Statistical methods

Item 21b: Definition of who is included in each analysis (eg, all randomised participants), and in which group

Examples

“The primary statistical analyses were performed according to the treatment to which the participants were randomly assigned. The analyses of the efficacy and safety outcomes (other than adverse events) included all available data from all randomized participants who contributed at least 1 value after baseline for the outcome of interest. The data that were obtained after a participant enrolled in another trial of an investigational treatment were excluded from the analyses. However, the participant was included in the analyses if that participant contributed at least 1 value after baseline for the outcome of interest prior to enrolling in another trial [375]."

“Efficacy outcomes were assessed using intention-to-treat analysis (ie, the full set of all randomly assigned patients). Safety outcomes were assessed using the safety analysis set of all randomly allocated patients exposed to at least one dose of randomised intervention [376].

“Efficacy analyses and other exploratory analyses were performed in the full analysis set (defined as all patients randomly assigned to the study, including those who did not receive a dose of study treatment). Safety analyses were performed in the safety analysis set (defined as patients who received at least one dose of study treatment). The per protocol set was defined as all patients in the full analysis set who complied with the protocol in terms of exposure to study treatment, availability of tumour assessments, and absence of major protocol deviations likely to affect efficacy outcomes. Sensitivity analyses of the primary endpoint were performed on the per protocol analysis set [377]."

“The primary analysis population was defined as all participants who completed baseline and 36-week assessments. The primary analysis of the primary outcome, AMCA [amended motor club assessment] score at 36 weeks, followed a modified intention-to-treat approach, regardless of compliance to the intervention, but did exclude patients who were deemed ineligible after randomisation, those who withdrew from the trial and were unwilling for their previously collected data to be used, or those who did not provide baseline and week 36 measurements [378]."

Explanation

A key strength of a randomised trial design is the avoidance of bias when randomly allocating trial participants to interventions. To preserve the benefits of randomisation, all randomised participants are included in the analysis and retained in the group to which they were allocated. Meeting these two conditions defines an intention-to-treat analysis—which is widely recommended as the preferred analysis strategy [379-381]. However, strict adherence to an intention-to-treat analysis is often difficult to achieve owing to missing outcomes for some trial participants (item 21c) or non-adherence to the trial intervention protocol. While imputation of missing outcomes would allow an intention-to-treat analysis, it does not guarantee an avoidance of bias except under strong assumptions about the missing data which may be unknown.

Various strategies for performing intention-to-treat analyses in the presence of missing outcome data are available [382]. When the number of missing outcomes is not large, the analysis population could be all randomised participants with outcome observed (known as an “available case” population) under a plausible missing data mechanism, and sensitivity analyses could be performed exploring departures from this assumption (thereby using all randomised participants at least in sensitivity analyses) [382]. Concerns may arise when the frequency or the causes of dropping out differ between the intervention groups. Striving for intention-to-treat analysis by imputing values for participants with missing outcomes may lead to use of inadequate methods such as last observation carried forward [382-385].

Regardless of whether all randomised participants (completely observed outcomes or imputed outcomes) or a subset of randomised participants with observed outcomes are included in the primary analysis, the analysis population should be described. Authors often describe performing analyses on a “modified intention-to-treat” population to cover departures from a strict intention-to-treat that excludes participants who did not adequately adhere to the protocol such that they did not receive some minimum amount of the intervention—in such cases, what defines the minimum amount of the intervention should be explained (eg, those participants receiving at least one dose of the medication). It is also common to include analyses based on a per protocol population, which includes participants completing the study with no major protocol deviations. Excluding participants may compromise the randomisation and lead to biased estimates of treatment effects if appropriate methods are not used. Other analysis populations are possible (eg, a safety population), and their rationale and definition should be explained. Thus, authors should clearly define which participants are included in each analysis and in which intervention group and avoid terms such as “modified intention-to-treat” or “per protocol” analysis.