We illustrate the use of a primary data analysis method for comparing adaptive interventions that are embedded in a sequential, multiple assignment, randomized trial (SMART). Here we illustrate the use of the SAS GENMOD procedure to analyze a fake data set similar to the ADHD example described in Nahum-Shani et al. (2010).

A SMART is a multi-stage randomized trial, where each stage corresponds to a critical decision. Each participant progresses through the stages and is randomly assigned to one of several intervention options at each stage (Murphy, 2005). In this context, one type of primary data analysis focuses on addressing research questions concerning the comparison of adaptive interventions that are embedded in the SMART design.

In this example two-stage SMART, participants’ responses to the first-stage intervention determine whether they will be re-randomized. In such designs, either responders or non-responders enter the second stage of the intervention while the others remain in the first stage of the intervention. More specifically, in the example in the paper, children with ADHD were randomized at the first stage of the intervention to either low-dose behavioral intervention (coded as 1) or low-dose medication (coded as -1). Non-responders to the first-stage of the intervention were then re-randomized to two second-stage intervention options: either intensifying the same intervention (coded as 1) or augmenting it with the other type of intervention (coded as -1). Responders to the first-stage intervention did not enter the second stage; they continued receiving the first-stage intervention option.

Below is a figure illustrating the sequential, multiple-assignment, randomized trial (SMART) for the Adaptive Interventions for Children with ADHD study described above and in the paper.

The aim of this SMART is to understand whether to begin with medication or behavioral therapy for children with ADHD, and whether to intensify or augment initial treatment for children who do not respond to treatment.

• PI: William Pelham
• Location: Florida International University
• Funding: U.S. Department of Education-funded, completed project

This experimental design can be extended to more than two stages and to settings in which both responders and non-responders are re-randomized; for simplicity we focus on a two-stage setting.

(1, -1): First, offer low-dose behavioral intervention; then add medication for non-responders and continue low-dose behavioral intervention for responders.

(-1,-1): First, offer low-dose medication; then add behavioral intervention for non-responders and continue low-dose medication for responders.

(-1, 1): First, offer low-dose of medication; then intensify the dose of medication for non-responders and continue low-dose medication for responders.

(1, 1): First, offer low-dose behavioral intervention; then intensify the dose of behavioral intervention for non-responders and continue low-dose behavioral intervention for responders.

To learn how to compare adaptive interventions like those above follow these steps:

• download fake data set from SMART,
• download variables in data set to view description of the variables used in the fake data set,
• download SAS code for comparing adaptive interventions,
• import the fake data set into SAS and run the SAS code, and
• compare the results of the analysis with those available in output file.

For references and more information about this SMART design and primary data analysis refer to Nahum-Shani et al. (2012)¹.

Murphy, S. A. (2005). An experimental design for the development of adaptive treatment strategies. Statistics in Medicine, 24(10), 1455–1481.

Nahum-Shani, I., Qian, M., Almirall, D., Pelham, W., Gnagy, B., Fabiano, G., … Murphy, S. A. (2012). Experimental design and primary data analysis methods for comparing adaptive interventions. Psychological Methods, 17, 457-77.

If you use this code in your own research, please cite the article listed below.

Nahum-Shani, I., Qian, M., Almirall, D., Pelham, W., Gnagy, B., Fabiano, G., … Murphy, S. A. (2012). Experimental design and primary data analysis methods for comparing adaptive interventions. Psychological Methods, 17, 457-77. PMC Journal- In process

¹Because the analysis in the current example was conducted on fabricated data, the results reported in the output file are different from those reported in the paper.