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Reporting of Factorial Randomized Trials: Extension of the CONSORT 2010 Statement. IMPORTANCE: Transparent reporting of randomized trials is essential to facilitate critical appraisal and interpretation of results. Factorial trials, in which 2 or more interventions are assessed in the same set of participants, have unique methodological considerations. However, reporting of factorial trials is suboptimal. OBJECTIVE: To develop a consensus-based extension to the Consolidated Standards of Reporting Trials (CONSORT) 2010 Statement for factorial trials. DESIGN: Using the Enhancing the Quality and Transparency of Health Research (EQUATOR) methodological framework, the CONSORT extension for factorial trials was developed by (1) generating a list of reporting recommendations for factorial trials using a scoping review of methodological articles identified using a MEDLINE search (from inception to May 2019) and supplemented with relevant articles from the personal collections of the authors; (2) a 3-round Delphi survey between January and June 2022 to identify additional items and assess the importance of each item, completed by 104 panelists from 14 countries; and (3) a hybrid consensus meeting attended by 15 panelists to finalize the selection and wording of items for the checklist. FINDINGS: This CONSORT extension for factorial trials modifies 16 of the 37 items in the CONSORT 2010 checklist and adds 1 new item. The rationale for the importance of each item is provided. Key recommendations are (1) the reason for using a factorial design should be reported, including whether an interaction is hypothesized, (2) the treatment groups that form the main comparisons should be clearly identified, and (3) for each main comparison, the estimated interaction effect and its precision should be reported. CONCLUSIONS AND RELEVANCE: This extension of the CONSORT 2010 Statement provides guidance on the reporting of factorial randomized trials and should facilitate greater understanding of and transparency in their reporting.

This CONSORT extension development occurred in parallel with the Standard Protocol Items: Recommendations for Interventional Trials (SPIRIT) extension for factorial trials.20 First, we performed a scoping review using a MEDLINE search from inception to May 2019 to create an initial list of reporting recommendations applicable to factorial trials. Second, we performed a 3-round Delphi survey (January to June 2022; 104 panelists from 14 countries) to identify additional items and assess the importance of each item. Third, an expert consensus meeting (September 6-7, 2022; 15 panelists) was held to establish the final checklist. Item wording was finalized after the meeting through iterative discussions.

The checklist for the reporting of factorial randomized trials includes 16 modified items and 1 new item (Table 2). Reporting items for abstracts of factorial randomized trials are provided in Table 3.21,22 The scoping review identified 31 recommendations pertinent to reporting factorial trials, which were evaluated in the Delphi survey. Thirty-two recommendations met the criteria to be evaluated at the consensus meeting (1 recommendation was added in round 2 of the Delphi survey). Given the variation in terminology used to describe factorial trials, items in this statement have been written to replace the original CONSORT items. Users are advised to refer to definitions of key terms in Box 1. This article contains brief explanations of the modified items in the CONSORT factorial extension. Details for interpretation of each item, and examples of good reporting, will be presented in a separate “explanation and elaboration” article. Notifying readers of the factorial design alerts them to potential implications of the design for analysis and interpretation.2,4,5,8,23,24 Different research hypotheses require different methodology. By clarifying the rationale for using the factorial design, as well as whether an interaction is hypothesized, readers are signposted toward the key objectives and alerted to the assumptions and methodological features required.1,4–6,24

Notifying readers of the factorial design alerts them to potential implications of the design for analysis and interpretation.2,4,5,8,23,24 Different research hypotheses require different methodology. By clarifying the rationale for using the factorial design, as well as whether an interaction is hypothesized, readers are signposted toward the key objectives and alerted to the assumptions and methodological features required.1,4–6,24 In factorial trials, interventions can be compared in different ways. In a 2 × 2 factorial trial with factors A and B, the treatment effect for intervention A vs its comparator can be estimated by comparing (1) participants randomized to receive A vs not A; (2) those randomized to receive A alone vs neither A nor B; or (3) those randomized to receive A plus B vs B alone. These alternative comparisons can target different estimands and are underpinned by different assumptions (Box 2).4,6,11 An estimand describes the target treatment effect to be estimated from the trial. Most factorial trials use a “full” factorial design, whereby all participants are eligible to be randomized to all combinations of factors and factor levels.9,25,26 Other designs include “fractional” factorial designs (where some combinations of factors are omitted) and “partial” factorial designs (where some participants are only eligible to be randomized to certain factors), which require alternative methodology.1,27

