An Empirical Method of Detecting Time-Dependent Confounding: An Observational Study of Next Day Delirium in a Medical ICU


  • T. E. Murphy Yale Program on Aging, Yale School of Medicine, New Haven, CT, USA
  • P.H. Van Ness Yale Program on Aging, Yale School of Medicine, New Haven, CT, USA
  • K.L.B. Araujo Yale Program on Aging, Yale School of Medicine, New Haven, CT, USA
  • M.A. Pisani Section of Pulmonary, Critical Care and Sleep Medicine, Yale School of Medicine, New Haven, CT, USA



Time dependent confounding, cross-correlation, longitudinal, marginal structural model, ICU.


Longitudinal research on older persons in the medical intensive care unit (MICU) is often complicated by the time-dependent confounding of concurrently administered interventions such as medications and intubation. Such temporal confounding can bias the respective longitudinal associations between concurrently administered treatments and a longitudinal outcome such as delirium. Although marginal structural models address time-dependent confounding, their application is non-trivial and preferably justified by empirical evidence. Using data from a longitudinal study of older persons in the MICU, we constructed a plausibility score from 0 – 10 where higher values indicate higher plausibility of time-dependent confounding of the association between a time-varying explanatory variable and an outcome. Based on longitudinal plots, measures of correlation, and longitudinal regression, the plausibility scores were compared to the differences in estimates obtained with non-weighted and marginal structural models of next day delirium. The plausibility scores of the three possible pairings of daily doses of fentanyl, haloperidol, and intubation indicated the following: low plausibility for haloperidol and intubation, moderate plausibility for fentanyl and haloperidol, and high plausibility for fentanyl and intubation. Comparing multivariable models of next day delirium with and without adjustment for time-dependent confounding, only intubation’s association changed substantively. In our observational study of older persons in the MICU, the plausibility scores were generally reflective of the observed differences between coefficients estimated from non-weighted and marginal structural models.


Ely EW, Gautam S, Margolin R, Francis J, May L, Speroff T, et al. The impact of delirium in the intensive care unit on hospital length of stay. Intensive Care Medicine 2001; 27(12): 1892-900. DOI:

Ely EW, Shintani A, Truman B, Speroff T, Gordon SM, Harrell FE, Jr., et al. Delirium as a predictor of mortality in mechanically ventilated patients in the intensive care unit. JAMA: the journal of the American Medical Association 2004; 291(14): 1753-62. DOI:

Murphy TE, Van Ness PH, Araujo KL, Pisani MA. Bayesian time-series analysis of arepeated-measures Poisson outcome with excess zeroes. American Journal of Epidemiology 2011; 174(11): 1230-7. DOI:

Pisani MA, Inouye SK, McNicoll L, Redlich CA. Screening for pre-existing cognitive impairment in older intensive care unit patients: use of proxy assessment. Journal of the American Geriatrics Society 2003; 51: 689-93. DOI:

Pisani MA, Murphy TE, Van Ness PH, Araujo KLB, Inouye SK. Characteristics associated with delirium in older patients in a medical intensive care unit. Archives of Internal Medicine 2007; 167(15): 1629-34. DOI:

Milbrandt EB, Deppen S, Harrison PL, Shintani AK, Speroff T, Stiles RA, et al. Costs associated with delirium in mechanically ventilated patients. Critical Care Medicine 2004; 32(4): 955-62. DOI:

Ouimet S, Kavanagh BP, Gottfried SB, Skrobik Y. Incidence, risk factors and consequences of ICU delirium. Intensive Care Medicine 2007; 33(1): 66-73. DOI:

Kalisvaart KJ, de Jonghe JF, Bogaards MJ, Vreeswijk R, Egberts TC, Burger BJ, et al. Haloperidol prophylaxis for elderly hip-surgery patients at risk for delirium: a randomized placebo-controlled study. Journal of the American Geriatrics Society 2005; 53(10): 1658-66. DOI:

Pandharipande P, Shintani A, Peterson J, Pun BT, Wilkinson GR, Dittus RS, et al. Lorazepam is an independent risk factor for transitioning to delirium in intensive care unit patients. Anesthesiology 2006; 104(1): 21-6. DOI:

Patel SB, Poston JT, Pohlman A, Hall JB, Kress JP. Rapidly reversible, sedation-related delirium versus persistent delirium in the intensive care unit. American Journal of Respiratory and Critical Care Medicine 2014; 189(6): 658-65. DOI:

Pisani MA, Kong SYJ, Kasl SV, Murphy TE, Araujo KLB, Van Ness PH. Days of delirium are associated with 1-year mortality in an older intensive care unit population. Am J Respir Crit Care Med 2009; 180: 1092-7. DOI:

Pisani MA, Murphy TE, Araujo KLB, Slattum P, Van Ness PH, Inouye SK. Benzodiazepine and opioid use and the duration of intensive care unit delirium in an older population. Critical Care Medicine 2009; 37: 177-83. DOI:

Robins JM. Marginal structural models. Proceedings of the Section on Bayesian Statistical Science 1997: 1-10.<269::AID-SIM763>3.0.CO;2-J

Robins JM. Correction for non-compliance in equivalence trials. Statistics in Medicine 1998; 17: 269-302. DOI:<269::AID-SIM763>3.0.CO;2-J

Robins JM. Marginal structural models versus nested models as tools for causal inference. . In: Halloran E, Berry D, editors. Statistical Models in Epidemiology: The Environment and Clinical Trials. New York: Springer-Verlag 1999; p. 95-134. DOI:

Robins JM, Hernan MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology 2000; 11(5): 550-60. DOI:

Pisani MA, Redlich CA, McNicoll L, Ely EW, Inouye SK. Underrecognition of preexisting cognitive impairment by physicians in older icu patients. Chest 2003; 124: 2267-74. DOI:

Pisani MA, Bramley K, Vest MT, Akgun KM, Araujo KL, Murphy TE. Patterns of opiate, benzodiazepine, and antipsychotic drug dosing in older patients in a medical intensive care unit. American journal of critical care: an official publication, American Association of Critical-Care Nurses 2013; 22(5): e62-9. DOI:

Pisani MA, Araujo KL, Murphy TE. Association of cumulative dose of haloperidol with next-day delirium in older medical ICU patients. Critical Care Medicine 2015; 43(5): 996-1002. DOI:

Baker JA, Lovell K, Harris N. A best-evidence synthesis review of the administration of psychotropic pro re nata (PRN) medication in in-patient mental health settings. Journal of Clinical Nursing 2008; 17: 1122-31. DOI:

SAS. SAS User's Manual. 9.2 ed. Cary, NC: SAS Institute; 2009. p. Windows Based Software.

Hernan MA, Brumback B, Robins JM. Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology 2000; 11(5): 561-70. DOI:




How to Cite

Murphy, T. E., Ness, P. V., Araujo, K., & Pisani, M. (2016). An Empirical Method of Detecting Time-Dependent Confounding: An Observational Study of Next Day Delirium in a Medical ICU. International Journal of Statistics in Medical Research, 5(1), 41–47.



Special Issue - Methods for Estimating Treatment Effects of Persons with Multiple Chronic Conditions