Use an IRGT if you can randomize individual participants but need to deliver the intervention in groups or through a shared intervention agent 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 shared intervention agent, it is more efficient and easier to use a traditional RCT.

There are no textbooks on IRGTs, but there are several papers (Baldwin et al., 2011; Lohr et al., 2014; Moerbeek, 2020; Murray et al., 2020; Pals et al., 2008; Roberts et al., 2016; Roberts and Roberts, 2005). There are also sources for information on power and sample size in IRGTs (Heo et al., 2017; Moerbeek, 2020; 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 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. These would be examples of changing from a single membership model to a multiple membership model. 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). Several authors provide methods for analyzing data to account for such changes (Candlish et al., 2018; Luo et al., 2015; Moyer et al., 2024; Roberts and Walwyn, 2013; Sterba, 2017).

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 coefficient of variation (CV) of group size is less than 0.23, such variation can be ignored (Eldridge et al., 2006). 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; Hemming et al., 2020; Lauer et al., 2015; Liu et al., 2021; Moerbeek and Teerenstra, 2016; van Breukelen et al., 2007; Wang et al., 2020; Xu et al., 2019; You et al., 2011). There are also a few 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 or who work with the same agent, and the number of participants in each group or for each agent. 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 several papers that address this question (Hemming et al., 2020; Moerbeek and Teerenstra, 2016; Pals et al., 2008). You can also use the sample size calculator in this section of the Research Methods Resources website.

It is true that this approach will improve the fidelity of implementation. The problem is that this single agent approach completely confounds the shared intervention agent with the study condition: everyone who gets the intervention gets exposed to that agent. In that situation, it is impossible to separate the effect of the intervention from the effect of the agent. It is possible that a charismatic agent 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. It is better to use an IRGT design in which multiple agents are used in the intervention condition so that variability due to agents can be separated from variability due to the intervention. 

In a parallel GRT, the groups are the units of assignment and are nested within study conditions, with different groups in each condition. In an IRGT, the groups are created in the intervention condition to facilitate delivery of the intervention; those groups may be defined by their instructor or facilitator, surgeon, therapist, or other agent, or they may be virtual groups. So long as the groups are nested within study conditions, they must be included in the analysis as levels of a random effect; ignoring them, or including them as levels of a fixed effect, will result in an inflated type 1 error rate. That is true for GRTs (Campbell and Walters, 2014; Donner and Klar, 2000; Eldridge and Kerry, 2012; Hayes and Moulton, 2017; Murray, 1998) and for IRGTs (Baldwin et al., 2011; Bauer et al., 2008; Candlish et al., 2018; Kahan and Morris, 2013a; Lee and Thompson, 2005a; Lee and Thompson, 2005b; Pals et al., 2008; Pals et al., 2011; Roberts and Roberts, 2005; Roberts and Walwyn, 2013). This is because nested factors must be modeled as random effects (

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This explanation also offers a potential solution – if the investigator can avoid nesting groups or agents within study conditions, the requirement to model those groups or agents as levels of a random effect disappears. The alternative to nesting is crossing, so if it is possible to cross the levels of the grouping factor with study conditions, then the grouping factor becomes a stratification factor and the investigator is free to model the grouping factor as a random effect, as a fixed effect, or to ignore the grouping factor in the analysis. –

For example, if schools are randomized to study conditions, the study is a GRT. But if students within schools are randomized to study conditions, the schools will be crossed with study conditions and we have a stratified RCT; the investigator can model the schools as a random effect, as a fixed effect, or ignore it in the analysis. As another example, if the therapists used to deliver the intervention in an IRGT also deliver an alternative intervention in the control condition, and their workloads in the two conditions are balanced, the therapists will be crossed with study condition and the investigator can model therapist as a random effect, as a fixed effect, or ignore therapist in the analysis. In either example, the choice between modeling the grouping factor as random, as fixed, or ignoring it will depend on factors like power and generalizability.

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 like 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 shared intervention agent, 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, (Baldwin et al., 2011; Bauer et al., 2008; Candlish et al., 2018; Kahan and Morris, 2013a; Lee and Thompson, 2005b; Lee and Thompson, 2005a; Pals et al., 2008; Pals et al., 2011; Roberts and Roberts, 2005; Roberts and Walwyn, 2013).

The recommended solution to these challenges is like 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 parallel 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; Candlish et al., 2018; Kahan and Morris, 2013a; Lee and Thompson, 2005b; Lee and Thompson, 2005a; Pals et al., 2011; Pals et al., 2008; 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 not significant, 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.

Whether or not multiple membership can be ignored depends on the design of the IRGT and prevalence of multiple membership. For crossed designs with continuous outcomes, simulation studies have shown multiple membership can be ignored in many settings if agents are represented using single membership analytic models (Moyer et al., 2024). If agent caseloads are balanced, accounting for agents can ignored altogether (Kahan and Morris, 2013a; Moyer et al., 2024). A disadvantage of a crossed design is the potential for contamination – if contamination is not a major concern, the benefits of the crossed design may outweigh this disadvantage (Hemming et al., 2021; Torgerson, 2001). Simulation studies of nested designs have shown poor performance in estimating ICC or maintaining nominal type I error rates when multiple membership is prevalent but ignored (Moyer et al., 2024; Roberts and Walwyn, 2013). When instances of multiple membership are infrequent or of very limited magnitude, it may be possible to employ single membership even in the nested case. However, even in cases where multiple membership is ignorable it is prudent to record all interactions a participant has with agents and fit a multiple membership analytic model, at least as a secondary analysis.