2010;39:2008-30. Available from: https://doi.org/10.1080/03610920902948228.

48.

Perga F Pierre de, and Apollonius, of. Varia Opera Mathematica. olosæ: apud Johannem Pech. 1679. Available from: https://doi.org/10.5479/sil.128299.39088002705879.

49.

Greenwood OR, Yule GU. An Inquiry into the Nature of Frequency Distributions Representative of Multiple Happenings with Particular Reference to the Occurrence of Multiple Attacks of Disease or of Repeated Accidents. J R Stat Soc. 1920;83:255–79. Available from: https://doi.org/10.1111/j.2397-2335.1920.tb00606.x John Wiley & Sons, Ltd.CrossRef

50.

Eggenberger F, Pólya G. über die Statistik verketteter Vorgange. Z Angew Math Mech. 1923;3:279-89. https://doi.org/10.1002/zamm.19230030407.

51.

He H, Tang W, Wang W, Crits-Christoph P. Structural zeroes and zero-inflated models. Shanghai Arch Psychiatry. 2014;26:236–42 China.

52.

Nelder JA, Wedderburn RWM. Generalized Linear Models. J R Stat Soc Ser A. 1972;135:370-84. Available from: https://doi.org/10.2307/2344614.

53.

McCullagh PNJ. Generalized Linear Models. 2nd ed. London: Chapman and Hall; 1989.CrossRef

54.

Johnson AE, Pollard TJ, Shen L, Lehman LW, Feng M, Ghassemi M, et al. MIMIC-III, a freely accessible critical care database. England. 2016;3:160035.

55.

Johnson A, Pollard T, Mark R. MIMIC-III Clinical Database Demo (version1.4). 2019. Available from: https://doi.org/10.13026/C2HM2Q.

56.

Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PC, Mark RG, et al. PhysioBank, PhysioToolkit, and PhysioNet. American Heart Association. 2000;101:e215–20. Available from: https://doi.org/10.1161/01.CIR.101.23.e215.

57.

Enders CK. Maximum Likelihood Estimation. In Encyclopedia of statistics in behavioral science. American Cancer Society; 2005. https://doi.org/10.1002/0470013192.bsa200.

58.

Beaujean AA, Grant MB. Tutorial on using regression models with count outcomes using R. Practical Assessment, Research, and Evaluation, Vol. 21, Article 2. 2016. Available from: https://doi.org/10.7275/pj8c-h254.

59.

Akaike H. A New Look at the Statistical Model Identification. In: Parzen E, Tanabe K, Kitagawa G, editors. Selected Papers of Hirotugu Akaike. Springer Series in Statistics. 1974. Available from: https://doi.org/10.1007/978-1-4612-1694-0_16.

60.

Schwarz G. Estimating the Dimension of a Model. Ann Statist. 1978;6(2):461-4. Available from: https://doi.org/10.1214/aos/1176344136.

61.

ZZeileis A, Kleiber C, Jackman S. Regression Models for Count Data in R Journal of Statistical Software. 2008;27(8):1–25. Available from: https://doi.org/10.18637/jss.v027.i08.

62.

Nekesa F, Odhiambo C, Chaba L. Comparative assessment of zero-inflated models with application to HIV exposed infants data. Open J Stat. 2019;9:664–85. Available from: https://doi.org/10.4236/ojs.2019.96043.CrossRef

63.

Minami M, Lennert-Cody CE, Gao W, Román-Verdesoto M. Modeling shark bycatch: The zero-inflated negative binomial regression model with smoothing. Fish Res. 2007;84:210–21 Available from: (https://www.sciencedirect.com/science/article/pii/S0165783606003821).CrossRef

64.

Saffari SE, Adnan R, Greene. Handling of Overdispersion of Count Data via Truncation using Poisson Regression Model. Journal of Computer Science & Computational Mathematics. 2011;1(1). Available from: https://doi.org/10.20967/jcscm.2011.01.001.

65.

Sawyer R. Sample Size and the Accuracy of Predictions Made from Multiple Regression Equations. Am Educ Res J. 1982;7:91–104. Available from: https://doi.org/10.3102/10769986007002091.CrossRef

66.

Tang W, Lu N, Chen T, Wang W, Gunzler DD, Han Y, et al. On performance of parametric and distribution-free models for zero-inflated and over-dispersed count responses. Stat Med. 2015;34:3235–45 England: John Wiley & Sons, Ltd.CrossRef

67.

Brewer MJ, Butler A, Cooksley SL. The relative performance of AIC, AICC and BIC in the presence of unobserved heterogeneity. Methods Ecol Evol. 2016;7:679–92. Available from: https://doi.org/10.1111/2041-210X.12541.

68.

