Survivor-Complier Effects in the Presence of Selection on Treatment, With Application to a Study of Prompt ICU Admission

Abstract

Pre-treatment selection or censoring ('selection on treatment') can occur when two treatment levels are compared ignoring the third option of neither treatment, in 'censoring by death' settings where treatment is only defined for those who survive long enough to receive it, or in general in studies where the treatment is only defined for a subset of the population. Unfortunately, the standard instrumental variable (IV) estimand is not defined in the presence of such selection, so we consider estimating a new survivor-complier causal effect. Although this effect is generally not identified under standard IV assumptions, it is possible to construct sharp bounds. We derive these bounds and give a corresponding data-driven sensitivity analysis, along with nonparametric yet efficient estimation methods. Importantly, our approach allows for high-dimensional confounding adjustment, and valid inference even after employing machine learning. Incorporating covariates can tighten bounds dramatically, especially when they are strong predictors of the selection process. We apply the methods in a UK cohort study of critical care patients to examine the mortality effects of prompt admission to the intensive care unit, using ICU bed availability as an instrument.

Does Transfer to Intensive Care Units Reduce Mortality? A Comparison of an Instrumental Variables Design to Risk Adjustment

“…For patients admitted to the ICU, the median time to the ICU was 4 hours (IQR: 11) if there were 4 or fewer beds available, and the median time to the ICU was 3 hours (IQR: 8). See 21 for a study that uses the SPOTlight data to study whether timing to the ICU affected mortality.…”

Evaluating A Key Instrumental Variable Assumption Using Randomization Tests

“…During data collection, ICU bed availability at the time of assessment for ICU admission was measured for use as an instrument for ICU transfer. [28][29][30][31] That is, if there are few ICU beds available when the patient is assessed, this discourages ICU transfer. In the data, ICU bed availability ranges from 0 to 19 with a median of 4 and an IQR of 4.…”

“…This observation can be used to justify conducting an IV analysis on these data, which has been done in several recent works. [28][29][30][31]…”

Sharp instruments for classifying compliers and generalizing causal effects

“…The margin condition requires that there are not too many compliance scores near the quantile q. This is essentially equivalent to the margin condition used in standard classification problems [4], optimal treatment regime settings [30,46], as well as other problems involving estimation of non-smooth covariate-adjusted bounds [27].…”