# Extension of Regression Discontinuity Designs (RDD) to evaluate time effects – A quasi-experimental approach using the data from the new form of care “Integrated cross-sectoral psycho-oncology (nFC- isPO)”

## TL;DR

This paper introduces a new method to analyze repeated measures in quasi-experimental studies, using data from a cancer care program to assess treatment effects over time.

## Contribution

The paper extends regression discontinuity designs to incorporate repeated measures using linear mixed models, enabling more robust quasi-experimental analysis.

## Key findings

- The average treatment effect increased in magnitude over time but did not reach statistical significance.
- The proposed LMM-RDD method outperformed traditional RDD in handling missing data and unbalanced measures.
- The time effect between treatment outcomes was not statistically significant.

## Abstract

Randomised controlled trials (RCTs) are considered the gold standard in clinical research. However, randomization isn’t always feasible, e.g., due to ethical considerations. As a result, quasi-experimental designs, such as the regression-discontinuity design (RDD), have been advocated as valuable alternatives and are increasingly employed in health sciences. So far, however, there is no way to take repeated measures into account in an RDD analysis, although repeated measures are not uncommon in medical research. This article proposes an extension of the RDD methodology to incorporate repeated measures within the statistical analysis.

The article introduces consistent mathematical notation for combining a univariate RDD with a linear mixed model (LMM) to account for repeated measures. The application is presented using data from the nFC-isPO (N = 1,417), where the Hospital Anxiety and Depression Scale (HADS) was employed to assess anxiety and depression in newly diagnosed cancer patients over a 12-month treatment period. The HADS scores were measured at baseline (T1), after 4 months (T2) and after 12 months (T3). Patients were assigned to control (psychosocial care) or treatment (psycho-oncological-psychotherapeutic care) group based on a predetermined HADS threshold at T1.

The average treatment effect (ATE) was similar in both univariate RDD and LMM-RDD when applied to complete cases. Including all available data (T2 and/or T3), univariate RDD analyses were based on different samples for each time point. At T2, the ATE sign reversed from negative to positive, suggesting a change in discontinuity direction. At T3, the ATE magnitude nearly doubled compared to the complete case analysis. LMM-RDD estimated treatment effects were higher than those from univariate RDD. Nevertheless, none reached statistical significance. The time effect (Δt), representing the difference in treatment effects between two time points (complete case: Δt=0.577; T2 and/or T3 available: Δt=0.491), was not significant (p = 0.855; 95%-CI: [−5.589; 6.743]; p = 0.869, 95%-CI: [−5.328; 6.310]).

Extending the RDD to incorporate repeated measures within a linear mixed model (LMM-RDD) provides a more robust and comprehensive analytical approach when an RCT is not feasible. This approach not only addresses the challenges of missing data and an unbalanced number of outcome measures, but also allows for the identification of time-varying treatment effects that may not be discernible using traditional RDD.

The study was registered in the German Clinical Trials Registry on 30 October 2018 under the ID “DRKS00015326”.