mized to all combinations of factors and factor levels.9,25,26 Other designs include “fractional” factorial designs (where some combinations of factors are omitted) and “partial” factorial designs (where some participants are only eligible to be randomized to certain factors), which require alternative methodology.1,27 Differences in eligibility criteria across factors can have implications for the design and analysis and can increase the risk of bias if not handled properly. For instance, participants who are not eligible for randomization to a specific factor should not be included in the comparison for that factor, because their inclusion means the analysis is no longer based on a randomized comparison, which can lead to confounding bias.1,27 Sample size calculations for factorial designs are more complicated than in standard parallel-group designs. In some factorial trials, the planned main comparisons may require different sample sizes if they are expected to produce different effect sizes or if the choice of primary outcome varies for each factor.6,28 If an interaction is hypothesized, the sample size may need to be increased.1,2,6,24 Comparison: What treatment groups will be compared against each other. For example, the effect of intervention A may be estimated by comparing all participants randomized to active A (treatment groups active A plus high-dose B and active A plus low-dose B) with all participants randomized to placebo A (treatment groups placebo A plus high-dose B and placebo A plus low-dose B).

each other. For example, the effect of intervention A may be estimated by comparing all participants randomized to active A (treatment groups active A plus high-dose B and active A plus low-dose B) with all participants randomized to placebo A (treatment groups placebo A plus high-dose B and placebo A plus low-dose B). Estimand: A description of the treatment effect to be estimated from the trial, including specification of the treatment conditions, population, end point, summary measure, and strategies to handle intercurrent events. Factorial trials should additionally specify how the other factor(s) are to be handled in the estimand (eg, whether interest lies in the effect of active A plus low-dose B vs placebo A plus low-dose B or else active A plus high-dose B vs placebo A plus high-dose B). Factor: Each intervention and its comparator(s) together comprise a factor (eg, active A and placebo A together comprise one factor and high-dose B and low-dose B together make up the other factor). Factorial analysis: Also called an “at-the-margins” analysis. All participants randomized to active A (treatment groups active A plus high-dose B and active A plus low-dose B) are compared against all those randomized to placebo A (placebo A plus high-dose B and placebo A plus low-dose B) and similarly for the factor B comparison. Factorial trial: When 2 or more interventions are assessed in the same participants within a single study.

Factorial analysis: Also called an “at-the-margins” analysis. All participants randomized to active A (treatment groups active A plus high-dose B and active A plus low-dose B) are compared against all those randomized to placebo A (placebo A plus high-dose B and placebo A plus low-dose B) and similarly for the factor B comparison. Factorial trial: When 2 or more interventions are assessed in the same participants within a single study. Fractional factorial design: Some combinations of factors are omitted. For example, in a trial with 3 factors (A, B, and C), participants may be randomized to 4 of the 8 possible combinations. Full factorial design: All factors and levels are combined so the design comprises all possible combinations of factor levels and all participants are eligible to be randomized for each factor.

Fractional factorial design: Some combinations of factors are omitted. For example, in a trial with 3 factors (A, B, and C), participants may be randomized to 4 of the 8 possible combinations. Full factorial design: All factors and levels are combined so the design comprises all possible combinations of factor levels and all participants are eligible to be randomized for each factor. Interaction: Interactions occur when the effect of one treatment depends on whether participants also receive the other treatment (eg, active A may be less effective when used alongside high-dose B than when used with low-dose B). Interactions may occur for biological or social reasons (eg, if receipt of one treatment affects the mechanism of action for the other). Interactions may also occur due to choice of analysis scale (eg, active A may be equally effective with high-dose B as with low-dose B when measured on the risk ratio scale, but less effective on the risk difference scale). Trials interested in evaluating whether treatments interact are typically interested in biological/social interactions, while trials that use analyses that require an assumption of no interaction are affected by any type of interaction. Level within factors: The specific interventions within a factor are the levels (eg, active A and placebo A are the 2 levels of factor A). Main comparison(s): The comparison(s) that will primarily be used to draw conclusions about effectiveness of each intervention.

