PERFORMANCE GUARANTEES FOR INDIVIDUALIZED TREATMENT RULES

Because many illnesses show heterogeneous response to treatment, there is increasing interest in individualizing treatment to patients [Arch. Gen. Psychiatry 66 (2009) 128-133]. An individualized treatment rule is a decision rule that recommends treatment according to patient characteristics. We con...

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Bibliographic Details
Published in:The Annals of statistics 2011-04, Vol.39 (2), p.1180-1210
Main Authors: Qian, Min, Murphy, Susan A.
Format: Article
Language:English
Subjects:
62H99
62J07
62P10
Applications
Approximation
Biology, psychology, social sciences
Clinical trials
Datasets
Decision making
Error rates
Estimation methods
Estimators
Exact sciences and technology
General topics
Illnesses
Individualization
l1-penalized least squares
Least squares
Linear models
Mathematics
Medical sciences
Medical treatment
Oracles
Patients
Probability and statistics
Prognosis
Sciences and techniques of general use
Statistics
Studies
value
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Summary:Because many illnesses show heterogeneous response to treatment, there is increasing interest in individualizing treatment to patients [Arch. Gen. Psychiatry 66 (2009) 128-133]. An individualized treatment rule is a decision rule that recommends treatment according to patient characteristics. We consider the use of clinical trial data in the construction of an individualized treatment rule leading to highest mean response. This is a difficult computational problem because the objective function is the expectation of a weighted indicator function that is nonconcave in the parameters. Furthermore, there are frequently many pretreatment variables that may or may not be useful in constructing an optimal individualized treatment rule, yet cost and interpretability considerations imply that only a few variables should be used by the individualized treatment rule. To address these challenges, we consider estimation based on l₁-penalized least squares. This approach is justified via a finite sample upper bound on the difference between the mean response due to the estimated individualized treatment rule and the mean response due to the optimal individualized treatment rule.
ISSN:0090-5364
2168-8966
DOI:10.1214/10-AOS864