Instrumental variable analysis to estimate treatment effects: a simulation study showing potential benefits of conditioning on hospital

Abstract

Background: Instrumental variable (IV) analysis holds the potential to estimate treatment effects from observational data. IV analysis potentially circumvents unmeasured confounding but makes a number of assumptions, such as that the IV shares no common cause with the outcome. When using treatment preference as an instrument, a common cause, such as a preference regarding related treatments, may exist. We aimed to explore the validity and precision of a variant of IV analysis where we additionally adjust for the provider: adjusted IV analysis.

Methods: A treatment effect on an ordinal outcome was simulated (beta - 0.5 in logistic regression) for 15.000 patients, based on a large data set (the IMPACT data, n = 8799) using different scenarios including measured and unmeasured confounders, and a common cause of IV and outcome. We compared estimated treatment effects with patient-level adjustment for confounders, IV with treatment preference as the instrument, and adjusted IV, with hospital added as a fixed effect in the regression models.

Results: The use of patient-level adjustment resulted in biased estimates for all the analyses that included unmeasured confounders, IV analysis was less confounded, but also less reliable. With correlation between treatment preference and hospital characteristics (a common cause) estimates were skewed for regular IV analysis, but not for adjusted IV analysis.

Conclusion: When using IV analysis for comparing hospitals, some limitations of regular IV analysis can be overcome by adjusting for a common cause.

Trial registration: We do not report the results of a health care intervention.

Keywords: Between-hospital variation; Comparative effectiveness research; Confounding by indication; Instrumental variable analysis; Observational data; Unmeasured confounders.

Fig. 1

A directed acyclic graph (DAG) showing the causal assumption of the observational data and confounding caused by alternative pathways through the unobserved (U) confounders and through hospital (H). H: hospital. Z: treatment preference as instrument: proportion of treated patients within each hospital. T: treatment. C: patient characteristics. PS: propensity score. Y: outcome. U: unobserved confounders

Fig. 2

Distribution of the IV (treatment preferences) plotted per prognostic factor in the motivating example showing the distribution of the treatment preference of the hospitals attributed to each patient, per level of the prognostic factor: sex, Glasgow Coma Scale (GCS) motor score, pupillary reactivity, the Traumatic Coma Data Bank computed tomography (TCDB CT) scan classification, the presence of subarachnoid hemorrhages (SAH) and age. CT classification is based on the Marshall classification

Fig. 3

Estimated treatment effects (β) and corresponding standard errors after analysis with 5 different models in scenario 1-6: 1)Null scenario: no effect of treatment, 2) RCT scenario: treatment randomly assigned, 3) Confounder-adjusted, 4) Confounder-adjusted with instrument, 5) Confounder-adjusted and subject to selection bias, 6) Confounder-adjusted and subject to selection bias with instrument

Fig. 4

Estimated treatment effects and corresponding standard errors after analysis with no correlation between general hospital characteristics and treatment preference, and with mean correlation coefficients of 0.3 and 0.5

Fig. 5

Histogram of all estimated βs in the simulations in scenario 7 of both unadjusted IV (model d) and adjusted IV (model e)