Interaction: Interactions occur when the effect of one treatment depends on whether participants also receive the other treatment (eg, active A may be less effective when used alongside high-dose B than when used with low-dose B). Interactions may occur for biological or social reasons (eg, if receipt of one treatment affects the mechanism of action for the other). Interactions may also occur due to choice of analysis scale (eg, active A may be equally effective with high-dose B as with low-dose B when measured on the risk ratio scale, but less effective on the risk difference scale). Trials interested in evaluating whether treatments interact are typically interested in biological/social interactions, while trials that use analyses that require an assumption of no interaction are affected by any type of interaction. Level within factors: The specific interventions within a factor are the levels (eg, active A and placebo A are the 2 levels of factor A). Main comparison(s): The comparison(s) that will primarily be used to draw conclusions about effectiveness of each intervention. Multiarm analysis: Also called an “inside-the-table” analysis. The treatment groups active A plus low-dose B, placebo A plus high-dose B, and active A plus high-dose B are each compared against placebo A plus low-dose B (double-control). Treatment group: The unique combinations of factors and levels to which participants can be randomized (eg, active A plus high-dose B comprise one treatment group and active A plus low-dose B another).

Multiarm analysis: Also called an “inside-the-table” analysis. The treatment groups active A plus low-dose B, placebo A plus high-dose B, and active A plus high-dose B are each compared against placebo A plus low-dose B (double-control). Treatment group: The unique combinations of factors and levels to which participants can be randomized (eg, active A plus high-dose B comprise one treatment group and active A plus low-dose B another). Partial factorial design: Some participants are not randomized to certain factors. For example, a subset of participants will only be randomized between active A vs control A and will receive control B automatically. The plan for interim analyses and subsequent stopping guidelines may be different for each factor.27 If one factor is stopped before the other, there may be implications for randomization, choice of comparator, or analysis.1,27,29 Participants may be randomized to factors at different time points (eg, for factor A at diagnosis of disease then for factor B after treatment A is complete). The time point of randomization for each factor may inform key design features, such as the baseline period, duration of follow-up, and likelihood of treatments interacting.2 Extension for factorial trials: Statistical methods used for each main comparison for primary and secondary outcomes, including:

Participants may be randomized to factors at different time points (eg, for factor A at diagnosis of disease then for factor B after treatment A is complete). The time point of randomization for each factor may inform key design features, such as the baseline period, duration of follow-up, and likelihood of treatments interacting.2 Extension for factorial trials: Statistical methods used for each main comparison for primary and secondary outcomes, including: Whether the target treatment effect for each main comparison pertains to the effect in the presence or absence of other factors The statistical methods alone are not always sufficient to allow readers to understand the exact treatment effect (estimand) being estimated.30–32 In factorial trials, the treatment groups used for comparison are not always the same as those in which there is interest in estimating the treatment effect.11,33 For example, many factorial trials use a factorial analysis to compare “all A” vs “all not A” for reasons of efficiency, even though interest really lies in the effect of A alone vs control (the effect of A in the absence of B) or, alternatively, the effect of A plus B vs B alone (the effect of A in the presence of B) if treatment B has been demonstrated to be effective.11 A clear description of the target treatment effect, including whether it pertains to the effect in the presence or absence of other factors, allows readers to understand the exact question being addressed.11,30,31,34

