Table 2.

 Effect estimates for association between delirium and mortality in intensive care unit using various statistical approaches

Variables	Logistic regression	Competing risks survival regression	Marginal structural model
Adjustment factors:
Baseline covariables	Yes	Yes	Yes
Time varying onset of delirium	No	Yes	Yes
Competing risks of death and discharge	No	Yes	Yes
Evolution of disease before delirium onset*	No	No	Yes
Effect estimate†‡:
Crude	2.60 (1.76 to 3.85)	3.14 (2.32 to 5.04)	3.14 (2.32 to 5.04)§¶
Adjusted**	1.77 (1.15 to 2.72)	2.08 (1.40 to 3.09)	1.19 (0.75 to 1.89)††‡‡

*Logistic regression and survival analysis can also be used to correct for evolution of disease severity; however, over-adjustment and collider stratification bias might occur. The marginal structural model prevents these biases.¹⁹

†Logistic regression analysis gives an odds ratio, whereas survival analysis and marginal structural model provide a subdistribution hazard ratio.

‡Delirium was included as a time dependent variable in competing risks survival regression and marginal structural models.

§Crude subdistribution hazard ratio of marginal structural model was calculated assuming the weights to be equal to 1 and is therefore equal to estimation of competing risks survival analysis.

¶Adjusted cause specific hazard ratios of competing risks survival regression were 0.64 (95% confidence interval 0.39 to 1.03) for mortality and 0.53 (0.46 to 0.61) for discharge.

**Multivariable analysis was adjusted for baseline variables (age, sex, Charlson comorbidity index, acute physiology and chronic health evaluation IV score, admission type, and sepsis on admission). The marginal structural model was furthermore adjusted to time varying variables: sequential organ failure assessment score, sepsis status, temperature, sodium, urea concentration, acidosis, haematocrit, mechanical ventilation, and sedative and analgesic drugs.

††Adjusted cause specific hazard ratios of the marginal structural model analysis were 0.38 (95% confidence interval 0.22 to 0.65) for mortality and 0.65 (0.55 to 0.76) for discharge.

‡‡Inversed probability weight estimates were: mean 0.974 (range 0.127-8.51) and median 0.894 (interquartile range 0.731-1.072).