Scientists and practitioners are aware that the effectiveness of a treatment varies between individuals. When studying effects on a group level, there is an implicit assumption that the treatment works the same way for all group members. Without examining effects at the level of the individual, we have no way of knowing the causal mechanism through which a treatment works (or does not work) for them, and we might reach the wrong conclusions if we try to generalize findings obtained from a group to an individual. The field of personalized medicine solves these issues by collecting detailed biological and health information from each patient and evaluating individual-specific treatment effects (Schleidgen, Klingler, Bertram, Rogowski, & Marckmann, 2013).
In psychology, moderation analysis is often the method of choice for discovering conditions in which the treatment leads to desired changes in the outcome. This top-down approach for evaluating the characteristics of individuals for which the treatment is effective is not ideal because accounting for all relevant moderators leads to extremely complex models. A bottom-up approach might be preferable, and fortunately there is a vast literature on methods for evaluating the effectiveness of treatments for a single individual (see e.g. Manolov & Moeyaert, 2017).
Methods for Single Case Experimental Designs (SCEDs)
Single Case Experimental Designs (SCEDs) are research designs in which a single unit (participant) is measured repeatedly in several levels of the treatment (Onghena, 2005). SCEDs are akin to within-subjects experiments, but the analysis is performed at the level of the individual instead of the level of the group. Unlike most case studies and observational time series research, SCEDs are defined by the existence of an experimental manipulation (Onghena, 2005). Whereas SCEDs allow for testing hypotheses about changes in the outcome of interest caused by the treatment, almost all statistical methods for SCEDs are designed for univariate analyses. In order to answer important questions in clinical settings, statistical methodology for SCEDs ought to be extended to mediation analysis (Maric, Wiers, & Prins, 2012).
Causal mediation analysis with group-level data
Randomization of participants to treatment is often considered necessary in order to claim that changes in the outcome are due to treatment. In mediation analysis, it is possible to randomize participants to values of the independent variable, but usually not to values of the mediator. This obstacle to making causal claims about the effect of the mediator on the outcome has led to numerous methodological developments in the field of causal inference in mediation analysis. Some of these developments focus on necessary assumptions and procedures for causal interpretations of the indirect effect (Coffman & Zhong, 2012; Jo, Stuart, MacKinnon, & Vinokur, 2011; Mayer, Thoemmes, Rose, Steyer, & West, 2014; Valeri & VanderWeele, 2013), and others on quantifying the sensitivity of the observed indirect effect to unmeasured confounders (Cox, Kisbu-Sakarya, Miočević, & MacKinnon, 2013; Imai, Keele, & Tingley, 2010; VanderWeele, 2010).
In a clinical setting, it is often of interest to evaluate whether a treatment had a causal indirect effect on the outcome regardless of whether the analysis is conducted at the level of the group or the individual. Whereas there have been several proposed methods for mediation analysis in SCEDs, ranging from visual analysis supplemented by ipsative z-scores (Gaynor & Harris, 2008), to the SCED version of the joint significance test (Geuke, Maric, Miočević, Wolters, & de Haan, 2019) and Bayesian methods for parameter estimation and informative hypothesis testing for the mediated effect in SCEDs (Miočević, Klaassen, Geuke, Moeyaert, & Maric, 2019), none of the currently available methods allow for causal interpretations of the indirect effect.
Workshop on ‘Single Subject Causal Mediation Analysis’
Examining causal mechanisms through which treatments achieve effects is important for identifying the most potent program components and for conducting more evidence-based personalized (mental) health care (Maric, Wiers, & Prins, 2012). Coming up with methods for single subject causal mediation analysis was facilitated by bringing together clinical psychologists who collect repeated measures data in N = 1 trials (e.g., in therapy) and statisticians for social sciences working on mediation analysis, single subject data analysis, and causal inference. In August 2019, we organized a five-day meeting at the Lorentz Center in Leiden, Netherlands. The goal of the meeting was to brainstorm and test out ways to upgrade existing statistical methods for SCEDs with new developments in causal mediation analysis to allow for causal interpretations of the indirect effect.