B alone (the effect of A in the presence of B) if treatment B has been demonstrated to be effective.11 A clear description of the target treatment effect, including whether it pertains to the effect in the presence or absence of other factors, allows readers to understand the exact question being addressed.11,30,31,34 Approach to analysis, such as factorial or multiarm Different statistical methods can be used to analyze a factorial trial depending on the estimand of interest. In a factorial (or “at-the-margins”) analysis, all participants randomized to factor A (A alone and A plus B) are compared with all those not randomized to A (B alone and double-control).2,4,6,11,35,36 Alternatively, in a multiarm (or “inside-the-table”) analysis, the trial is analyzed as if a multiarm design had been used.2,4–6,10–12,17,23,35,36 The 2 approaches offer different benefits and require different assumptions (Box 2). How the approach was chosen, such as prespecified or based on estimated interaction Using a test of interaction to guide the choice of analysis can introduce bias and is not recommended.17 Clarification of whether the final analysis approach was prespecified based on prior knowledge or an assumption of no interaction or chosen based on the size of the estimated interaction helps alert readers to any risk of bias associated with the analysis approach. Method(s) used to evaluate statistical interaction(s)

Using a test of interaction to guide the choice of analysis can introduce bias and is not recommended.17 Clarification of whether the final analysis approach was prespecified based on prior knowledge or an assumption of no interaction or chosen based on the size of the estimated interaction helps alert readers to any risk of bias associated with the analysis approach. Method(s) used to evaluate statistical interaction(s) It is recommended practice to evaluate the presence of statistical interactions, either because analyses rely on the assumption that treatments do not interact or because the interaction is itself of direct interest.2,4–6,10,11,24 The presence of an interaction may depend on the scale of analysis (eg, an interaction may be present on the risk difference scale, but not the risk ratio scale), so careful consideration should be given to the choice of scale. Reporting details of how interaction(s) were evaluated, and on what scale, enables readers to understand the appropriateness of method(s). If factorial approach used, whether factors were adjusted for each other Factorial analyses can be adjusted for whether participants were randomized to the other factor(s) by including a term for this in the statistical model.2,6,11,28 This can increase statistical power and, in some cases, failure to adjust for the other factors can introduce bias for certain estimands.11 If applicable, how nonconcurrent recruitment to factors was handled

Factorial analyses can be adjusted for whether participants were randomized to the other factor(s) by including a term for this in the statistical model.2,6,11,28 This can increase statistical power and, in some cases, failure to adjust for the other factors can introduce bias for certain estimands.11 If applicable, how nonconcurrent recruitment to factors was handled Nonconcurrent recruitment, in which certain participants are not randomized for some factors (eg, if the trial used a partial factorial design or recruitment to one factor is paused or terminated), can induce bias if not handled correctly during analysis (see item 4a).1,27 For factorial trials, especially those beyond a 2 × 2 design, it can be difficult for readers to identify the relevant participant flow because this information may differ across main comparisons. Presenting this information for each main comparison increases clarity and understanding.2,4–6,8,10,35 If periods of recruitment are different across factors, participants enrolled after one factor has stopped recruitment will only be eligible to be randomized for the ongoing factor(s), posing similar statistical issues as in a partial factorial design (see CONSORT item 4a).27 An estimand describes a research question a trial sets out to address (Box 1). Different types of estimands may be specified for factorial trials depending on the aims. An estimand for the effect of treatment A could be defined based on a comparison of treatment A vs not A if no one received treatment B or as the effect of A vs not A if everyone received treatment B.

An estimand describes a research question a trial sets out to address (Box 1). Different types of estimands may be specified for factorial trials depending on the aims. An estimand for the effect of treatment A could be defined based on a comparison of treatment A vs not A if no one received treatment B or as the effect of A vs not A if everyone received treatment B. The former may be more common for “2-in-1” factorial trials because it provides the effect of treatment A that would be seen in a parallel-group design where treatment B is not used. However, either estimand may be of interest. Alternatively, an estimand for treatment A could also be defined based on the effect of A vs not A averaged across those who do and those who do not receive treatment B.a Because this estimand does not typically reflect how treatments are used in practice, other choices are usually more relevant for 2-in-1 trials. For trials in which the aim is to determine whether treatments interact, the estimand may be based around the difference between the effect of treatment A if no one received treatment B vs the effect if everyone received treatment B. The method of statistical analysis should be determined by the estimand (ie, research question).

