Testing for a Sweet Spot in Randomized Trials

INTRODUCTION: Randomized trials recruit diverse patients, including some individuals who may be unresponsive to the treatment. Here we follow up on prior conceptual advances and introduce a specific method that does not rely on stratification analysis and that tests whether patients in the intermediate range of disease severity experience more relative benefit than patients at the extremes of disease severity (sweet spot). METHODS: We contrast linear models to sigmoidal models when describing associations between disease severity and accumulating treatment benefit. The Gompertz curve is highlighted as a specific sigmoidal curve along with the Akaike information criterion (AIC) as a measure of goodness of fit. This approach is then applied to a matched analysis of a published landmark randomized trial evaluating whether implantable defibrillators reduce overall mortality in cardiac patients (n = 2,521). RESULTS: The linear model suggested a significant survival advantage across the spectrum of increasing disease severity (β = 0.0847, P < 0.001, AIC = 2,491). Similarly, the sigmoidal model suggested a significant survival advantage across the spectrum of disease severity (α = 93, β = 4.939, γ = 0.00316, P < 0.001 for all, AIC = 1,660). The discrepancy between the 2 models indicated worse goodness of fit with a linear model compared to a sigmoidal model (AIC: 2,491 v. 1,660, P < 0.001), thereby suggesting a sweet spot in the midrange of disease severity. Model cross-validation using computational statistics also confirmed the superior goodness of fit of the sigmoidal curve with a concentration of survival benefits for patients in the midrange of disease severity. CONCLUSION: Systematic methods are available beyond simple stratification for identifying a sweet spot according to disease severity. The approach can assess whether some patients experience more relative benefit than other patients in a randomized trial.