Top

Published in:

Open Access 01-12-2021 | Research article

Modelling hospital outcome: problems with endogeneity

Authors: John L. Moran, John D. Santamaria, Graeme J. Duke, The Australian & New Zealand Intensive Care Society (ANZICS) Centre for Outcomes & Resource Evaluation (CORE)

Published in: BMC Medical Research Methodology | Issue 1/2021

Abstract

Background

Mortality modelling in the critical care paradigm traditionally uses logistic regression, despite the availability of estimators commonly used in alternate disciplines. Little attention has been paid to covariate endogeneity and the status of non-randomized treatment assignment. Using a large registry database, various binary outcome modelling strategies and methods to account for covariate endogeneity were explored.

Methods

Patient mortality data was sourced from the Australian & New Zealand Intensive Society Adult Patient Database for 2016. Hospital mortality was modelled using logistic, probit and linear probability (LPM) models with intensive care (ICU) providers as fixed (FE) and random (RE) effects. Model comparison entailed indices of discrimination and calibration, information criteria (AIC and BIC) and binned residual analysis. Suspect covariate and ventilation treatment assignment endogeneity was identified by correlation between predictor variable and hospital mortality error terms, using the Stata™ “eprobit” estimator. Marginal effects were used to demonstrate effect estimate differences between probit and “eprobit” models.

Results

The cohort comprised 92,693 patients from 124 intensive care units (ICU) in calendar year 2016. Patients mean age was 61.8 (SD 17.5) years, 41.6% were female and APACHE III severity of illness score 54.5(25.6); 43.7% were ventilated. Of the models considered in predicting hospital mortality, logistic regression (with or without ICU FE) and RE logistic regression dominated, more so the latter using information criteria indices. The LPM suffered from many predictions outside the unit [0,1] interval and both poor discrimination and calibration. Error terms of hospital length of stay, an independent risk of death score and ventilation status were correlated with the mortality error term. Marked differences in the ventilation mortality marginal effect was demonstrated between the probit and the "eprobit" models which were scenario dependent. Endogeneity was not demonstrated for the APACHE III score.

Conclusions

Logistic regression accounting for provider effects was the preferred estimator for hospital mortality modelling. Endogeneity of covariates and treatment variables may be identified using appropriate modelling, but failure to do so yields problematic effect estimates.

Available only for authorised users

Power G, Harrison DA. Why try to predict ICU outcomes? Curr Opin Crit Care. 2014;20(5):544–9. https://doi.org/10.1097/MCC.0000000000000136.CrossRefPubMed

Knaus WA, Wagner DP, Draper EA, Zimmerman JE, Bergner M, Bastos PG, et al. The APACHE III prognostic system. Risk prediction of hospital mortality for critically ill hospitalized adults. Chest. 1991;100(6):1619–36. https://doi.org/10.1378/chest.100.6.1619.CrossRefPubMed

Zimmerman JE, Kramer AA, McNair DS, Malila FM. Acute physiology and chronic health evaluation (APACHE) IV: hospital mortality assessment for today's critically ill patients. Crit Care Med. 2006;34(5):1297–310. https://doi.org/10.1097/01.CCM.0000215112.84523.F0.CrossRefPubMed

Solomon P, Kasza J, Moran J. ANZICS CfOaRE: identifying unusual performance in Australian and New Zealand intensive care units from 2000 to 2010. BMC Med Res Methodol. 2014;14(1):53. https://doi.org/10.1186/1471-2288-14-53.CrossRefPubMedPubMedCentral

Hilbe J. Logistic regression models. Boca Raton: Taylor & Francis Group; 2009. https://doi.org/10.1201/9781420075779.CrossRef

Bliss CI. The method of probits. Science. 1934;79(2037):38–9. https://doi.org/10.1126/science.79.2037.38.CrossRefPubMed

Berkson J. Why I prefer logits to probits. Biometrics. 1951;7(4):327–9. https://doi.org/10.2307/3001655.CrossRef

Cameron AC, Trivedi PK. Binary outcome models. In: Microeconometrics Using Stata: Revised Edition. College Station: Stata Press; 2010. p. 459–89.

Hellevik O. Linear versus logistic regression when the dependent variable is a dichotomy. Qual Quant. 2009;43(1):59–74. https://doi.org/10.1007/s11135-007-9077-3.CrossRef

10.