For trials in which the aim is to determine whether treatments interact, the estimand may be based around the difference between the effect of treatment A if no one received treatment B vs the effect if everyone received treatment B. The method of statistical analysis should be determined by the estimand (ie, research question). Two-in-1 trials typically use a factorial analysis because this realizes the efficiency gains inherent to the factorial design. However, because this analysis averages across the 2 strata of those randomized to receive and not receive B, it only estimates the “effect of treatment A if no one receives B” if treatments A and B do not interact. When treatments do interact, it estimates the mean effect of A across the strata of B. Therefore, assessment of the interaction is essential to determine whether the factorial analysis is estimating the desired estimand. A multiarm (“inside-the-table”) analysis could also be used to estimate the effect of treatment A if no one receives B, and is unbiased regardless of whether treatments A and B interact. However, it does not realize the efficiency gained through using a factorial design, so it is less frequently used for 2-in-1 trials. aThis averaging could correspond to the study proportions randomized to receive treatment B and not B or to some other proportions defined by the investigators. The exact method of determining the mean therefore needs to be made explicit.

A multiarm (“inside-the-table”) analysis could also be used to estimate the effect of treatment A if no one receives B, and is unbiased regardless of whether treatments A and B interact. However, it does not realize the efficiency gained through using a factorial design, so it is less frequently used for 2-in-1 trials. aThis averaging could correspond to the study proportions randomized to receive treatment B and not B or to some other proportions defined by the investigators. The exact method of determining the mean therefore needs to be made explicit. bA factorial analysis can be used to estimate either (1) the effect of A if no one received B; (2) the effect of A if everyone received B; or (3) the effect of A averaged over those who received and did not receive B according to the study proportions. The first 2 of these estimates require the assumption of no interaction, but the analysis for the third does not. A multiarm analysis can be used to estimate by either comparing A alone vs double-control (as described above) or comparing A plus B vs B alone. These do not require the assumption of no interaction. If interest lies in the effect of A averaged over those who do and do not receive B according to proportions other than the study proportions, this could be estimated by first estimating the effect of A separately in both stratum (those who receive and do not receive B) then taking a weighted average of these according to the desired proportions. This analysis does not require the assumption of no interaction.11

o proportions other than the study proportions, this could be estimated by first estimating the effect of A separately in both stratum (those who receive and do not receive B) then taking a weighted average of these according to the desired proportions. This analysis does not require the assumption of no interaction.11 Extension for factorial trials: For each primary and secondary outcome, results for each main comparison, the estimated effect size, and its precision (such as 95% CI) For each primary outcome, the estimated interaction effect and its precision For factorial trials predicated on the assumption of no interaction (2-in-1 trials) or those in which the interaction is of main interest, evaluation of interactions is essential to interpretation.2,4–6,10,11,24 The size of the estimated interaction effect should be presented along with a measure of precision, such as the 95% CI.2,5,6 For trials in which evaluation of interaction(s) is not deemed essential, this decision should be justified. Outcomes and other postrandomization data such as adherence, harms, and participant flow may be affected when treatments interact.26 Presentation of such data by treatment group (eg, groups A alone, B alone, A plus B, and double-control in a 2 × 2 trial), in addition to presentation by main comparisons, allows readers to assess to what extent such data may be unduly influenced by interactions due to the factorial design.3–6,8,10

Different research hypotheses require different methodology. By clarifying the rationale for using the factorial design, as well as whether an interaction is hypothesized, readers are signposted toward the key objectives and alerted to the assumptions and methodological features required.1,4–6,24

In factorial trials, interventions can be compared in different ways. In a 2 × 2 factorial trial with factors A and B, the treatment effect for intervention A vs its comparator can be estimated by comparing (1) participants randomized to receive A vs not A; (2) those randomized to receive A alone vs neither A nor B; or (3) those randomized to receive A plus B vs B alone. These alternative comparisons can target different estimands and are underpinned by different assumptions (Box 2).4,6,11 An estimand describes the target treatment effect to be estimated from the trial.

