A Causal Framework for Evaluating ICU Discharge Strategies

Sagar Nagaraj Simha; Juliette Ortholand; Dave Dongelmans; Jessica D. Workum; Olivier W. M. Thijssens; Ameen Abu-Hanna; Giovanni Cinà

stat.MEMar 26, 2026

A Causal Framework for Evaluating ICU Discharge Strategies

Authors: Sagar Nagaraj Simha, Juliette Ortholand, Dave Dongelmans, Jessica D. Workum, Olivier W. M. Thijssens, Ameen Abu-Hanna, Giovanni Cinà

Organizations: Department of Medical Informatics, Amsterdam UMC, University of Amsterdam, NL · Department of Intensive Care Medicine, Amsterdam UMC, University of Amsterdam, NL · Department of Intensive Care, Elisabeth-TweeSteden Hospital, Tilburg, NL · Department of Intensive Care, Erasmus MC, Rotterdam, NL · Pacmed, Amsterdam, NL · Institute of Logic, Language and Computation, University of Amsterdam, NL

Abstract

In this applied paper, we address the difficult open problem of when to discharge patients from the Intensive Care Unit. This can be conceived as an optimal stopping scenario with three added challenges: 1) the evaluation of a stopping strategy from observational data is itself a complex causal inference problem, 2) the composite objective is to minimize the length of intervention and maximize the outcome, but the two cannot be collapsed to a single dimension, and 3) the recording of variables stops when the intervention is discontinued. Our contributions are two-fold. First, we generalize the implementation of the g-formula Python package, providing a framework to evaluate stopping strategies for problems with the aforementioned structure, including positivity and coverage checks. Second, with a fully open-source pipeline, we apply this approach to MIMIC-IV, a public ICU dataset, demonstrating the potential for strategies that improve upon current care.

Figures & tables

Figure 1: The ICU discharge trade-off represented in the space of potential outcomes for our multi-objective stopping problem. Given a fixed dataset, each strategy returns an average 90-day mortality on the y-axis as well as an average length of ICU stay on the x-axis. The red box defines the set of strategies that constitute an improvement over current clinical practice, i.e. strategies leading to lower mortality and lower utilization of ICU beds. The blue dashed area defines the set of strategies we are actually able to evaluate given the available data.

Component	Clinical decision rule (12-hour grid)
Respiratory failure	Invasive controlled ventilation; OR SpO 2 $<85\%$ ; OR O 2 flow $>85$ ; OR (ventilation mode unknown AND [SpO 2 $<85\%$ OR O 2 flow $>85$ OR PaCO 2 $>80$ OR respiratory rate $>45$ /min]).
Hemodynamic instability	Mean arterial pressure $<50$ mmHg; OR lactate $>6$ mmol/L; OR heart rate $>160$ /min.
Neurologic failure	Glasgow Coma Scale $<6$ .
Severe metabolic derangement	Arterial bicarbonate $<10$ mmol/L.

Table 1: Dynamic discharge strategy (DS1) based on physiologic need for organ support: ICU care is continued if any of the red flags above are present, otherwise patients are discharged.

Figure 2: Positivity and coverage diagnostics over time for all evaluated dynamic strategies separated between patients kept and discharged. Top: coverage rate (fraction of history-compatible observations at epoch

t

for which the clinician’s action matches the target strategy’s prescription). Bottom: absolute match count (fraction of history-compatible observations at epoch

t

for which the clinician’s action matches the target strategy’s prescription and the decision at time

t

	All-cause mortality (%)			Difference to		Mortality split (%)		Length of ICU stay (days)
Intervention	Observed	G-formula estimate		natural course (%)		In ICU	After discharge	Median (IQR)		Mean
Natural course	20.08	19.1	(18.4, 21.5)	–	–	6.2	12.9	2.00	(1.00–4.00)	3.44
Discharge 3rd day	–	17.4	(16.7, 20.1)	-1.8	(-3.3, 0.5)	5.2	12.2	3	(3–3)	3
Strategy DS1	–	18.0	(15.8, 18.9)	-1.2	(-4.4, -0.6)	3.6	14.4	0.5	(0.5–1.0)	1.76
Strategy [ Knight, 2003 ]	–	86.0	(83.4, 89.4)	+66.9	(63.5, 69.5)	85.5	0.5	35.0	(15.5–62.5)	40.56

Table 2: Estimated 90-day all-cause mortality (in-ICU or post-discharge death) under dynamic and static discharge strategies using the parametric g-formula (NICE estimator). Mean and 95% confidence intervals are shown. Follow-up corresponds to 180 half-day intervals (90 days).

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Variable name	Summary over last 12h	Distribution
Ventilation mode	last status	categorical
Hours since last recorded vent mode	last value	zero-inflated normal
Arterial pco2	mean	truncated normal
Arterial po2	mean	bounded normal
Oxygen flow	last value	bounded normal
O2 saturation	mean	bounded normal

Appendix

Table 3: Clinical variables with their 12-hour aggregation type and distribution

Test name	Variable	Test condition
Respiratory: airway	airway	airway patent
Respiratory: FiO 2	fio2	fio2 $\leq$ 0.6
Respiratory: blood oxygen	spo2	spo2 $\geq$ 95 (%)
Respiratory: bicarbonate	hco3	hco3 $\geq$ 19 (mmol/L)
Respiratory: rate	resp (rate)	10 $\leq$ resp $\leq$ 30 (bpm)
Cardiovascular: blood pressure	bp (systolic)	bp $\geq$ 100 (mm Hg)

Appendix

Table 4: Codified discharge criteria applied to electronic health record data. All criteria must be satisfied prior to ICU discharge.

Figure 3: Positivity diagnostics over time for all evaluated strategies. Top: coverage rate

\rho_{t}

(fraction of history-compatible observations at epoch

t

for which the clinician’s action matches the target strategy’s prescription). Middle: effective sample size ratio

\mathrm{ESS}_{t}/N_{t}

among matching observations (IS weight evenness; 1 = uniform,

1/N_{t}

= fully concentrated). Bottom: absolute match count

N_{t}

. The red dashed line in the top and middle panels marks the 0.3 warning threshold.

Figure 4: PCA positivity scatter plots for the three static threshold strategy at 3 days, across decision epochs $t\in\{12,24,\ldots,120\}$ h (columns). Each panel projects the first two PCA components of the covariate space. Rows 1 & 3 : blue dots indicate patients for whom the strategy prescribes keep and the clinician kept; grey dots indicate patients for whom the strategy prescribes keep but the clinician discharged (positivity violation). Rows 2 & 4 : orange dots indicate agreement on discharge; grey dots indicate patients the strategy would discharge but clinicians retained (positivity violation). Panel titles report cohort size $n$ and coverage rate $\rho_{t}$ .

Panel of Figure 5 — Figure 5: PCA positivity scatter plots for the dynamic strategies (Natural course, Knight strategy, and DS1 strategy; top to bottom), across decision epochs $t\in\{12,24,\ldots,120\}$ h (columns). Layout and colour coding are identical to Figure 4 .

Figure 6: Time-indexed standardized mean differences comparing observed and simulated covariate evolution under the natural course.

Figure 7: Covariate distribution comparison under the natural course and MIMIC-IV data for In-ICU death. The close overlap across physiologic variables demonstrates that the natural course simulation reproduces the empirical covariate distributions at In-ICU death.

Figure 8: Covariate distribution comparison under the natural course and MIMIC-IV data. The close overlap across physiologic variables demonstrates that the natural course simulation reproduces the empirical covariate distributions at discharge.

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Abstract

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