Stukel TA, Fisher ES, Wennberg DE, Alter DA, Gottlieb DJ, Vermeulen MJ. Analysis of observational studies in the presence of treatment selection Bias: effects of invasive cardiac management on AMI survival using propensity score and instrumental variable methods. JAMA. 2007;297(3):278–85. https://doi.org/10.1001/jama.297.3.278.CrossRefPubMedPubMedCentral

11.

Moons KGM, Altman DG, Reitsma JB, Ioannidis JPA, Macaskill P, Steyerberg EW, et al. Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD): explanation and elaboration. Ann Intern Med. 2015;162(1):W1–W73. https://doi.org/10.7326/M14-0698.CrossRefPubMed

12.

Harrell FE Jr. Regression modelling strategies: with applications to linear models, logistic regression, and survival analysis. 2nd ed. New York: Springer International Publishing; 2015. https://doi.org/10.1007/978-3-319-19425-7.CrossRef

13.

Harrison DAP, Brady ARM, Parry GJP, Carpenter JRD, Rowan KD. Recalibration of risk prediction models in a large multicenter cohort of admissions to adult, general critical care units in the United Kingdom. Crit Care Med. 2006;34(5):1378–88. https://doi.org/10.1097/01.CCM.0000216702.94014.75.CrossRefPubMed

14.

Horrace WC, Oaxaca RL. Results on the bias and inconsistency of ordinary least squares for the linear probability model. Econ Lett. 2006;90(3):321–7. https://doi.org/10.1016/j.econlet.2005.08.024.CrossRef

15.

Chen G, Tsurumi H. Probit and Logit model selection. Commun Stat. 2010;40(1):159–75. https://doi.org/10.1080/03610920903377799.CrossRef

16.

Bland JR, Cook AC. Random effects probit and logit: understanding predictions and marginal effects. Appl Econ Lett. 2019;26(2):116–23. https://doi.org/10.1080/13504851.2018.1441498.CrossRef

17.

Qin D. Let’s take the bias out of econometrics. J Econ Methodol. 2019;26(2):81–98. https://doi.org/10.1080/1350178X.2018.1547415.CrossRef

18.

Bilger M, Manning WG. Measuring overfitting in nonlinear models: a new method and an application to health expenditures. Health Econ. 2015;24(1):75–85. https://doi.org/10.1002/hec.3003.CrossRefPubMed

19.

Briscoe J, Akin J, Guilkey D. People are not passive acceptors of threats to health: endogeneity and its consequences. Int J Epidemiol. 1990;19(1):147–53. https://doi.org/10.1093/ije/19.1.147.CrossRefPubMed

20.

Hazlett C. Estimating causal effects of new treatments despite self-selection: the case of experimental medical treatments. J Causal Inference. 2019;7:1.CrossRef

21.

Hernan MA, Robins JM. Instruments for causal inference: an Epidemiologist’s dream? Epidemiology. 2006;17(4):360–72. https://doi.org/10.1097/01.ede.0000222409.00878.37.CrossRefPubMed

22.

Hernan MA, Robins JM. Estimating causal effects from epidemiological data. J Epidemiol Community Health. 2006;60(7):578–86. https://doi.org/10.1136/jech.2004.029496.CrossRefPubMedPubMedCentral

23.

Moran J, Solomon P. A review of statistical estimators for risk-adjusted length of stay: analysis of the Australian and new Zealand intensive care adult patient data-base, 2008-2009. BMC Med Res Methodol. 2012;12(1):68. https://doi.org/10.1186/1471-2288-12-68.CrossRefPubMedPubMedCentral

24.

Knaus WA, Wagner DP, Zimmerman JE, Draper EA. Variations in mortality and length of stay in intensive care units. Ann Intern Med. 1993;118(10):753–61. https://doi.org/10.7326/0003-4819-118-10-199305150-00001.CrossRefPubMed

25.

Render ML, Kim HM, Deddens J, Sivaganesin S, Welsh DE, Bickel K, et al. Variation in outcomes in veterans affairs intensive care units with a computerized severity measure. Crit Care Med. 2005;33(5):930–9. https://doi.org/10.1097/01.CCM.0000162497.86229.E9.CrossRefPubMed

26.

Basu AP, Manning WGP. Issues for the Next Generation of Health Care Cost Analyses. Med Care. 2009;47(7_Supplement_1):S109–14.CrossRefPubMed

27.

Stow PJ, Hart GK, Higlett T, George C, Herkes R, McWilliam D, et al. Development and implementation of a high-quality clinical database: the Australian and new Zealand Intensive Care Society adult patient database. J Crit Care. 2006;21(2):133–41. https://doi.org/10.1016/j.jcrc.2005.11.010.CrossRefPubMed

28.

