Adjusted horizontal stacked bar graphs ("Grotta bars") for consistent presentation of observational stroke study results

Abstract

Background: Modified Rankin Scale (mRS) scores are used to measure functional outcomes after stroke. Researchers create horizontal stacked bar graphs (nicknamed "Grotta bars") to illustrate distributional differences in scores between groups. In well-conducted randomized controlled trials, Grotta bars have a causal interpretation. However, the common practice of exclusively presenting unadjusted Grotta bars in observational studies can be misleading in the presence of confounding. We demonstrated this problem and a possible solution using an empirical comparison of 3-month mRS scores among stroke/TIA patients discharged home versus elsewhere after hospitalization.

Patients and methods: Using data from the Berlin-based B-SPATIAL registry, we estimated the probability of being discharged home conditional on prespecified measured confounding factors and generated stabilized inverse probability of treatment (IPT) weights for each patient. We visualized mRS distributions by group with Grotta bars for the IPT-weighted population in which measured confounding was removed. We then used ordinal logistic regression to quantify unadjusted and adjusted associations between being discharged home and the 3-month mRS score.

Results: Of 3184 eligible patients, 2537 (79.7%) were discharged home. In the unadjusted analyses, those discharged home had considerably lower mRS compared with patients discharged elsewhere (common odds ratio, cOR = 0.13, 95% CI: 0.11-0.15). After removing measured confounding, we obtained substantially different mRS distributions, visually apparent in the adjusted Grotta bars. No statistically significant association was found after confounding adjustment (cOR = 0.82, 95% CI: 0.60-1.12).

Discussion and conclusion: The practice of presenting only unadjusted stacked bar graphs for mRS scores together with adjusted effect estimates in observational studies can be misleading. IPT weighting can be implemented to create Grotta bars that account for measured confounding, which are more consistent with the presentation of adjusted results in observational studies.

Trial registration: ClinicalTrials.gov NCT03027453.

Keywords: Stroke; causal inference; data visualization; home discharge; modified Rankin Scale.

Figure 1.

Flow diagram for study population.

Figure 2.

Distribution of modified Rankin Scale (mRS) scores at 3-month after hospital admission among patients with transient ischemic attack or stroke in B-SPATIAL registry stratified according to discharge status in the original study population (top) and in the pseudo-population generated after applying inverse probability of treatment weighting (bottom).

Figure 3.

Road map to build adjusted Grotta bars inspired by our clinical application. This step-by-step protocol relies on inverse probability of treatment weighting with stabilized weights (without truncation) for a research question about effect of a binary exposure measured at a single time point (in two shades of yellow) on the outcome, modified Rankin Scale (mRS; in four shades of blue, representing four levels). In this simple scenario, the confounding variable has four levels (light to dark red) with higher levels leading the individual to be less likely to receive the exposure and more likely to have a worse outcome. The stabilized weights are depicted in gray, with darker colors indicating larger weights. We assumed conditional exchangeability, positivity, consistency, no measurement error, and no model misspecification, as is customary in causal inference research. In some applications, truncation during step 3 may be deemed appropriate (for further reading on this topic, see Cole and Hernán). *For simplicity and didactic purposes, we depicted mRS as a variable with four levels (with darker colors indicating worse outcomes) instead of seven levels.