The regression trunk approach to discover treatment covariate interaction

The regression trunk approach (RTA) is an integration of regression trees and multiple linear regression analysis. In this paper RTA is used to discover treatment covariate interactions, in the regression of one continuous variable on a treatment variable withmultiple covariates. The performance of RTA is compared to the classical method of forward stepwise regression. The results of two simulation studies, in which the true interactions are modeled as threshold interactions, show that RTA detects the interactions in a higher number of cases (82.3% in the first simulation study, and 52.3% in the second) than stepwise regression (56.5% and 20.5%). In a real data example the final RTA model has a higher cross-validated variance-accounted-for (29.8%) than the stepwise regression model (12.5%). All of these results indicate that RTA is a promising alternative method for demonstrating differential effectiveness of treatments.

[1]  W. Loh,et al.  Generalized regression trees , 1995 .

[2]  J. Morgan,et al.  Problems in the Analysis of Survey Data, and a Proposal , 1963 .

[3]  R. Gonzalez.  Applied Multivariate Statistics for the Social Sciences , 2003 .

[4]  J. Rice.  Mathematical Statistics and Data Analysis , 1988 .

[5]  J. Ogrodniczuk,et al.  Follow-up findings for interpretive and supportive forms of psychotherapy and patient personality variables. , 1999, Journal of consulting and clinical psychology.

[6]  Daryl Pregibon,et al.  Tree-based models , 1992 .

[7]  Phillip L. Ackerman,et al.  An aptitude–treatment interaction approach to transfer within training. , 1996 .

[8]  R. Conger,et al.  Assessing the Benefits of a Parenting Skills Training Program: A Theoretical Approach to Predicting Direct and Moderating Effects. , 1999 .

[9]  R W Neufeld,et al.  Aptitude-treatment interaction research in the clinical setting: a review of attempts to dispel the "patient uniformity" myth. , 1988, Psychological bulletin.

[10]  A. V. van Balkom,et al.  Cognitive Therapy by Allocation versus Cognitive Therapy by Preference in the Treatment of Panic Disorder , 2000, Psychotherapy and Psychosomatics.

[11]  J. Ross Quinlan,et al.  C4.5: Programs for Machine Learning , 1992 .

[12]  Wolfgang Gaul,et al.  Classification and Positioning of Data Mining Tools , 1999 .

[13]  Matching smokers to treatment: self-control versus social support. , 1995, Journal of consulting and clinical psychology.

[14]  C. L. Mallows.  Some comments on C_p , 1973 .

[15]  V. Shoham-Salomon,et al.  Client-treatment interaction in the study of differential change processes. , 1991, Journal of consulting and clinical psychology.

[16]  Sunil J Rao,et al.  Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis , 2003 .

[17]  J. Barber,et al.  The role of avoidance and obsessiveness in matching patients to cognitive and interpersonal psychotherapy: empirical findings from the treatment for depression collaborative research program. , 1996, Journal of consulting and clinical psychology.

[18]  Jacob Cohen.  Statistical Power Analysis for the Behavioral Sciences , 1969, The SAGE Encyclopedia of Research Design.

[19]  A. V. van Balkom,et al.  Locus of Control Orientation in Panic Disorder and the Differential Effects of Treatment , 2002, Psychotherapy and Psychosomatics.

[20]  P. Lachenbruch.  Statistical Power Analysis for the Behavioral Sciences (2nd ed.) , 1989 .

[21]  R. Snow,et al.  Aptitude-treatment interaction as a framework for research on individual differences in psychotherapy. , 1991, Journal of consulting and clinical psychology.

[22]  W. Loh,et al.  SPLIT SELECTION METHODS FOR CLASSIFICATION TREES , 1997 .

[23]  David J. Hand,et al.  Construction and Assessment of Classification Rules , 1997 .

[24]  Willem J. van der Linden,et al.  Using aptitude measurements for the optimal assignment of subjects to treatments with and without mastery scores , 1981 .

[25]  A. V. van Balkom,et al.  Paroxetine, clomipramine, and cognitive therapy in the treatment of panic disorder. , 1999, The Journal of clinical psychiatry.

[26]  J. Koziol,et al.  Changepoint statistics for assessing a treatment-covariate interaction. , 1996, Biometrics.

[27]  J. Meulman,et al.  Prediction in Medicine by Integrating Regression Trees into Regression Analysis with Optimal Scaling , 2001, Methods of Information in Medicine.

[28]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[29]  H. Marsh,et al.  Effects of Metacognitive Strategy Training within a Cooperative Group Learning Context on Computer Achievement and Anxiety: An Aptitude-Treatment Interaction Study , 1997 .

[30]  W. Loh,et al.  REGRESSION TREES WITH UNBIASED VARIABLE SELECTION AND INTERACTION DETECTION , 2002 .

[31]  Colin L. Mallows,et al.  Some Comments on Cp , 2000, Technometrics.

[32]  C. R. Snyder,et al.  Handbook of psychological change : psychotherapy processes & practices for the 21st century , 2000 .

[33]  L. Humphreys,et al.  Pseudo-Orthogonal and Other Analysis of Variance Designs Involving Individual-Differences Variables. , 1974 .

[34]  Leo Breiman,et al.  Classification and Regression Trees , 1984 .

[35]  L. Cronbach,et al.  Aptitudes and instructional methods: A handbook for research on interactions , 1977 .

[36]  Alberto Maria Segre,et al.  Programs for Machine Learning , 1994 .

[37]  J. Stevens,et al.  Applied multivariate statistics for the social sciences, 4th ed. , 2002 .

[38]  C. Mallows.  More comments on C p , 1995 .