{"id":341,"date":"2010-12-15T10:49:37","date_gmt":"2010-12-15T15:49:37","guid":{"rendered":"https:\/\/cyrussamii.com\/?p=341"},"modified":"2010-12-15T10:49:37","modified_gmt":"2010-12-15T15:49:37","slug":"clustering-unit-level-randomization-and-insights-from-multisite-trials","status":"publish","type":"post","link":"https:\/\/cyrussamii.com\/?p=341","title":{"rendered":"Clustering, unit level randomization, and insights from multisite trials"},"content":{"rendered":"<p>Another update to the previous post (<a href=\"https:\/\/cyrussamii.com\/?p=61\">link<\/a>) on clustering of potential outcomes even when randomization occurs at the unit level within clusters: Researching the topic a bit more, I discovered that the literature on &#8220;multisite trials&#8221; addresses precisely these issues.  E.g., this paper by Raudenbush and Liu (2000; <a href=\"http:\/\/www.ssicentral.com\/hlm\/techdocs\/RaudenbushandLiu00.pdf\">link<\/a>) examines consequences of site-level heterogeneity in outcomes and treatment effects.  They formalize a balanced multisite experiment with an hierarchical linear model, $latex Y_{ij} = \\beta_{0j} + \\beta_{1j}X_{ij} + r_{ij}$ where $latex r_{ij} \\sim i.i.d.N(0,\\sigma^2)$, and $latex X_{ij}$ is a centered treatment variable (-0.5 for control, 0.5 for treated).  In this case, an unbiased estimator for the site-specific treatment effect, $latex \\hat \\beta_{1j}$, is given by the difference in means between treated and control at site $latex j$, and the variance of this estimator over repeated experiments in different sites is given by, $latex \\tau_{11} + 4\\sigma^2\/n$, where $latex \\tau_{11}$ is the variance of the $latex \\beta_{1j}$&#8217;s over sites, and $latex n$ is the (constant) number of units at each site.  Then, an unbiased estimator for the average treatment effect over all sites, $latex 1,\\hdots,J$, is simply the average of these site-specific estimates, with variance $latex \\frac{\\tau_{11} + 4\\sigma^2\/n}{J}$.  What distinguishes this model from the one that I examined in the previous post is that once the site-specific intercept is taken into account, there remains no residual clustering (hence the i.i.d. $latex r_{ij}$&#8217;s).  Also, heterogeneity in treatment effects is expressed in terms of a simple random effect (implying constant within group correlation conditional on treatment status).  These assumptions are what deliver the clean and simple expression of the variance of the site-specific treatment effect estimator, which may understate the variance in the situations that I examined where residual clustering was present.  It would be useful to study how well this expression approximates what happens in the more complicated data generating process that I set up.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Another update to the previous post (link) on clustering of potential outcomes even when randomization occurs at the unit level within clusters: Researching the topic a bit more, I discovered that the literature on &#8220;multisite trials&#8221; addresses precisely these issues. E.g., this paper by Raudenbush and Liu (2000; link) examines consequences of site-level heterogeneity in &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/cyrussamii.com\/?p=341\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Clustering, unit level randomization, and insights from multisite trials&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-341","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/posts\/341","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=341"}],"version-history":[{"count":29,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/posts\/341\/revisions"}],"predecessor-version":[{"id":371,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/posts\/341\/revisions\/371"}],"wp:attachment":[{"href":"https:\/\/cyrussamii.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=341"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=341"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=341"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}