Evaluating Markers for Guiding Treatment
JNCI J Natl Cancer Inst (
Evaluating Markers for Guiding Treatment
Stuart G. Baker 0
Marco Bonetti 0
0 Affiliations of authors: Division of Cancer Prevention, National Cancer Institute , Bethesda, MD (SGB); Carlo F. Dondena Centre for Research on Social Dynamics and Public Policies and Bocconi University , Milan, Italy, MB
Background: The subpopulation treatment effect pattern plot (STEPP) is an appealing method for assessing the clinical impact of a predictive marker on patient outcomes and identifying a promising subgroup for further study. However, its original formulation lacked a decision analytic justification and applied only to a single marker. Methods: We derive a decision-analytic result that motivates STEPP. We discuss the incorporation of multiple predictive markers into STEPP using risk difference, cadit, and responders-only benefit functions. Results: Applying STEPP to data from a breast cancer treatment trial with multiple markers, we found that none of the three benefit functions identified a promising subgroup for further study. Applying STEPP to hypothetical data from a trial with 100 markers, we found that all three benefit functions identified promising subgroups as evidenced by the large statistically significant treatment effect in these subgroups. Conclusions: Because the method has desirable decision-analytic properties and yields an informative plot, it is worth applying to randomized trials on the chance there is a large treatment effect in a subgroup determined by the predictive markers.
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As early as 1977, Byar and Corle (
1
) noted that models
incorporating baseline variables “made it possible to change the center
of interest from the question ‘which treatment is best’ to ‘which
treatment is best for which kinds of patients’.” In current
terminology, these baseline variables are called predictive markers
(
2,3
). A standard approach for evaluating predictive markers
involves testing the association between outcome and the
marker-treatment interaction (
4,5
). Recent approaches
discussed in the Journal include novel definitions of sensitivity,
specificity, negative predictive value, and positive predictive
values (
6
) and treatment-specific plots for the estimated
probability of outcome vs the marker (
7
). A recent Journal editorial (
8
)
proposed evaluating the additional benefit of a new marker
relative to existing markers, an extension requiring a multiple
marker formulation. We present an alternative approach to
evaluating predictive markers that involves a simple graphical
display with confidence intervals and can include multiple
markers.
Methods
Decision Analytic Foundation
The use of predictive markers for guiding treatment usually
involves marker-based treatment selection: Administer the new
treatment if the marker exceeds a cutpoint s, and administer
the old treatment (standard of care) otherwise. To characterize
the net benefit (benefit minus harm) of marker-based treatment
selection, we combine the additive utility model of Vickers,
Kattan, and Sargent (
9
) with a decision analysis for predictive
markers (
10
). For binary outcomes, let DIF(s) denote the
difference in the probabilities of a favorable outcome for new vs old
Published by Oxford University Press 2016. This work is written by US Government employees and is in the public domain in the United States.
treatment, conditional on the marker exceeding cutpoint s. Let
Frac(s) denote the fraction of the population with the marker
exceeding cutpoint s. As derived in the Supplementary Materials
(available online), the net benefit equation is
ðNet benefit of marker–based treatment selection at cutpoint sÞ
¼ ðNet benefit of the old treatmentÞ þ ðDIFðsÞ - HÞ B
FracðsÞ;
(
1
)
where B is the increased benefit of a favorable over an
unfavorable outcome and H is the increased benefit of new vs old
treatment that counterbalances any additional harm from side
effects of the new treatment.
The key role of DIF(s) in the net benefit equation provides
new motivation for the tail-oriented version of the
subpopulation treatment effect pattern plot of Bonetti and Gelber (
11,12
).
We use the acronym STEPP to refer to the tail-oriented version
of the subpopulation treatment effect pattern plot although
STEPP generally also applies to another version. In its original
formulation, STEPP graphs an estimate of DIF(s) vs the median
of the values of the marker that exceeds s. For this
implementation related to decision analysis, STEPP graphs an estimate of
DIF(s) vs either s or a quantile of s. The estimate of DIF(s) could
be a difference in the fractions with favorable outcome for
binary endpoints or a difference in Kaplan-Meier survival
estimates at a prespecified time point for survival outcomes.
Typically, as s increases, the estimate of DIF(s) and the width of
its confidence interval increase. Accounting for the variability in
estimation, we define the optimal cutpoint as the smallest
value of cutpo (...truncated)