Christodoulou E, Ma J, Collins GS, Steyerberg EW, Verbakel JY, Van Calster B. A systematic review shows no performance benefit of machine learning over logistic regression for clinical prediction models. J Clin Epidemiol. 2019;110:12–22. https://doi.org/10.1016/j.jclinepi.2019.02.004.CrossRefPubMed

29.

Bian J, Buchan I, Guo Y, Prosperi M. Statistical thinking, machine learning. J Clin Epidemiol. 2019;116:136–7. https://doi.org/10.1016/j.jclinepi.2019.08.003.CrossRefPubMed

30.

Van Calster B, Verbakel JY, Christodoulou E, Steyerberg EW, Collins GS. Statistics versus machine learning: definitions are interesting (but understanding, methodology, and reporting are more important). J Clin Epidemiol. 2019;116:137–8. https://doi.org/10.1016/j.jclinepi.2019.08.002.CrossRefPubMed

31.

Paul E, Bailey M, Pilcher D. Risk prediction of hospital mortality for adult patients admitted to Australian and New Zealand intensive care units: development and validation of the Australian and New Zealand risk of death model. J Crit Care. 2013;28(6):935–41. https://doi.org/10.1016/j.jcrc.2013.07.058.CrossRefPubMed

32.

Moran JL, Solomon PJ. (ANZICS) ftACfOaRECotAaNZICS: fixed effects modelling for provider mortality outcomes: analysis of the Australia and New Zealand intensive care society (ANZICS) adult patient data-base. PLoS One. 2014;9:e102297. https://doi.org/10.1371/journal.pone.0102297.CrossRefPubMedPubMedCentral

33.

Gelman A, Hill J. Data analysis using regression and Multilelvel/ hierarchal models. New York: Cambridge University Press; 2007.

34.

Rabe-Hesketh S, Skrondal A. Random intercept models with covariates. In: Multilevel and longitudinal modeling using Stata volume 1: continuous responses. 3rd ed. College Station, TX: Stata Press; 2012. p. 123–71.

35.

Allison PD, Williams RA, Hippel V: Better Predicted Probabilities from Linear Probability Models. Available @ https://wwwstatacom/meeting/us20/slides/us20_Allisonpdf; downloaded 15th September 2020 2020.

36.

Haggstrom GW. Logistic regression and discriminant analysis by ordinary least squares. J Bus Econ Stat. 1983;1(3):229–38.

37.

Allison PD: Better Predicted Probabilities from Linear Probability Models. Available @https://statisticalhorizonscom/better-predicted-probabilities; Downloaded 7th November 2020 2020.

38.

von Hippel P, Williams R, Allison P: reg2logit -- Approximate logistic regression parameters using OLS linear regression. Avaiable @ https://econpapersrepecorg/software/bocbocode/S458865htm; Downloaded 7th November 2020 2020.

39.

Cox NJ, Steichen T: CONCORD: Stata module for concordance correlation. Statistical Software Components S404501, Boston College Department of Economics; Version 310, revised 10 Nov 2010.

40.

Paul P, Pennell ML, Lemeshow S. Standardizing the power of the Hosmer-Lemeshow goodness of fit test in large data sets. Stat Med. 2013;32(1):67–80. https://doi.org/10.1002/sim.5525.CrossRefPubMed

41.

Nattino G, Lemeshow S, Phillips G, Finazzi S, Bertolini G. Assessing the calibration of dichotomous outcome models with the calibration belt. Stata J. 2017;17(4):1003–14. https://doi.org/10.1177/1536867X1801700414.CrossRef

42.

Bilger M: overfit: module to calculate shrinkage statistics to measure overfitting as well as out- and in-sample predictive bias. @ http://econpapersrepecorg/scripts/searchpf?ft=overfit; Downloaded 1st March 2016.

43.

Esnor J, Snell KI, Martins EC: ovefit: Stata module to produce calibration plot of prediction model performance. Statistical Software Components S458486, Boston College Department of Economics; revised 04 January 2020. 2020.

44.

Steyerberg EW, Vergouwe Y. Towards better clinical prediction models: seven steps for development and an ABCD for validation. Eur Heart J. 2014;35(29):1925–31. https://doi.org/10.1093/eurheartj/ehu207.CrossRefPubMedPubMedCentral

45.