Most factorial trials use a “full” factorial design, whereby all participants are eligible to be randomized to all combinations of factors and factor levels.9,25,26 Other designs include “fractional” factorial designs (where some combinations of factors are omitted) and “partial” factorial designs (where some participants are only eligible to be randomized to certain factors), which require alternative methodology.1,27

Differences in eligibility criteria across factors can have implications for the design and analysis and can increase the risk of bias if not handled properly. For instance, participants who are not eligible for randomization to a specific factor should not be included in the comparison for that factor, because their inclusion means the analysis is no longer based on a randomized comparison, which can lead to confounding bias.1,27

Sample size calculations for factorial designs are more complicated than in standard parallel-group designs. In some factorial trials, the planned main comparisons may require different sample sizes if they are expected to produce different effect sizes or if the choice of primary outcome varies for each factor.6,28 If an interaction is hypothesized, the sample size may need to be increased.1,2,6,24 Comparison: What treatment groups will be compared against each other. For example, the effect of intervention A may be estimated by comparing all participants randomized to active A (treatment groups active A plus high-dose B and active A plus low-dose B) with all participants randomized to placebo A (treatment groups placebo A plus high-dose B and placebo A plus low-dose B). Estimand: A description of the treatment effect to be estimated from the trial, including specification of the treatment conditions, population, end point, summary measure, and strategies to handle intercurrent events. Factorial trials should additionally specify how the other factor(s) are to be handled in the estimand (eg, whether interest lies in the effect of active A plus low-dose B vs placebo A plus low-dose B or else active A plus high-dose B vs placebo A plus high-dose B). Factor: Each intervention and its comparator(s) together comprise a factor (eg, active A and placebo A together comprise one factor and high-dose B and low-dose B together make up the other factor).

Estimand: A description of the treatment effect to be estimated from the trial, including specification of the treatment conditions, population, end point, summary measure, and strategies to handle intercurrent events. Factorial trials should additionally specify how the other factor(s) are to be handled in the estimand (eg, whether interest lies in the effect of active A plus low-dose B vs placebo A plus low-dose B or else active A plus high-dose B vs placebo A plus high-dose B). Factor: Each intervention and its comparator(s) together comprise a factor (eg, active A and placebo A together comprise one factor and high-dose B and low-dose B together make up the other factor). Factorial analysis: Also called an “at-the-margins” analysis. All participants randomized to active A (treatment groups active A plus high-dose B and active A plus low-dose B) are compared against all those randomized to placebo A (placebo A plus high-dose B and placebo A plus low-dose B) and similarly for the factor B comparison. Factorial trial: When 2 or more interventions are assessed in the same participants within a single study. Fractional factorial design: Some combinations of factors are omitted. For example, in a trial with 3 factors (A, B, and C), participants may be randomized to 4 of the 8 possible combinations. Full factorial design: All factors and levels are combined so the design comprises all possible combinations of factor levels and all participants are eligible to be randomized for each factor.

Multiarm analysis: Also called an “inside-the-table” analysis. The treatment groups active A plus low-dose B, placebo A plus high-dose B, and active A plus high-dose B are each compared against placebo A plus low-dose B (double-control). Treatment group: The unique combinations of factors and levels to which participants can be randomized (eg, active A plus high-dose B comprise one treatment group and active A plus low-dose B another). Partial factorial design: Some participants are not randomized to certain factors. For example, a subset of participants will only be randomized between active A vs control A and will receive control B automatically.

The plan for interim analyses and subsequent stopping guidelines may be different for each factor.27 If one factor is stopped before the other, there may be implications for randomization, choice of comparator, or analysis.1,27,29

Participants may be randomized to factors at different time points (eg, for factor A at diagnosis of disease then for factor B after treatment A is complete). The time point of randomization for each factor may inform key design features, such as the baseline period, duration of follow-up, and likelihood of treatments interacting.2

