on the time rather than the baseline covariate is the basis for treatment assignment (Reichardt, 2006).

Khuder and colleagues (2007) present a nice illustration of an ITS. An Ohio city instituted a ban on smoking in indoor workplaces and public places in March 2002. All cases of angina, heart failure, atherosclerosis, and acute myocardial infarction in city hospitals were identified from hospital discharge data. Following the introduction of the smoking ban, a significant reduction of heart disease–related hospital admissions was seen.

From a design standpoint, causal inferences from the simple ITS perspective need to be tempered because the basic design fails to address three major threats to the certainty of the causal relationship between an intervention and the observed outcomes (internal validity) (Shadish et al., 2002; West et al., 2000). First, some other confounding event (e.g., introduction of a new heart medication) may occur at about the same time as the introduction of the intervention. Second, some interventions may change the population of participants in the area. For example, some cities have offered college scholarships to all students who graduate from high school. In such cases, in addition to any effect of the program on the achievement of city residents, the introduction of the program may foster immigration of highly education-oriented families to the city, changing the nature of the student population. Third, record-keeping practices may change at about the time of the intervention. For example, new criteria for the diagnosis of angina or myocardial infarction may change the number of heart disease cases even in the absence of any effect of the intervention.

From a statistical standpoint, several potential problems with longitudinal data need to be addressed. Any long-term natural trends (e.g., a general decrease in heart disease cases) or cycles (e.g., more admissions during certain seasons of the year) in the data need to be modeled so their effects can be removed. In addition, time series data typically reflect serial dependence: observations closer in time tend to be more similar than observations further apart in time. These problems need to be statistically modeled to remove their effects, permitting proper estimates of the causal effect of the intervention and its standard error. Time series analysis strategies have been developed to permit researchers to address these issues (e.g., Chatfield, 2004). In addition, as in the RD design, the actual introduction of the intervention may be fuzzy. In the Khuder et al. study, for example, there was evidence that the enforcement and full implementation of the smoking ban required some months after the ban was enacted. In such cases, a function describing the pattern of implementation of the intervention may need to be included in the model (e.g., Hennigan et al., 1982).

In the Campbell tradition, causal inferences drawn from the basic ITS design can be greatly strengthened by the addition of design elements that address threats to validity. Khuder and colleagues included another, similar Ohio city that did not institute a smoking ban (control series), finding no parallel change in heart disease admissions after the March 2002 timepoint when the smoking ban was introduced in the treatment city. They also found that hospital admissions for diagnoses unrelated



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