Gelman A, Hill J. Logistic Regression. In: Data analysis using Regression and Multilelvel/ Hierarchal Models. New York: Cambridge University Press; 2007. p. 79–108.

46.

Kasza J. Stata tip 125: binned residual plots for assessing the fit of regression models for binary outcomes. Stata J. 2015;15(2):599–604. https://doi.org/10.1177/1536867X1501500219.CrossRef

47.

Kuha J. AIC and BIC: comparisons of assumptions and performance. Sociol Methods Res. 2004;33(2):188–229. https://doi.org/10.1177/0049124103262065.CrossRef

48.

Breen R, Karlson KB, Holm A. Interpreting and Understanding Logits, Probits, and Other Nonlinear Probability Models. In: Cook KS, Massey DS, editors. Annual Review of Sociology, vol. 44; 2018. p. 39–54.

49.

Chatla SB, Shmueli G. An Extensive Examination of Regression Models with a Binary Outcome Variable. J Assoc Inf Syst. 2017;18(4):1.

50.

Horowitz JL, Savin NE. Binary response models: Logits, Probits and Semiparametrics. J Econ Perspect. 2001;15(4):43–56. https://doi.org/10.1257/jep.15.4.43.CrossRef

51.

Long JS, Freese J. Methods of interpretation. In: Regression Models for Categorical Dependent Variables using Stata. College Station: Stata Press; 2014. p. 133–84.

52.

Karlson KB. Another look at the method of Y-standardization in Logit and Probit models. J Math Sociol. 2015;39(1):29–38. https://doi.org/10.1080/0022250X.2014.897950.CrossRef

53.

Hintze JL, Nelson RD. Violin plots: a box plot-density trace synergism. Am Stat. 1998;52(2):181–4.

54.

Winter N, Nichols A: VIOPLOT: Stata module to produce violin plots. @ http://econpapersrepec.org/scripts/search/searchasp?ft=vioplot2010, Accessed June 2010.

55.

Williams R. Using the margins command to estimate and interpret adjusted predictions and marginal effects. Stata J. 2012;12(2):308–31. https://doi.org/10.1177/1536867X1201200209.CrossRef

56.

Mood C. Logistic regression: why we cannot do what we think we can do, and what we can do about it. Eur Sociol Rev. 2010;26(1):67–82. https://doi.org/10.1093/esr/jcp006.CrossRef

57.

Wolfe R, Hanley J. If we’re so different, why do we keep overlapping? When 1 plus 1 doesn't make 2. Can Med Assoc J. 2002;166(1):65–6.

58.

Long JS, Freese J. Models for binary outcomes: Interpretation. In: Regression Models for Categorical Dependent Variables using Stata. College Station: Stata Press; 2014. p. 227–308.

59.

Leeper TJ, Arnold J, Arel-Bundock V: margins: Marginal Effects for Model Objects: version 0.3.23. Available @ https://cranr-projectorg/web/packages/margins/indexhtml 2018.

60.

Roberts MR, Whited TM: Endogeneity in Empirical Corporate Finance. Soimon School Working Paper No FR11–29; Available at SSRN: https://ssrncom/abstract=1748604 2012.

61.

Abdallah W, Goergen M, O'Sullivan N. Endogeneity: how failure to correct for it can cause wrong inferences and some remedies. Br J Manag. 2015;26(4):791–804. https://doi.org/10.1111/1467-8551.12113.CrossRef

62.

Cameron AC, Trivedi PK. Endoegenous regressors. In: Microeconometircs in Stata: Revise Edition. edn. Clloege Station: Stata Press; 2010. p. 479–86.

63.

Koné S, Bonfoh B, Dao D, Koné I, Fink G. Heckman-type selection models to obtain unbiased estimates with missing measures outcome: theoretical considerations and an application to missing birth weight data. BMC Med Res Methodol. 2019;19(1):231. https://doi.org/10.1186/s12874-019-0840-7.CrossRefPubMedPubMedCentral

64.

Odgaard-Jensen J, Vist GE, Timmer A, Kunz R, Akl EA, Schünemann H, et al. Randomisation to protect against selection bias in healthcare trials. Cochrane Database Syst Rev. 2011;4:MR000012.

65.

Shadish WR, Clark MH, Steiner PM. Can nonrandomized experiments yield accurate answers? A randomized experiment comparing random and nonrandom assignments. J Am Stat Assoc. 2008;103(484):1334–43. https://doi.org/10.1198/016214508000000733.CrossRef

66.

