Cluster randomised controlled trials (c-RCT) are increasingly being used to evaluate the intended effects of complex interventions in primary care [1] and other health and social care settings [2]. The decision to choose cluster randomisation over individual patient randomisation is typically justified by the intervention being directed at the level of the cluster (practitioner, practice, hospital, etc.), or on the grounds of perceived risk of experimental contamination, or on cost, compliance, investigator cooperation, and other logistic considerations [3]. While c-RCT designs may offer a solution to these problems, and sometimes offer additional advantages (e.g. external validity), they also raise a number of specific methodological and ethical issues. Among these issues, vulnerability to selection bias is an important concern in c-RCT designs where individual participants are identified and recruited after randomisation, especially when the person identifying and recruiting participants is not blinded to allocation and the process of identification and/or recruitment is open to interpretation [4].

Prevention of bias is the ideal and a range of strategies have been proposed to minimise selection bias in the design and implementation phases of c-RCTs [5, 6]. However, in instances where these strategies are not, or cannot be, adopted, or where their success is not assured, it is important to carefully evaluate the potential role of selection bias in the interpretation of the trial findings. In the context of epidemiological studies, quantitative bias analysis (QBA) has been proposed as an approach to evaluating the role of bias in published research and an alternative to the traditional handling of this by qualitative judgements and educated guesses in the Discussion sections of articles [7–10]. Quantitative bias analysis involves quantifying the magnitude, direction, and effect of bias present in studies [11]. There are three types of bias that can be adjusted for; misclassification, unmeasured confounders, and selection bias which this paper will investigate. Selection bias occurs when the intervention and outcome are both conditioned on subject participation; a common problem in c-RCTs where subjects are not individually randomised. If all eligible participants do not get enrolled into the study and this is related to outcome and intervention, then any association found from the analyses conducted on the data with those who did contribute data will be different to any associations that would be found when using all eligible subjects [12]. The motivation for conducting a QBA is to adjust the estimate for the association between exposure/intervention and outcome for the presence of selection bias, induced by conditional participation.

To our knowledge, to date there has been little application of QBA to c-RCTs including the specific matter of how robust the findings are to difference in selection between intervention and control arms after randomisation. We conducted a small, non-systematic scoping review of Cochrane Library full-text papers published between 2013 and 2016 and reporting original findings c-RCTs available in the Cochrane Library. We chose Cochrane due to its broad scope of published trial papers. We identified a total of 35 trials; 13 commented on selection bias, of which four discussed its role on study findings, but none reported any formal quantitative evaluation of its role.

The aim of this paper was to apply quantitative bias techniques to a c-RCT whose design rendered it vulnerable to selection bias, in order to evaluate the extent to which different degrees of selection bias would modify the estimated effect of intervention and the conclusions drawn from it.

It is plausible that a selection (bias) OR of 1.2 to 1.4 towards higher-risk patient recruitment to the intervention compared to the control arm occurred within the POST trial. The imbalance in recruitment between the two arms could have introduced selection bias; however, it could also be down to chance. There could have been selection bias present in this study even if the number of patients in each arm had been the same.

To our knowledge the applications of QBA in the existing academic literature are few. The studies that have applied this methodology are cohort or case-control, and involve longitudinal data. In a study investigating the association between smoking and the development of multiple types of cancer, QBA adjusting for misclassification of smoking status was conducted. The results showed that the higher relative risks (RR) were consistently lower than the misclassification-adjusted estimates [17]. Another study investigated misclassification in a case-control setting. They looked into the association dietary patterns on the increase in risk of prostate cancer. After adjustment for misclassification they found slight differences in the ORs in that they were slightly higher than those observed, and that the simulation limits were nearly double the observed [18]. A recent paper involving the use of QBA adjusted for unmeasured confounding. This study looked into the effect an unmeasured confounder had on the association between firearm availability and suicide. Their study showed that the unmeasured confounder would need to be as strong a risk factor as the most potent currently known, such as psychopathology, and socio-economic factors to affect the observed results [19]. However, the authors did go on to suggest that quantifying the extent to which it may change observed results helps to strengthen the results themselves [19].

