Beyond One-Variable-at-a-Time Subgroup Analyses: Illustrating the Predictive Approaches to Treatment Effect Heterogeneity Framework in the Third International Stroke Trial

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Heterogeneous treatment effects (HTEs) refer to non-random variations in treatment effects among individuals in both magnitude and direction. The assessment of HTEs may empower clinicians to individualize treatment decisions according to specific patient characteristics.1 In randomized controlled trials (RCTs), HTEs are traditionally examined with subgroup analyses, although the limitations of such analyses—ranging from multiplicity of comparisons, spurious findings, and low power of the interaction analyses—are well established.2 The past decades have seen major advances to overcome the clinical and statistical limitations of these so-called one-variable-at-a-time subgroup analyses, culminating in the recommendations of the Predictive Approaches to Treatment effect Heterogeneity (PATH) statement.3 In essence, the PATH framework describes 2 approaches to examine HTEs in RCTs by considering multiple variables per patient: The risk score approach and the effect score approach.4 The risk score approach groups patients according to their predicted risks of experiencing the outcome of interest rather than by levels of a single variable (eg, age category). The basic idea is then to examine possible variations of the treatment effect in the intervention and control group in these risk groups. Thus, the risk score approach considers risk-based variations in treatment benefit.3 The effect score approach attempts to model the effect of a particular intervention compared to the alternative treatment (eg, placebo) on a patient level, for example, by including the interaction of the treatment variable with a potential relative effect modifier (eg, age) in a regression model. Here, we focus on the risk score approach and illustrate its clinical relevance using a real-world RCT. METHODS The Third International Stroke Trial (IST-3) was a multi-center, placebo-controlled randomized trial of intravenous thrombolytic therapy of the drug Alteplase (rt-PA) for patients with acute ischemic stroke during the years 2000–2011.5 The data are publicly available.6 For ethical research considerations (eg, with respect to the approval by the appropriate Institutional Review Board and written informed consent), we refer to the primary publication of the IST-3 trial.5 We examined possible HTEs for the primary binary outcome of the IST-3 trial: the proportion of patients alive and independent as measured by the Oxford Handicap Score with scores 0–2 at 6 months follow-up. Outlined in the PATH statement, the following steps were involved in our predictive HTE approach (note that risk here refers to a favorable outcome and the terms risk and probability are used interchangeably): A risk score model for the primary outcome. Here, we computed a multivariable logistic regression-based risk prediction model for the primary outcome using directly the baseline variables of the IST-3 trial. Importantly, the model does not feature the allocated treatment as a covariate—it is “treatment-blinded” (Table). A statistical test if the treatment effect of Alteplase versus placebo varies across the predicted baseline risks: The presence of HTEs was determined with a likelihood ratio test of the interaction between treatment and the linear predictor, where the latter was extracted from the multivariable logistic regression of step (1). Note that the likelihood ratio test involved a second logistic regression model with only treatment and the linear predictor (and their interaction) as covariates. Separation (“binning”) of the predicted probabilities of a favorable outcome into quartiles and grouping of patients according to these risk quartiles (Q1–Q4). Evaluation of the treatment benefit in the risk-based subgroups Q1–Q4. The treatment benefit was evaluated on the absolute risk difference scale. Table. - Summary Statistics of Selected Baseline Variables Collected at Randomization of the IST-3 