Estimating Dosage Effects: Applying Generalized Propensity Score Methods in Social Work Research

Background and Purpose: Social interventions are often delivered in varying doses, either as a planned element of a study or as a function of differential implementation by intervention agents. Program effects can vary across research participants who experience different dosages of treatment. Evaluating dosage effects is crucial for finding optimal levels of treatment and for distinguishing effects due to varying implementation. However, dosage analysis remains an understudied area.

Estimating dosage effects is challenging because it requires balancing multiple dosage groups simultaneously. Traditional matching methods fall short in accomplishing this task. The recent development of generalized propensity score (GPS) methods provide a new means to balance dosage groups. The purposes of this study were to: (a) review issues in dosage analysis; (b) describe the recent development of GPS methods; and (c) demonstrate the application of GPS methods with continuous measures of treatment exposure. GPS methods with continuous treatment measurement is a novel development in the family of GPS methods and, to our best knowledge, it has not been applied in social work research.

Methods: The study reviewed dosage analyses in social sciences and the development of GPS methods over the past decade. Dosage analysis using a GPS method with continuous treatment variable was demonstrated. The demonstration used a modified STATA program. Data were from a cluster randomized trial of a social-emotional skills training program for elementary school students. The sample consisted of 400 students from 30 classrooms in 6 schools. The dosage analysis focused on dosage effects on one key outcome--social competence.

Results: From the literature review, dosage analyses often have two limitations: (a) most studies involved only two dosage groups, although dosage took multiple levels or varied continuously; and (b) analyses often failed to control for selection bias. Selection biases influence outcomes because low and high dose participants usually differ on characteristics associated with outcome measures. As a result, dosage analysis requires statistically balancing multiple groups simultaneously. The relatively new development of GPS methods provide viable means for accomplishing this task.  GPS methods extend propensity score methods from binary treatment settings to multivalued and continuous treatment settings.

An application of GPS methods with continuous treatment measure in evaluating dosage effects of a social-emotional skills training program showed that the program produced significant dosage effects on social competence (p=.001). A trend relationship was found between the effects on social competence and the level of dosage (i.e., amount of exposure to the intervention), although the relationship was not strictly linear.

Conclusions and Implications: Dosage analysis is an important, complex, and understudied research area. The recent development of GPS methods provides a viable means for conducting dosage analyses. Application of GPS methods is not limited to evaluation studies. Dosage can take on different forms (e.g., length of incarceration, number of placement in foster care). Accordingly, GPS methods can be applied to assess dosage effects in variety of settings.