Table 1.

Overview of statistical methods and results while addressing vs. neglecting immortal time and confounding biases.

Model	Approach	Statistical analysis method for outcome models	Hazard ratio (HR, [95% CI])			Immortal-time bias		Baseline confounding bias
			In-hospital death	Discharge home	Transfer	Occurrence	Description	Occurrence	Description
1	Conventional	Univariable Cox regression model with treatment status incorrectly assigned at baseline	0.66 [0.47–0.93]	0.84 [0.59–1.21]	1.30 [0.86–1.94]	Yes	Ever-treated patients misclassified as treated from admission; never-treated as untreated	Yes	Baseline covariates not included in regression model
2	Conventional	Univariable, time-dependent Cox regression model with time-varying treatment status	0.79 [0.59–1.06]	0.91 [0.66–1.25]	1.38 [0.96–1.97]	No	Treated patients time classified to “untreated / “treated” periods using start-stop notation; pre-treatment time classified as “untreated”	Yes
3	Conventional	Multivariable, time-dependent Cox regression model with baseline covariates and time-varying treatment status	0.76 [0.58–1.00]	0.92 [0.68–1.24]	1.41 [1.01–1.99]	No		No	Baseline covariates included in regression model
4	Inverse probability treatment weighting	Weighted, time-dependent Cox regression model with weights as a covariate and time-varying treatment status	0.76 [0.52–1.08]	0.98 [0.67–1.42]	1.50 [1.00–2.24]	No		No	Baseline covariates included in inverse probability treatment weights via propensity scores
5	Target trial emulation with clone-censor-weight approach	Weighted cause-specific Cox regression with censoring weights as a covariate and treatment arm	0.68 [0.46–1.02]	1.22 [0.82–1.81]	1.26 [0.77–2.07]	No	Two clones: one in ‘X’-treated arm and one in non-‘X’-treated arm	No	Cloning results in balanced covariates between two arms at baseline, inverse probability censoring weights applied to correct for selection bias

HR, Hazard ratio; CI, Confidence interval.