Constructing treatment selection rules based on an estimated treatment effect function: different approaches to take stochastic uncertainty into account have a substantial effect on performance

BMC Medical Research Methodology
Maren Eckert, Werner Vach

Abstract

Today we are often interested in the predictive value of a continuous marker with respect to the expected difference in outcome between a new treatment and a standard treatment. We can investigate this in a randomized control trial, allowing us to assess interactions between treatment and marker and to construct a treatment selection rule. A first step is often to estimate the treatment effect as a function of the marker value. A variety of approaches have been suggested for the second step to define explicitly the rule to select the treatment, varying in the way to take uncertainty into account. Little is known about the merits of the different approaches. Four construction principles for the second step are compared. They are based on the root of the estimated function, on confidence intervals for the root, or on pointwise or simultaneous confidence bands. All of them have been used implicitly or explicitly in the literature. As performance characteristics we consider the probability to select at least some patients, the probability to classify patients with and without a benefit correctly, and the gain in expected outcome at the population level. These characteristics are investigated in a simulation study. As to be expected...Continue Reading

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