JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1060 10.6339/22-JDS1060 Computing in Data Science Subpopulation Treatment Effect Pattern Plot (STEPP) Methods with R and Stata VenturiniSergiosergio.venturini@unicatt.it1∗ BonettiMarco23 LazarAnn A.45 ColeBernard F.6 WangXin Victoria78 GelberRichard D.78 YipWai-Ki9 Department of Economic and Social Sciences, Università Cattolica del Sacro Cuore, Via Bissolati 74, 26100 Cremona, Italy Carlo F. Dondena Research Centre, Università Commerciale L. Bocconi, Via Röntgen 1, 20136 Milano, Italy Bocconi Institute for Data Science and Analytics, Università Commerciale L. Bocconi, Via Röntgen 1, 20136 Milano, Italy Division of Oral Epidemiology, Department of Preventive and Restorative Dental Sciences, University of California, San Francisco, 3333 California Street, San Francisco, CA 94118, USA Division of Biostatistics, Department of Epidemiology and Biostatistics, University of California, San Francisco, 3333 California Street, San Francisco, CA 94118, USA Department of Mathematics and Statistics, University of Vermont, 33 Colchester Avenue, Burlington, VT 05405, USA Department of Data Science, Dana-Farber Cancer Institute, 450 Brookline Avenue, Mailstop CLS 11007, Boston, MA 02215, USA Department of Biostatistics, Harvard T.H. Chan School of Public Health, 677 Huntington Avenue, Boston, MA 02215, USA Agenus, Inc., 3 Forbes Road, Lexington, MA 02421, USA Corresponding author. Email: sergio.venturini@unicatt.it. 2023982022211106126 Supplementary Material

The R and Stata scripts containing the code related to the examples discussed in the paper and a second application that involves a binary outcome are available in the supplementary material on the journal website.

552022372022 2023 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2023 Open access article under the CC BY license.

We introduce the stepp packages for R and Stata that implement the subpopulation treatment effect pattern plot (STEPP) method. STEPP is a nonparametric graphical tool aimed at examining possible heterogeneous treatment effects in subpopulations defined on a continuous covariate or composite score. More pecifically, STEPP considers overlapping subpopulations defined with respect to a continuous covariate (or risk index) and it estimates a treatment effect for each subpopulation. It also produces confidence regions and tests for treatment effect heterogeneity among the subpopulations. The original method has been extended in different directions such as different survival contexts, outcome types, or more efficient procedures for identifying the overlapping subpopulations. In this paper, we also introduce a novel method to determine the number of subjects within the subpopulations by minimizing the variability of the sizes of the subpopulations generated by a specific parameter combination. We illustrate the packages using both synthetic data and publicly available data sets. The most intensive computations in R are implemented in Fortran, while the Stata version exploits the powerful Mata language.

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