Hernán MA, Hernández-Díaz S, Robins JM. A structural approach to selection bias. Epidemiology. 2004;15(5):615–25. https://doi.org/10.1097/01.ede.0000135174.63482.43.CrossRefPubMed

67.

StataCorp CST: Stata extended regression models reference manual release 16. Available @ https://wwwstatacom/manuals/ermpdf; Accessed 19th September 2020.

68.

Lousdal ML. An introduction to instrumental variable assumptions, validation and estimation. Emerg Themes Epidemiol. 2018;15(1):1. https://doi.org/10.1186/s12982-018-0069-7.CrossRefPubMedPubMedCentral

69.

Martens EP, Pestman WR, Klungel OH. Conditioning on the propensity score can result in biased estimation of common measures of treatment effect: A Monte Carlo study (p n/a) by Peter C. Austin, Paul Grootendorst, Sharon-Lise T. Normand, Geoffrey M. Anderson, Statistics in Medicine, Published Online: 16 June 2006. Stat Med. 2007;26(16):3208–10. https://doi.org/10.1002/sim.2618.CrossRefPubMed

70.

Mennemeyer ST. Can econometrics rescue epidemiology? Ann Epidemiol. 1997;7(4):249–50. https://doi.org/10.1016/S1047-2797(97)00021-5.CrossRefPubMed

71.

Freedman DA. On the so-called “Huber Sandwich estimator” and “robust standard errors”. Am Stat. 2006;60(4):299–302. https://doi.org/10.1198/000313006X152207.CrossRef

72.

Dahlqwist E, Kutalik Z, Sjölander A. Using instrumental variables to estimate the attributable fraction. Stat Methods Med Res. 2019;29(8):2063–73. https://doi.org/10.1177/0962280219879175.CrossRefPubMed

73.

StataCorp: margins. Marginal means, predictive margins, and marginal effects. Available @ https://wwwstatacom/manuals13/rmarginspdf 2019.

74.

ANZICS CORE - Adult patient database: APD data dictionary: version 5.10, March 2020. Available @ https://wwwanzicscomau/adult-patient-database-apd/; downloaded 7th September 2020.

75.

Wynants L, Vergouwe Y, Van Huffel S, Timmerman D, Van Calster B. Does ignoring clustering in multicenter data influence the performance of prediction models? A simulation study. Stat Methods Med Res. 2018;27(6):1723–36. https://doi.org/10.1177/0962280216668555.CrossRefPubMed

76.

Vach W. Specific Regression Models. In: Regression models as a Tool in Medical research. edn. Boca Raton: CRC Press; 2013. p. 407–8.

77.

Cameron AC, Trivedi PK. Comparioson of binary models and parameter estimates. In: Microeconometircs in Stata: Revise Edition. edn. Clloege Station: Stata Press; 2010. p. 465–6.

78.

Davies HT, Crombie IK, Tavakoli M. When can odds ratios mislead? BMJ. 1998;316(7136):989–91. https://doi.org/10.1136/bmj.316.7136.989.CrossRefPubMedPubMedCentral

79.

Feng C, Wang B, Wang H. The relations among three popular indices of risks. Stat Med. 2019;38(23):4772–87. https://doi.org/10.1002/sim.8330.CrossRefPubMed

80.

Allison PD. Comparing logit and probit coefficients across groups. Sociol Methods Res. 1999;28(2):186–208. https://doi.org/10.1177/0049124199028002003.CrossRef

81.

Kuha J, Mills C. On group comparisons with logistic regression models. Sociol Methods Res. 2020;49(2):498–525. https://doi.org/10.1177/0049124117747306.CrossRef

82.

Burgess S. Estimating and contextualizing the attenuation of odds ratios due to non collapsibility. Commun Stat Theory Methods. 2017;46(2):786–804. https://doi.org/10.1080/03610926.2015.1006778.CrossRef

83.

Cameron AC, Trivedi PK. Nonlinear regression methods. In: Microeconometircs in Stata: Revise Edition. edn. Clloege Station: Stata Press; 2010. p. 341–54.

84.

Angrist JD, Pischke JS. Making regression make sense. In: Mostly harmless econometrics: An empiricist's companion. edn. Princeton: Princeton University Press; 2008. p. 27–110.CrossRef

85.