Extension for factorial trials: Statistical methods used for each main comparison for primary and secondary outcomes, including: Whether the target treatment effect for each main comparison pertains to the effect in the presence or absence of other factors The statistical methods alone are not always sufficient to allow readers to understand the exact treatment effect (estimand) being estimated.30–32 In factorial trials, the treatment groups used for comparison are not always the same as those in which there is interest in estimating the treatment effect.11,33 For example, many factorial trials use a factorial analysis to compare “all A” vs “all not A” for reasons of efficiency, even though interest really lies in the effect of A alone vs control (the effect of A in the absence of B) or, alternatively, the effect of A plus B vs B alone (the effect of A in the presence of B) if treatment B has been demonstrated to be effective.11 A clear description of the target treatment effect, including whether it pertains to the effect in the presence or absence of other factors, allows readers to understand the exact question being addressed.11,30,31,34

Factorial analyses can be adjusted for whether participants were randomized to the other factor(s) by including a term for this in the statistical model.2,6,11,28 This can increase statistical power and, in some cases, failure to adjust for the other factors can introduce bias for certain estimands.11 If applicable, how nonconcurrent recruitment to factors was handled Nonconcurrent recruitment, in which certain participants are not randomized for some factors (eg, if the trial used a partial factorial design or recruitment to one factor is paused or terminated), can induce bias if not handled correctly during analysis (see item 4a).1,27

For factorial trials, especially those beyond a 2 × 2 design, it can be difficult for readers to identify the relevant participant flow because this information may differ across main comparisons. Presenting this information for each main comparison increases clarity and understanding.2,4–6,8,10,35

If periods of recruitment are different across factors, participants enrolled after one factor has stopped recruitment will only be eligible to be randomized for the ongoing factor(s), posing similar statistical issues as in a partial factorial design (see CONSORT item 4a).27 An estimand describes a research question a trial sets out to address (Box 1). Different types of estimands may be specified for factorial trials depending on the aims. An estimand for the effect of treatment A could be defined based on a comparison of treatment A vs not A if no one received treatment B or as the effect of A vs not A if everyone received treatment B. The former may be more common for “2-in-1” factorial trials because it provides the effect of treatment A that would be seen in a parallel-group design where treatment B is not used. However, either estimand may be of interest. Alternatively, an estimand for treatment A could also be defined based on the effect of A vs not A averaged across those who do and those who do not receive treatment B.a Because this estimand does not typically reflect how treatments are used in practice, other choices are usually more relevant for 2-in-1 trials. For trials in which the aim is to determine whether treatments interact, the estimand may be based around the difference between the effect of treatment A if no one received treatment B vs the effect if everyone received treatment B. The method of statistical analysis should be determined by the estimand (ie, research question).

An estimand describes a research question a trial sets out to address (Box 1). Different types of estimands may be specified for factorial trials depending on the aims. An estimand for the effect of treatment A could be defined based on a comparison of treatment A vs not A if no one received treatment B or as the effect of A vs not A if everyone received treatment B. The former may be more common for “2-in-1” factorial trials because it provides the effect of treatment A that would be seen in a parallel-group design where treatment B is not used. However, either estimand may be of interest. Alternatively, an estimand for treatment A could also be defined based on the effect of A vs not A averaged across those who do and those who do not receive treatment B.a Because this estimand does not typically reflect how treatments are used in practice, other choices are usually more relevant for 2-in-1 trials. For trials in which the aim is to determine whether treatments interact, the estimand may be based around the difference between the effect of treatment A if no one received treatment B vs the effect if everyone received treatment B.

The method of statistical analysis should be determined by the estimand (ie, research question). Two-in-1 trials typically use a factorial analysis because this realizes the efficiency gains inherent to the factorial design. However, because this analysis averages across the 2 strata of those randomized to receive and not receive B, it only estimates the “effect of treatment A if no one receives B” if treatments A and B do not interact. When treatments do interact, it estimates the mean effect of A across the strata of B. Therefore, assessment of the interaction is essential to determine whether the factorial analysis is estimating the desired estimand. A multiarm (“inside-the-table”) analysis could also be used to estimate the effect of treatment A if no one receives B, and is unbiased regardless of whether treatments A and B interact. However, it does not realize the efficiency gained through using a factorial design, so it is less frequently used for 2-in-1 trials. aThis averaging could correspond to the study proportions randomized to receive treatment B and not B or to some other proportions defined by the investigators. The exact method of determining the mean therefore needs to be made explicit.