Allison PD. Logistic Regression Using SAS®: Theory and Application. 2nd ed. Cary, NC: SAS Institute Inc.; 2012.

69.

Soyiri IN, Reidpath DD, Sarran C. Asthma length of stay in hospitals in London 2001–2006: demographic, diagnostic and temporal factors. PLoS One. 2011;6(11):e27184. Available from: https://doi.org/10.1371/journal.pone.0027184.CrossRefPubMedPubMedCentral

70.

Arora S, Kaur P, Panaich SS, Sagar H, Levine D. Asthma Exacerbations, Length of Stay and Hospitalization Costs: Insights from the Nationwide Inpatient Sample. J Allergy Clin Immunol. 2015;135(2):AB241.CrossRef

71.

Blumer A, Ehrenfeucht A, Haussler D, Warmuth MK. Occam’s Razor. Inf Process Lett. 1987;24:377–80. Available from: https://www.sciencedirect.com/science/article/pii/0020019087901141.

72.

Al-Mahtot M, Barwise-Munro R, Wilson P, Turner S. Changing characteristics of hospital admissions but not the children admitted-a whole population study between 2000 and 2013. Eur J Pediatr. 2018;177(3):381–8. Available from: https://doi.org/10.1007/s00431-017-3064-z.CrossRefPubMed

73.

Turner S, Raja EA. The association between opening a short stay pediatric assessment unit and trends in short stay hospital admissions. BMC Health Serv Res. 2021;21(1):523. Available from: https://doi.org/10.1186/s12913-021-06541-x.CrossRefPubMedPubMedCentral

74.

Thiruvengadam G, Lakshmi M, Ramanujam R. A Study of Factors Affecting the Length of Hospital Stay of COVID-19 Patients by Cox-Proportional Hazard Model in a South Indian Tertiary Care Hospital. J Prim Care Community Health. 2021. Available from: https://doi.org/10.1177/21501327211000231.

75.

Brock GN, Barnes C, Ramirez JA, Myers J. How to handle mortality when investigating length of hospital stay and time to clinical stability. BMC Med Res Methodol. 2011;11:144. Available from: https://doi.org/10.1186/1471-2288-11-144.CrossRefPubMedPubMedCentral

76.

Taylor SL, Sen S, Greenhalgh DG, Lawless M, Curri T, Palmieri TL. A competing risk analysis for hospital length of stay in patients with burns. JAMA Surg. 2015;150(5):450–6. Available from: https://doi.org/10.1001/jamasurg.2014.3490.CrossRefPubMedPubMedCentral

77.

Perez A, Chan W, Dennis RJ. Predicting the Length of Stay of Patients Admitted for Intensive Care Using a First Step Analysis. Health Serv Outcomes Res Methodol. 2006;6(3–4):127–38. Available from: https://doi.org/10.1007/s10742-006-0009-9.CrossRefPubMedPubMedCentral

78.

Sotoodeh M, Ho JC. Improving length of stay prediction using a hidden Markov model. AMIA Jt Summits Transl Sci Proc. 2019;2019:425–34 Available from: (https://pubmed.ncbi.nlm.nih.gov/31258996).PubMedPubMedCentral

79.

Xie H, Chaussalet TJ, Millard PH. A continuous time Markov model for the length of stay of elderly people in institutional long-term care. J R Statist SocA. 2005;168(1):51–61. Available from: https://doi.org/10.1111/j.1467-985X.2004.00335.x.CrossRef

80.

Zeger SL, Liang KY. Longitudinal data analysis for discrete and continuous outcomes. Biometrics. 1986;42(1):121-30.

81.

Wolfinger R, O’connell M. Generalized linear mixed models a pseudolikelihood approach. J Stat Comput Simul. 1993;48:233–43. Available from: https://doi.org/10.1080/00949659308811554.

82.

Goldstein H, Browne W, Rasbash J. Partitioning variation in multilevel models. Underst Stat. 2002;1:223–32. Available from: https://doi.org/10.1207/S15328031US0104_02.

Title: A comparison of statistical methods for modeling count data with an application to hospital length of stay
Authors: Gustavo A. Fernandez
Kristina P. Vatcheva
Publication date: 01-12-2022
Publisher: BioMed Central
Published in: BMC Medical Research Methodology / Issue 1/2022
Electronic ISSN: 1471-2288
DOI: https://doi.org/10.1186/s12874-022-01685-8

Keynote webinar | Spotlight on medication adherence

Springer Medicine

A comparison of statistical methods for modeling count data with an application to hospital length of stay

Abstract

Background

Methods

Results

Conclusions

Keynote webinar | Spotlight on medication adherence

Springer Medicine

Abstract

Background

Methods

Results

Conclusions

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