Moran JL, Santamaria J. Reconsidering lactate as a sepsis risk biomarker. PLoS One. 2017;12(10):e0185320. https://doi.org/10.1371/journal.pone.0185320.CrossRefPubMedPubMedCentral

86.

van Calster B, McLernon DJ, van Smeden M, Wynants L, Steyerberg EW. Initiative S: Calibration: the Achilles heel of predictive analytics. BMC Med. 2019;17:1.CrossRef

87.

Shah ND, Steyerberg EW, Kent DM. Big data and predictive analytics: recalibrating expectations. JAMA. 2018;320(1):27–8. https://doi.org/10.1001/jama.2018.5602.CrossRefPubMed

88.

Cortese G. How to use statistical models and methods for clinical prediction. Ann Transl Med. 2020;8:4.CrossRef

89.

Neyman J, Scott EL. Consistent estimates based on partially consistent observations. Econometrica. 1948;16(1):1–32. https://doi.org/10.2307/1914288.CrossRef

90.

Greene WH: Estimating Econometric Models With Fixed Effects. 2001 @ http://www.sternnyu.edu/eco/wkpapers/workingpapers01/01-10Greene.doc. , Accessed 13 Oct 2010.

91.

Greene W. The behaviour of the maximum likelihood estimator of limited dependent variable models in the presence of fixed effects. Econ J. 2004;7(1):98–119. https://doi.org/10.1111/j.1368-423X.2004.00123.x.CrossRef

92.

Moran JL, Solomon PJ. (ANZICS) ftACfOaRECotAaNZICS: fixed effects Modelling for provider mortality outcomes: analysis of the Australia and new Zealand Intensive Care Society (ANZICS) adult patient Data-Base. PLoS One. 2014;9(7):e102297. https://doi.org/10.1371/journal.pone.0102297.CrossRefPubMedPubMedCentral

93.

Mroz TA, Zayats YV. Arbitrarily normalized coefficients, information sets, and false reports of biases in binary outcome models. Rev Econ Stat. 2008;90(3):406–13. https://doi.org/10.1162/rest.90.3.406.CrossRef

94.

Timoneda JC. Estimating group fixed effects in panel data with a binary dependent variable: how the LPM outperforms logistic regression in rare events data. Soc Sci Res. 2021;93:102486. https://doi.org/10.1016/j.ssresearch.2020.102486.CrossRefPubMed

95.

Shmueli G. To explain or to predict? Stat Sci. 2010;25(3):289–310.CrossRef

96.

Chen Y, Senturk D, Estes JP, Campos LF, Rhee CM, Dalrymple LS, et al. Performance characteristics of profiling methods and the impact of inadequate case-mix adjustment. Commun Stat Simul Comput. 2019;2019:1.

97.

Kalbfleisch J, Wolfe R. On monitoring outcomes of medical providers. Stat Biosci. 2013;5(2):286–302. https://doi.org/10.1007/s12561-013-9093-x.CrossRef

98.

Roessler M, Schmitt J, Schoffer O. Ranking hospitals when performance and risk factors are correlated: A simulation-based comparison of risk adjustment approaches for binary outcomes. PLoS One. 2019;14:12.CrossRef

99.

Schunck R, Perales F. Within- and between-cluster effects in generalized linear mixed models: a discussion of approaches and the xthybrid command. Stata J. 2017;17(1):89–115. https://doi.org/10.1177/1536867X1701700106.CrossRef

100.

Danks L, Duckett SJ: All complications should count: Using our data to make hospitals safer (Methodological supplement). Available @ https://grattaneduau/wp-content/uploads/2018/02/897-All-complications-should-count-methodological-supplementpdf; Downloaded 19th February 2021 2018.

101.

Snijders TAB, Bosker RJ. Discrete Dependent Variables. In: Multilevel Ahalysis: an introduction to basic and advanced multilevel modeling. 2nd ed. London: Sage Publications Inc; 2012. p. 289–320.

102.

Neuburger J, Cromwell DA, Hutchings A, Black N, van der Meulen JH. Funnel plots for comparing provider performance based on patient-reported outcome measures. BMJ Qual Saf. 2011;20(12):1020–6. https://doi.org/10.1136/bmjqs-2011-000197.CrossRefPubMed

103.

Mogstad M, Romano JP, Shaikh AM, Wilhelm D: Inference on Ranks with Applications to Mobility Across Neighborhoods and Academic Achievement Across Countries. Available @ https://bfiuchicagoedu/wp-content/uploads/BFI_WP_202016pdf; Downloaded 16th Feb 2021 2020.

104.