Extension for factorial trials: For each primary and secondary outcome, results for each main comparison, the estimated effect size, and its precision (such as 95% CI) For each primary outcome, the estimated interaction effect and its precision For factorial trials predicated on the assumption of no interaction (2-in-1 trials) or those in which the interaction is of main interest, evaluation of interactions is essential to interpretation.2,4–6,10,11,24 The size of the estimated interaction effect should be presented along with a measure of precision, such as the 95% CI.2,5,6 For trials in which evaluation of interaction(s) is not deemed essential, this decision should be justified.

For factorial trials predicated on the assumption of no interaction (2-in-1 trials) or those in which the interaction is of main interest, evaluation of interactions is essential to interpretation.2,4–6,10,11,24 The size of the estimated interaction effect should be presented along with a measure of precision, such as the 95% CI.2,5,6 For trials in which evaluation of interaction(s) is not deemed essential, this decision should be justified.

Outcomes and other postrandomization data such as adherence, harms, and participant flow may be affected when treatments interact.26 Presentation of such data by treatment group (eg, groups A alone, B alone, A plus B, and double-control in a 2 × 2 trial), in addition to presentation by main comparisons, allows readers to assess to what extent such data may be unduly influenced by interactions due to the factorial design.3–6,8,10

This extension to the CONSORT 2010 Statement provides guidance for reporting factorial trials. The extension checklist represents the minimum essential requirements for reporting of factorial trials; for some trials there will be additional items that are important to report. For instance, if primary or secondary outcomes differ by factor, this should be reported. Similarly, if multiple testing is deemed to be an issue, authors should report how this was handled. This extension was developed in conjunction with the SPIRIT extension for factorial trials. Together, these guidelines provide a framework for cohesive reporting from the trial protocol to publication of results. The latest version of this and other CONSORT statements can be found online (https://www.equator-network.org/). This study has several limitations. First, this extension was developed for studies in which results for each factor would be published simultaneously in the same article. This may not always be feasible, for instance, due to the early stopping of one factor or because each factor requires different durations of follow-up. In this case, we recommend that each publication follows the checklist as far as possible, while recognizing that the information for some items might differ. For example, each article could report how the sample size was determined for the relevant comparison, rather than the sample size calculations for each comparison (although each calculation would need to clarify whether an interaction was assumed).

e, while recognizing that the information for some items might differ. For example, each article could report how the sample size was determined for the relevant comparison, rather than the sample size calculations for each comparison (although each calculation would need to clarify whether an interaction was assumed). Second, although the EQUATOR guidelines were followed to develop this guideline, Delphi respondents were self-selecting and consensus meeting panelists were purposively identified based on their expertise. Therefore, although results represent the views of a large, multinational group of experts and end users, the views of individuals not well represented by the Delphi survey or consensus meeting panelists may differ. However, the systematic and evidence-based approach used to develop this guideline, including a rigorous scoping review, should help mitigate the potential effects of these limitations.

This study has several limitations. First, this extension was developed for studies in which results for each factor would be published simultaneously in the same article. This may not always be feasible, for instance, due to the early stopping of one factor or because each factor requires different durations of follow-up. In this case, we recommend that each publication follows the checklist as far as possible, while recognizing that the information for some items might differ. For example, each article could report how the sample size was determined for the relevant comparison, rather than the sample size calculations for each comparison (although each calculation would need to clarify whether an interaction was assumed). Second, although the EQUATOR guidelines were followed to develop this guideline, Delphi respondents were self-selecting and consensus meeting panelists were purposively identified based on their expertise. Therefore, although results represent the views of a large, multinational group of experts and end users, the views of individuals not well represented by the Delphi survey or consensus meeting panelists may differ. However, the systematic and evidence-based approach used to develop this guideline, including a rigorous scoping review, should help mitigate the potential effects of these limitations.

This extension of the CONSORT 2010 Statement provides specific guidance for the reporting of factorial randomized trials to facilitate greater transparency and completeness in the reporting of these trials.