02.Causation06.Regression discontinuity design - sporedata/researchdesigneR GitHub Wiki

• When a continuous intervention is implemented, allowing you to evaluate its effectiveness around the margins that distinguish between the two levels of the intervention (see Regression Discontinuity Designs in Epidemiology: Causal Inference Without Randomized Trials

1. Pre-requisits for causal-analysis

We can use regression discontinuity designs when using a continuously measured random variable to assign the exposure of interest. This continuously measured random variable should lie above (or below) some threshold value. Given that subjects cannot precisely manipulate this variable, exposure assignment is close to random for observations near the threshold, and we can identify causal effects.

We can use this design when a threshold rule determines the exposure or treatment. For example, patient eligibility can be assigned based on a continuous biomarker such as cholesterol, blood glucose, or birth weight. These continuous measures determining treatment eligibility are subject to random variability due to measurement error, sampling variability, and chance factors that affect biomarkers such as ambient temperature. Random variability implies that patients who score immediately above and below the threshold will be similar, in expectation, on all observed and unobserved pretreatment characteristics, similar to a randomized controlled trial (RCT). The assignment variable could be any continuous pretreatment measure, including the outcome variable measured at baseline or another measure of risk; a baseline covariate that loosely correlates with the outcome; or even a random number, in which case regression discontinuity is identical to an RCT.

Regression discontinuity designs are feasible when the probability of treatment assignment changes discontinuously at some threshold value of a continuous assignment variable. This design assumes that in a small neighborhood around the threshold value, as that range goes toward 0, treatment assignment is ignorable, independent of the potential outcomes, similar to randomized experiments. Also, it assumes that all potential confounders are balanced in a small area around the cutoff.

Thus, the two identifying assumptions of regression discontinuity are:

1. the continuous assignment variable is continuous at the threshold value
2. the relationship between the continuous assignment variable and the potential outcomes is continuous at the threshold value

The plot below is called a bounce diagram, showing the difference between two groups over time. this difference was analyzed using a regression discontinuity design (RDD). The plot indicates an association between the intervention and an increase in income difference between the experimental and control groups. This result suggests that the experimental group presented higher income levels after the intervention than the control group.

Regression discontinuity designs in healthcare research

1. Books *
2. Articles
   • US Food and Drug Administration Approvals of Drugs and Devices Based on Nonrandomized Clinical Trials [1].
   • Practical guide to health policy evaluation using observational data.
   • Common references for causation.

[1] Razavi M, Glasziou P, Klocksieben FA, Ioannidis JP, Chalmers I, Djulbegovic B. US Food and Drug Administration Approvals of drugs and devices based on nonrandomized clinical trials: a systematic review and meta-analysis. JAMA network open. 2019 Sep 4;2(9):e1911111-.