Uanhoro JO, Wang Y, Oconnell AA. Problems With Using Odds Ratios as Effect Sizes in Binary Logistic Regression and Alternative Approaches. J Exp Educ. 2019;1:1.CrossRef

105.

Huang FL. Alternatives to logistic regression models in experimental studies. J Exp Educ. 2019:1–16. https://doi.org/10.1080/00220973.2019.1699769.

106.

Holm A, Ejrnæs M, Karlson K. Comparing linear probability model coefficients across groups. Qual Quant. 2015;49(5):1823–34. https://doi.org/10.1007/s11135-014-0057-0.CrossRef

107.

Truett J, Cornfield J, Kannel W. A multivariate analysis of the risk of coronary heart disease in Framingham. J Chronic Dis. 1967;20(7):511–24. https://doi.org/10.1016/0021-9681(67)90082-3.CrossRefPubMed

108.

Press SJ, Wilson S. Choosing between logistic regression and discriminant analysis. J Am Stat Assoc. 1978;73(364):699–705. https://doi.org/10.1080/01621459.1978.10480080.CrossRef

109.

Allison PD: Convergence Failures in Logistic Regression. Available @http://wwwpeoplevcuedu/~dbandyop/BIOS625/Convergence_Logisticpdf; downloaded 7 Nov 2020 2008.

110.

Mansournia MA, Geroldinger A, Greenland S, Heinze G. Separation in logistic regression: causes, consequences, and control. Am J Epidemiol. 2018;187(4):864–70. https://doi.org/10.1093/aje/kwx299.CrossRefPubMed

111.

Šinkovec H, Geroldinger A, Heinze G. Bring more data!-a good advice? Removing separation in logistic regression by increasing sample size. Int J Environ Res Public Health. 2019;16(23):4658. https://doi.org/10.3390/ijerph16234658.CrossRefPubMedCentral

112.

Beck N. Estimating grouped data models with a binary-dependent variable and fixed effects via a Logit versus a linear probability model: the impact of dropped units. Polit Anal. 2020;28(1):139–45. https://doi.org/10.1017/pan.2019.20.CrossRef

113.

Crisman-Cox C. Estimating substantive effects in binary outcome panel models: a comparison. J Polit. Vol. 0 Issue 0 Pages 000-000. https://doi.org/10.1086/709839.

114.

Cook SJ, Hays JC, Franzese RJ. Fixed effects in rare events data: a penalized maximum likelihood solution. Polit Sci Res Methods. 2020;8(1):92–105. https://doi.org/10.1017/psrm.2018.40.CrossRef

115.

Greenland S, Mansournia MA, Altman DG. Sparse data bias: a problem hiding in plain sight. BMJ. 2016;352:i1981.CrossRefPubMed

116.

Liu X, Chen W, Chen T, Zhang H, Zhang B. Marginal effects and incremental effects in two-part models for endogenous healthcare utilization in health services research. Health Serv Outcome Res Methodol. 2020;20(2–3):111–39. https://doi.org/10.1007/s10742-020-00211-x.CrossRef

117.

Zohoori N, Savitz DA. Econometric approaches to epidemiologic data: relating endogeneity and unobserved heterogeneity to confounding. Ann Epidemiol. 1997;7(4):251–7. https://doi.org/10.1016/S1047-2797(97)00023-9.CrossRefPubMed

118.

Berg GD, Mansley EC. Endogeneity bias in the absence of unobserved heterogeneity. Ann Epidemiol. 2004;14(8):561–5. https://doi.org/10.1016/j.annepidem.2003.09.020.CrossRefPubMed

119.

Leisman DE. Ten pearls and pitfalls of propensity scores in critical care research: a guide for clinicians and researchers. Crit Care Med. 2019;47(2):176–85. https://doi.org/10.1097/CCM.0000000000003567.CrossRefPubMed

120.

Leisman DE. The goldilocks effect in the ICU-when the data speak, but not the truth. Crit Care Med. 2020;48(12):1887–9. https://doi.org/10.1097/CCM.0000000000004669.CrossRefPubMed

121.

de Grooth H-J, Girbes ARJ, van der Ven F, Oudemans-van Straaten HM, Tuinman PR, de Man AME. Observational research for therapies titrated to effect and associated with severity of illness: misleading results from commonly used statistical methods*. Crit Care Med. 2020;48(12):1720–8. https://doi.org/10.1097/CCM.0000000000004612.CrossRefPubMed

122.

