Use an IRGT if you can randomize individual participants but need to deliver the intervention in groups or through a common interventionist or facilitator either for pedagogic or practical reasons. If you can randomize individual participants and can deliver the intervention to participants one at a time without going through a common interventionist or facilitator, it is more efficient and easier to use a traditional RCT.

There are no textbooks on IRGTs, but there are a number of papers (Baldwin et al., 2011; Pals et al., 2008b; Pals et al., 2008a; Roberts and Roberts, 2005). There are also sources for information on power and sample size in IRGTs (Heo et al., 2017; Moerbeek and Teerenstra, 2016).

The most accurate result will be available with t-scores. For studies in which the number of units randomized to conditions is 50 or more, z-scores will work well. As the number of randomization units decreases, the df available for the test of the intervention effect also decrease, and the difference between z-scores and t-scores increases.

It is important to distinguish between changing study conditions or study arms and changing groups or clusters. In a parallel group RCT, GRT, or IRGT, it is important to ensure that each participant remains in the study condition to which they were randomized. Those assigned to the intervention condition should not move to the control condition, and vice versa. Sometimes that is unavoidable, but it should be uncommon. If it does happen, standard practice is to analyze as randomized, under the intention-to-treat principle.

The other possibility is that a participant in a GRT or IRGT would change groups or clusters even as they stay in the same study condition or study arm. In a school-based trial, a participant from one intervention school might move to another intervention school. Or in an IRGT, a participant who usually went to the Tuesday night class might sometimes go to the Saturday morning class. Recent studies have shown that failure to account for changing group membership can result in an inflated type I error rate (Andridge et al., 2014). Roberts and Walwyn, 2013 provide a good method for analyzing data to account for such changes.

Standard sources assume that each group or cluster has the same number of observations, but that is almost never true in practice. So long as the ratio of the largest to the smallest group is no worse than about 2:1, such variation can be ignored. But as the variation grows more marked, analysts risk an inflated type I error rate if they ignore it (Johnson et al., 2015).

In addition, power falls as the variation in group or cluster size increases, so that it needs to be addressed in the sample size calculations. There are a number of publications on this issue for GRTs (Candel and van Breukelen, 2010; Candel and van Breukelen, 2016; Moerbeek and Teerenstra, 2016; van Breukelen et al., 2007; You et al., 2011). There are also a number of publications on this issue for IRGTs (Candel and van Breukelen, 2009; Moerbeek and Teerenstra, 2016).

This will depend on several factors, including the expected ICC that reflects the average correlation among observations taken on members of the same small group, and the number of participants in each group. There is no one answer that will be correct for all studies. The best approach is to perform a power analysis, or calculate sample size, using methods appropriate to IRGTs. There are a number of papers that address this question (Moerbeek and Teerenstra, 2016; Pals et al., 2008b; Pals et al., 2008a).

It is true that this approach will improve the fidelity of implementation. But the problem is that this approach completely confounds the instructor/facilitator with the study condition: everyone who gets the intervention gets exposed to that instructor/facilitator. In that situation, it is impossible to separate the effect of the intervention from the effect of the instructor/facilitator. It is possible that a charismatic instructor/facilitator could generate beneficial effects on the outcome of interest, even if the intervention itself is completely ineffective, and the investigator would not be able to distinguish those two effects.

The best estimate for the ICC will reflect the circumstances for the trial being planned. That estimate will be from the same target population, so that it reflects the appropriate groups or clusters (e.g., schools vs. clinics vs. worksites vs. communities); age groups (e.g., youth vs. young adults vs. seniors); ethnic, racial, and gender diversity; and other characteristics of the target population. That estimate will derive from data collected for the same outcome using the same measurement methods to be used for the primary outcome in the trial being planned. For example, if planning a trial to improve servings of fruits and vegetables in inner-city third-graders, it would be important to get an ICC estimate for servings of fruits and vegetables, measured in the same way as servings would be measured in the trial being planned, from third-graders in inner-city schools similar to the schools that would be recruited for the trial being planned.

Regression adjustment for covariates often improves power in a GRT or IRGT by reducing the residual error variance or the ICC (Murray and Blitstein, 2003). At the same time, it is important to remember that regression adjustment for covariates can reduce power in a GRT or IRGT by increasing the ICC (Murray, 1998). As such, it is important to choose covariates carefully. The best covariates will be related to the outcome and unevenly distributed between the study conditions or among the groups or clusters randomized to the study conditions.