Randomized Controlled Trial Complete case N = 3010 Multivariable logistic regression model Odds ratios Outcome at 6-mo follow-up Alive and independent as measured by the Oxford Handicap Score (0–2) Yes 1074 (35.7%; 95% CI, 34.0–37.4) No 1936 (64.3%; 95% CI, 62.6–66.0) Predictors Treatment Placebo 1509 (50.1%) Not included Alteplase (rt-PA) 1501 (49.9%) Age (y) 81.0 [72.0; 86.0] 0.96; 95% CI, 0.95–0.97; P < .001 Sex Female 1562 (51.9%) Male 1448 (48.1%) 0.98; 95% CI, 0.80–1.20; P = .8 Lived alone before stroke? Yes 1125 (37.4%) No 1885 (62.6%) 0.90; 95% CI, 0.74–1.09; P = .3 Recent ischemic change likely cause of this stroke? No 1772 (58.9%) Possibly yes 699 (23.2%) 0.98; 95% CI, 0.79–1.23; P = .9 Definitely yes 539 (17.9%) 0.77; 95% CI, 0.58–1.00; P = .053 Received antiplatelet drugs in last 48 h? Yes 1550 (51.5%) No 1460 (48.5%) 1.03; 95% CI, 0.85–1.23; P = .8 Patient in atrial fibrillation at randomization? Yes 908 (30.2%) No 2102 (69.8%) 1.27; 95% CI, 1.02–1.57; P = .035 Systolic BP (mm Hg) 155.0 [140.0; 170.0] 1.00; 95% CI, 1.00–1.00; P > .9 Diastolic BP (mm Hg) 80.0 [72.0; 91.0] 1.00; 95% CI, 0.99–1.00; P = .2 Estimated weight (kg) 70.0 [62.0; 80.0] 1.01; 95% CI, 1.00–1.01; P = .035 Best eye response (Glasgow Coma Scale) Nonspontaneously (never, to pain, to command) 443 (14.7%) Spontaneously 2567 (85.3%) 1.98; 95% CI, 1.22–3.24; P = .006 Best motor response (Glasgow Coma Scale) Normal 2581 (85.7%) Not normal (none, extend to pain, abnormal flex to pain, normal flex to pain, localizes movements to pain) 429 (14.3%) 1.00; 95% CI, 0.58–1.73; P > .9 Best verbal response (Glasgow Coma Scale) None 373 (12.4%) Noises only 339 (11.3%) 0.86; 95% CI, 0.49–1.52; P = .6 Inappropriate words 317 (10.5%) 1.64; 95% CI, 0.80–3.30; P = .2 Confused in time, place, or person 383 (12.7%) 1.02; 95% CI, 0.40–2.49; P > .9 Orientated in time, place, and person 1598 (53.1%) 1.41; 95% CI, 0.44–4.22; P = .6 Total Glasgow Coma Scale score 14.0 [12.0; 15.0] 0.86; 95% CI, 0.67–1.12; P = .2 Total NIH Stroke Scale score 11.0 [6.0; 17.0] 0.83; 95% CI, 0.81–0.85; P < .001 Stroke subtype LACI 328 (10.9%) PACI 1137 (37.8%) 1.01; 95% CI, 0.76–1.34; P > .9 POCI 245 (8.1%) 1.11; 95% CI, 0.76–1.61; P = .6 TACI 1300 (43.2%) 0.82; 95% CI, 0.59–1.16; P = .3 Model performance c Statistic 0.83 Brier score 0.16 Likelihood ratio test for interaction (treatment × linear predictor) 0.0003 The 2 treatment groups were a placebo group and a treatment group receiving Alteplase (rt-PA). Categorical variables are shown with counts and frequencies, whereas numerical variables are summarized with medians and interquartile ranges. The associated odds ratios of a multivariable logistic regression model (not including the treatment variable) for the primary outcome of the IST-3 trial—the proportion of patients alive and independent as measured by the Oxford Handicap Score 0–2 at 6-mo follow-up—are illustrated with means and 95% CI. Model performance is measured by the c statistic and the Brier score. The statistical significance of the interaction between treatment and the linear predictor of the multivariable logistic regression model was assessed with a likelihood ratio test.Abbreviations: 95% CI, 95% confidence interval; BP, blood pressure; IST-3, The Third International Stroke Trial; LACI, lacunar infarct; NIH, National Institutes of Health; PACI, partial anterior circulation infarct; POCI, posterior circulation infarct; rt-PA, recombinant tissue plasminogen activator; TACI, total anterior circulation infarct. All analyses were performed with R and the code can be found on github: https://github.com/marbhuber/predictive_hte_ist3/.7 RESULTS Our complete-case analysis features N = 3010 patients of the original N = 3035 patients and N = 1074 (35.7%; 95% confidence interval [CI], 34.0–37.4) patients had a favorable outcome. The Table further shows the associated odds ratios of the multivariable prediction model, illustrating, for example, a better outcome for younger patients and patients with a lower Total National Institutes of Health Stroke Scale score. The model

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