The Neonatal Airway and the Goldilocks Phenomenon

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.

An approach to explore for a sweet spot in randomized trials

OBJECTIVE

The objective of the study was to demonstrate how a conventional randomized trial can be analyzed through a stratified or a matched approach to identify a potential sweet spot where observed differences might be accentuated in the mid range of disease severity.

DESIGN AND SETTING

We review a landmark randomized trial of heart failure patients that tested whether implantable defibrillators reduce mortality (n = 2,521).

RESULTS

Overall, 22% (182/829) of the patients in the defibrillator group died compared with 29% (484/1,692) of patients in the control group. Proportional hazards analysis yielded a modest 25% survival benefit (hazard ratio = 0.75, 95% confidence interval: 0.63 to 0.89). Stratified analysis of the trial yielded a larger 52% survival benefit for those in the middle quintile of disease severity (hazard ratio = 0.48, 95% confidence interval: 0.29 to 0.79). In contrast, little of the survival benefit was explained by patients with the greatest disease severity (hazard ratio = 0.89, 95% confidence interval: 0.69 to 1.15). The discrepancy between crude and stratified analyses could be visualized by graphical displays and replicated with matched comparisons.

CONCLUSION

Our approach for analyzing a randomized trial could help identify a potential sweet spot of an accentuated treatment effect.