No. When a priori matching or stratification is used for balance, the matching or stratification factor may be included in the analysis of intervention effects, but that is not required, and it may be inefficient to do so. It is not required because the type 1 error rate is unaffected when the matching or stratification factor is ignored in the analysis of intervention effects (Diehr et al., 1995; Proschan, 1996). Both procedures reduce the df available for the test of the intervention effect, and if the number of df is limited, the unmatched or unstratified analysis may be more powerful than the matched or stratified analysis. In that circumstance, it is to the investigator’s advantage to match or stratify in the design to achieve balance on potential confounders, but to ignore the matching or stratification in the analysis to improve power or reduce sample size (Diehr et al., 1995). The choice of whether to include the matching or stratification factor in the analysis should be made a priori based on sample size calculations comparing the matched or stratified analysis to the unmatched or unstratified analysis.

The choice between a priori matching and a priori stratification for balance should be guided by whether the investigator anticipates doing analyses that do not involve intervention effects. Donner et al., 2007 have warned against ignoring matching in analyses that do not involve intervention effects, e.g., in an analysis to examine the association between a risk factor and an outcome. Ignoring matching in the analysis in this situation can lead to an inflated type 1 error rate when the correlation between the matching factor and either the outcome or the risk factor is at least modest (>0.2) and the number of members per group is not large (<100). Stratification with strata of size four avoids this problem, and improves efficiency almost as much as matching. For this reason, stratification with strata of size four is a prudent strategy for balancing potential confounders across study conditions because it is almost as efficient as matching and it does not limit the range of analyses that can be applied to the data.

These studies are individually randomized group treatment trials (IRGTs), sometimes called partially clustered designs. While these trials are common, most investigators do not recognize the implications of this design. IRGTs always have a hierarchical structure in the intervention condition. Participants may receive some of their treatment in groups, or they may receive their intervention individually, but through a common interventionist or facilitator, whether in person or through a video or other virtual connection (Lee and Thompson, 2005b). There may or may not be a similar structure in the control condition, depending on the nature of the control condition. Whether it exists in one or both study conditions, the hierarchical structure requires that the positive ICC expected in the data be accounted for in the sample size estimation and in the data analysis. Any analysis that ignores the positive ICC or what may be limited df will have a type 1 error rate that is inflated, often badly (Baldwin et al., 2011; Bauer et al., 2008; Kahan and Morris, 2013;  Lee and Thompson, 2005b; Lee and Thompson, 2005a; Pals et al., 2008b; Pals et al., 2011; Pals et al., 2008a; Roberts and Roberts, 2005; Roberts and Walwyn, 2013).

The recommended solution to these challenges is similar to the solution recommended for GRTs. It is important to employ a priori matching or stratification to balance potential confounders if the number of assignment units is limited, to reflect the hierarchical or partially hierarchical structure of the design in the analytic plan, and to estimate the sample size for the IRGT based on realistic and data-based estimates of the ICC and the other parameters indicated by the analytic plan. Extra variation and limited df always reduce power, so it is essential to consider these factors while the study is being planned, and particularly as part of the sample size estimation.

No. In public health and medicine, ICCs in group- or cluster-randomized trials are often small, usually ranging from 0.01–0.05 (Moerbeek and Teerenstra, 2016). While it is tempting to ignore such small correlations, doing so risks an inflated type I error rate, and the risk is substantial both in GRTs (Campbell and Walters, 2014; Donner and Klar, 2000; Eldridge and Kerry, 2012; Hayes and Moulton, 2017; Murray, 1998) and in IRGTs (Baldwin et al., 2011; Bauer et al., 2008; Kahan and Morris, 2013; Lee and Thompson, 2005b; Lee and Thompson, 2005a; Pals et al., 2008b; Pals et al., 2011; Pals et al., 2008a; Roberts and Roberts, 2005; Roberts and Walwyn, 2013). The prudent course is to reflect all nested factors as random effects and to plan the study to have sufficient power given a proper analysis.

No. That is another tempting strategy that can risk an inflated type I error rate. The standard error for the variance component is not well estimated when the value is close to zero, and if the df are limited, the power will be limited. As such, it is likely that the result will suggest that the ICC or variance component is negligible, when ignoring it will inflate the type I error rate. The prudent course is to reflect all nested factors as random effects and to plan the study to have sufficient power given a proper analysis.