The RD design is viewed as one of the strongest alternatives to the RCT from both Campbell’s (Cook, 2008; Shadish et al., 2002; Trochim, 1984) and Rubin’s (Imbens and Lemiuex, 2008; Rubin, 1977) perspectives. However, it introduces two new challenges to causal inference that do not characterize the RCT. First, it is assumed that the functional form of the relationship between the quantitative assignment variable and the outcome is properly modeled. Early work on the RD design in the behavioral sciences typically assumed that a regression equation representing a linear effect of the assignment score on the outcome plus a treatment effect estimated at the cutoff would be sufficient to characterize the relationship. More recent work in econometrics has emphasized the use of alternative methods to characterize the relationship between the assignment variable and the outcome separately above and below the threshold level. For example, with large sample sizes, nonparametric regression models can be fit separately above and below the threshold to minimize any possibility that the functional form of the relationship is not properly specified. Second, in some RD designs, the quantitative assignment variable does not fully determine treatment assignment. Econometricians make a distinction between “sharp” RD designs, in which the quantitative assignment variable fully determines treatment assignment, and “fuzzy” RD designs, in which a more complex treatment selection model determines assignment. These latter designs introduce considerably more complexity, but new statistical modeling techniques based on the potential outcomes perspective (see Hahn et al., 2001) minimize any bias in the estimate of treatment effects.

From Campbell’s perspective, several design elements can potentially be used to strengthen the basic design. Replication of the original study using a different threshold can help rule out the possibility that some form of nonlinear growth accounts for the results. Masking (blinding) the threshold score from participants, test scorers, and treatment providers, when possible, can minimize the possibility that factors other than the quantitative assignment variable determine treatment. Investigating the effects of the intervention on a nonequivalent dependent variable that is expected to be affected by many of the same factors as the primary outcome variable, but not the treatment, can strengthen the inference. In the case of fuzzy RD designs, sensitivity analyses in which different plausible assumptions are made about alternative functional forms of the relationship and selection models can also be conducted.

Interrupted Time Series (ITS) Analysis

Often policy changes go into effect on a specific date. To illustrate, the Federal Communications Commission (FCC) allowed television broadcasting to be introduced for the first time in several medium-sized cities in the United States in 1951. Bans on indoor smoking have been introduced in numerous cities (and states) on specific dates. If outcome data can be collected or archival data are available at regular fixed intervals (e.g., weekly, monthly), the ITS provides a strong design for causal inference. The logic of the ITS closely parallels that of the RD design except that the threshold



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