The format of the meeting was a combination of a conference, workshop and hackathon. The number of invited talks and poster presentations was limited in order to allow for at least one hour of work in small groups each day. The groups were composed of four-five researchers from different fields. Each interdisciplinary group was tasked with coming up with ideas and examples of methods for causal mediation analysis that they presented on the last day of the workshop.
The diverse areas of expertise of the meeting attendees led to rich discussions on topics ranging from the required frequency of measurement of the mediator and outcome to potential for randomization in a mediation model and necessary assumptions regarding other covariates in the model and timing of effects. We aim to disseminate the ideas, proposed methods and considerations that emerged during the meeting through publications and presentations at the meeting of the European Methodology Association in Valencia, July 2020. This research is still in progress, and the meeting in Leiden was a productive step in the formation of a community of researchers interested in advancing methods for causal mediation analysis with N = 1.
I would like to thank the Lorentz center for hosting the meeting on Single Subject Causal Mediation Analysis, my co-organizers Marija Maric from University of Amsterdam, Mariola Moeyaert from University of Albany, New York, and Axel Mayer from RWTH Aachen University, and of course, all researchers who attended and contributed their ideas and who are continuing to work on new methods for causal mediation analysis in SCEDs.
References
Coffman, D. L., & Zhong, W. (2012). Assessing mediation using marginal structural models in the presence of confounding and moderation. Psychological Methods, 17, 642–664.
Cox, M. G., Kisbu-Sakarya, Y., Miočević, M., & MacKinnon, D. P. (2013). Sensitivity plots for confounder bias in the single mediator model. Evaluation Review, 37(5), 405-431.
Gaynor, S. T., & Harris, A. (2008). Single-participant assessment of treatment mediators: Strategy description and examples from a behavioral activation intervention for depressed adolescents. Behavior Modification, 32(3), 372-402.
Geuke, G., Maric, M., Miočević, M., Wolters, L. H., & de Haan, E. (2019). Testing mediators of youth intervention outcomes using Single-Case Experimental Designs (SCEDs). New Directions for Child and Adolescent Development, 167, 39-64.
Imai, K., Keele, L., & Tingley, D. (2010). A general approach to causal mediation analysis. Psychological Methods, 15, 309–334.
Jo, B., Stuart, E. A., MacKinnon, D. P., & Vinokur, A. D. (2011). The use of propensity scores in mediation analysis. Multivariate Behavioral Research, 46, 425–452.
Manolov, R., Moeyaert, M. (2017). Recommendations for choosing single-case data analytical techniques. Behavior Therapy, 48(1), 97-114.
Maric, M., Wiers, R. W., & Prins, P. J. (2012). Ten ways to improve the use of statistical mediation analysis in the practice of child and adolescent treatment research. Clinical child and family psychology review, 15(3), 177-191.
Mayer, A., Thoemmes, F., Rose, N., Steyer, R., & West, S. G. (2014). Theory and analysis of total, direct, and indirect causal effects. Multivariate Behavioral Research, 49(5), 425-442.
Miočević, M., Klaassen, F., Geuke, G., Moeyaert, M. & Maric, M. (under review). Using Bayesian Methods to test Mediators of Intervention Outcomes in Single Case Experimental Designs (SCEDs).
Onghena, P. (2005). Single‐Case Designs. Encyclopedia of Statistics in Behavioral Science, 4, 1850–1854.
Schleidgen, S., Klingler, C., Bertram, T., Rogowski, W. H., & Marckmann, G. (2013). What is personalized medicine: sharpening a vague term based on a systematic literature review. BMC Medical Ethics, 14(1), 55.
Valeri, L., & VanderWeele, T. J. (2013). Mediation analysis allowing for exposure– mediator interactions and causal interpretation: Theoretical assumptions and implementation with SAS and SPSS macros. Psychological Methods, 18, 137–150.
VanderWeele, T. J. (2010). Bias formulas for sensitivity analysis for direct and indirect effects. Epidemiology, 21, 540–551.