Zohoori N. Does endogeneity matter? A comparison of empirical analyses with and without control for endogeneity. Ann Epidemiol. 1997;7(4):258–66. https://doi.org/10.1016/S1047-2797(97)00022-7.CrossRefPubMed

123.

Duke GJ, Moran JL, Santamaria JD, Roodenburg O. Safety of the endotracheal tube for prolonged mechanical ventilation. J Crit Care. 2021;61:144–51. https://doi.org/10.1016/j.jcrc.2020.10.018.CrossRefPubMed

124.

Kim S-H, Chan CW, Olivares M, Escobar G. ICU admission control: an empirical study of capacity allocation and its implication for patient outcomes. Manag Sci. 2015;61(1):19–38. https://doi.org/10.1287/mnsc.2014.2057.CrossRef

125.

Martens EP, Pestman WR, de Boer A, Belitser SV, Klungel OH. Instrumental variables application and limitations. Epidemiology. 2006;17(3):260–7. https://doi.org/10.1097/01.ede.0000215160.88317.cb.CrossRefPubMed

126.

Qin D. Resurgence of the Endogeneity-backed instrumental variable methods. Econ Open Access Open Assess E-J. 2015;9:1.

127.

Angrist JD, Pischke JS. Mostly harmless econometrics: an empiricist’s companion. Princeton: Princeton University Press; 2008. https://doi.org/10.2307/j.ctvcm4j72.CrossRef

128.

Foster EM. Instrumental variables for logistic regression: an illustration. Soc Sci Res. 1997;26(4):487–504. https://doi.org/10.1006/ssre.1997.0606.CrossRef

129.

Terza JV, Basu A, Rathouz PJ. Two-stage residual inclusion estimation: addressing endogeneity in health econometric modeling. J Health Econ. 2008;27(3):531–43. https://doi.org/10.1016/j.jhealeco.2007.09.009.CrossRefPubMed

130.

Koladjo BF, Escolano S, Tubert-Bitter P. Instrumental variable analysis in the context of dichotomous outcome and exposure with a numerical experiment in pharmacoepidemiology. BMC Med Res Methodol. 2018;18(1):61. https://doi.org/10.1186/s12874-018-0513-y.CrossRefPubMedPubMedCentral

131.

Burgess S, Small DS, Thompson SG. A review of instrumental variable estimators for Mendelian randomization. Stat Methods Med Res. 2017;26(5):2333–55. https://doi.org/10.1177/0962280215597579.CrossRefPubMed

132.

Burgess S, Collaboration CCG. Identifying the odds ratio estimated by a two-stage instrumental variable analysis with a logistic regression model. Stat Med. 2013;32(27):4726–47. https://doi.org/10.1002/sim.5871.CrossRefPubMedPubMedCentral

133.

Fan Q, Zhong W. Nonparametric additive instrumental variable estimator: a group shrinkage estimation perspective. J Bus Econ Stat. 2018;36(3):388–99. https://doi.org/10.1080/07350015.2016.1180991.CrossRef

134.

Sjolander A, Martinussen T. Instrumental variable estimation with the R package ivtools. Epidemiol Methods. 2019;8(1):20180024. https://doi.org/10.1515/em-2018-0024.CrossRef

Title: Modelling hospital outcome: problems with endogeneity
Authors: John L. Moran
John D. Santamaria
Graeme J. Duke
The Australian & New Zealand Intensive Care Society (ANZICS) Centre for Outcomes & Resource Evaluation (CORE)
Publication date: 01-12-2021
Publisher: BioMed Central
Published in: BMC Medical Research Methodology / Issue 1/2021
Electronic ISSN: 1471-2288
DOI: https://doi.org/10.1186/s12874-021-01251-8

Keynote webinar | Spotlight on medication adherence

Springer Medicine

Modelling hospital outcome: problems with endogeneity

Abstract

Background

Methods

Results

Conclusions

Keynote webinar | Spotlight on medication adherence

Springer Medicine

Abstract

Background

Methods

Results

Conclusions

Please log in to get access to this content

Other articles of this Issue 1/2021

Recruitment principles and strategies for supportive care research in pediatric oncology

Effects of personalized invitation letters on research participation among general practitioners: a randomized trial

Psychometric properties of instruments to measure parenting practices and children’s movement behaviors in low-income families from Brazil

Group testing can improve the cost-efficiency of prospective-retrospective biomarker studies

Quantifying the under-reporting of uncorrelated longitudal data: the genital warts example

Can the adverse childhood experiences (ACEs) checklist be utilized to predict emergency department visits among children and adolescents?