摘要：Objectives. We used 3 approaches to analyzing clustered data to assess the impact of model choice on interpretation. Methods. Approaches 1 and 2 specified random intercept models but differed in standard versus novel specification of covariates, which impacts ability to separate within- and between-cluster effects. Approach 3 was based on standard analysis of paired differences. We applied these methods to data from the National Collaborative Perinatal Project to examine the association between head circumference at birth and intelligence (IQ) at age 7 years. Results. Approach 1, which ignored within- and between-family effects, yielded an overall IQ effect of 1.1 points (95% confidence interval [CI]=0.9, 1.3) for every 1-cm increase in head circumference. Approaches 2 and 3 found comparable within-family effects of 0.6 points (95% CI = 0.4, 0.9) and 0.69 points (95% CI = 0.4, 1.0), respectively. Conclusions. Our findings confirm the importance of applying appropriate analytic methods to clustered data, as well as the need for careful covariate specification in regression modeling. Method choice should be informed by the level of interest in cluster-level effects and item-level effects. Public health research depends increasingly on clustered data study designs to evaluate the effectiveness of programs, interventions, and policies. Clustered data consist of data points recorded on multiple items within a cluster, such as those that arise in family studies (multiple siblings within a family), longitudinal studies (multiple time points within a person), school-based research (multiple students within a school), and complex surveys (multiple respondents within a geographic region or neighborhood). Although nonclustered (i.e., independent) data can easily be analyzed via standard statistical methods, clustered data can offer significant advantages over independent data; these include the ability to separate out family effects from sibling effects, time effects from person effects, school effects from student effects, and regional or neighborhood effects from respondent effects. To succeed in these objectives, data analysts must take care to choose techniques that (1) appropriately account for correlation among items within the same cluster and (2) effectively separate and characterize cluster-level effects and item-level effects. The issue of intracluster correlation has been considered by numerous authors. 1 – 3 These accounts have noted that if we presume independence when analyzing data that are cluster-correlated, then biased estimates of standard errors are likely to result. Typically, positive intracluster correlation may cause standard errors to be underestimated when the exposure of interest is fixed for the cluster and overestimated when the exposure varies within cluster. Use of inaccurate standard errors can lead to invalid test statistics and confidence intervals, and ultimately, misleading inferences on, say, the effectiveness of a new behavioral therapy for medication compliance or the success of a new smoking-prevention strategy. To avoid incorrect inferences, data analysts are encouraged to use statistical methods that account for intracluster correlation in an effort to preserve the validity of resulting conclusions. Fortunately, many of the most commonly used statistical software packages—e.g., Stata (StataCorp LP, College Station, TX), SAS (SAS Institute Inc, Cary, NC), and SPSS (SPSS Inc, Chicago, IL)—now incorporate state-of-the-art methods for analyzing clustered data. The separation of cluster-level and item-level effects of a particular exposure has received relatively less attention in the statistical literature, although it has not been entirely ignored. 4 – 8 The social sciences literature has long referred to the partitioning of “individual” versus “contextual” effects, which are analogous to item-level and cluster-level effects, respectively. Other near-synonyms in the statistical literature have included person-specific versus population-averaged effects, and within-cluster and between-cluster effects. It is easy to argue that many researchers are interested in both levels of effect; for example, a sociologist may be interested in both the neighborhood influences (e.g., socioeconomic level, as reflected by average income in the neighborhood) as well as the individual-specific factors (e.g., household-specific income) that modify smoking risk, to design the most effective interventions to prevent smoking among adolescents. We discuss different approaches for capturing both levels of effect in clustered designs. Our purpose was to review several different approaches for analyzing clustered data, with the previously mentioned objectives in mind. Although many earlier papers have emphasized the need for taking intracluster correlation into account, far fewer have highlighted methods for and advantages of distinguishing among cluster-level (or between-cluster) and item-level (or within-cluster) effects via careful model and covariate specification in regression. Separation of effects via careful modeling has the further advantage of reducing confounding by cluster; that is, the distortion of item-level effects by cluster-level correlates associated with exposure and outcome. The statistical approaches we focused on included random effects regression analysis of all items across many clusters, with and without adjustment for the cluster-averaged exposure covariate, and ordinary regression analysis of independent items consisting of differences between sibling pairs randomly selected from different clusters. For each approach, we also devoted attention to the proper interpretation of the exposure effect (i.e., whether it represents a “within-cluster” or “between-cluster” phenomenon), and use of purposeful covariate selection to discriminate between cluster-level and within-cluster effects. Note that we assume in what follows that the exposure measurement varies among items within a cluster (such as an individual student’s gender in a school-based study); hence, the methods and recommendations proposed do not apply to exposures that are fixed within a cluster (such as in cluster-randomized trials, in which treatment is completely synonymous with clinic or location).