The results of previous studies, and this report, show the value of conducting a QBA for most kinds of bias present in studies and trials. By adjusting for bias researchers can have more confidence in the results that they are reporting rather than resorting to a theoretical comment in the Discussion section, and it can also help to strengthen the results reported in the study, thereby affecting policies which are built on those reported results [19]. There are other methods for quantifying bias in c-RCTs, notably by using propensity score (PS) methodology when analysing c-RCT data as a cohort [20–22]. Propensity scores are used to adjust the comparison between intervention and control for baseline imbalance in observed and unobserved patient-level characteristics. It is unclear whether QBA is superior to the PS approach. However, approaches that use baseline imbalances could be used to help choose plausible bias scenarios and parameters for QBA.

The main strength of this study is that it is the first that has applied QBA to a c-RCT, thereby providing a framework with which researchers can apply this analysis to c-RCTs where selection bias may be of concern. Another advantage of bias analysis is the flexibility that a researcher has when deciding the direction of the selection bias. In this example we hypothesised, based on observed evidence, that those with low pain/good prognosis were less likely to be recruited into the intervention arm; however, the converse is also plausible, i.e those with high pain were less likely to be recruited to the intervention arm. The bias parameters can be altered to reflect this line of thought.

However, there are a few limitations. The first is that the outcome, pain, had to be transformed into binary for the analysis. This results in a loss of information [23], and potentially an underestimation in the variability of results between the two treatment groups. Secondly, due to the nature of QBA the results could not be adjusted for anything other than the selection bias, hence the resulting ORs are not adjusted for common patient demographics such as age and gender.

Another main limitation to the approach of our evaluation is that no ‘true’ selection probabilities could be calculated as no follow-up questionnaires were sent to those who did not participate. This step, although useful in theoretical platforms, is perhaps less practically implemented in cases such as clinical trials where recruitment is often difficult. The source of the selection bias in this trial can only be hypothetical as voiced by the researchers and it would be impossible to find out if GPs in the control practices were more inclined to recruit different types of patients than those in the intervention due to the nature of the intervention treatment. Another limitation of this study surrounds the formula developed for simple bias analysis. It does not differentiate between data from patients not enrolled in the trial, and those who were lost to follow-up. We were unable to conclude the origin of any selection bias present in this study, whether down to the imbalance in recruitment or to genuine selection bias on the part of the recruiting GPs.

Quantitative bias analysis is a useful tool for insight into the sources of bias present in a trial; however, PBA as used in this study is largely subjective and will be prone to the same counter arguments as that of Bayesian analysis. There are many similarities between PBA and Bayesian methodology, as MacLehose and Gustafson have shown. In broad terms PBA is simply a Bayesian algorithm where the observed data is not updated with each iteration. In both cases one begins with a prior distribution from which iterative samples are taken. The main difference comes from the conditional posterior distribution, where in the Bayesian approach the result depends on the samples taken from the previous iteration of sampling, in PBA the values of the sampled bias parameters are limited to the observed data, hence certain values of bias parameters may be possible in Bayesian platforms, but would be impossible in PBA [24]. However, despite their subtle differences, in some cases PBA can be seen as a Bayesian analysis with a uniform prior [24].

An important area for future research would be to investigate and develop the use of QBA in trial settings, as all existing academic literature has been applied to observational studies. it is acknowledged that in some cases applying QBA to the results of studies results in no difference in the results; however, there have been examples where applying this methodology has provided insights into the effect of bias on the observed results [17, 18].

The POST trial presents a useful case example for illustrating the possible impact that selection bias has on the conclusions of a trial. Using this example we have shown how bias analysis can add to interpretation of results of a c-RCT and planning to routinely obtain empirical data from people excluded from c-RCTs would enhance the utility of bias analysis.

There was some evidence to suggest that if the assumptions underlying our range of selection bias scenarios were true then selection bias could have affected the results of the POST trial. Rather than being harmful it would appear more likely that there was no difference between the intervention treatment and the control. Evidence of extreme levels of selection of mild patients into the intervention group would be needed to judge that outcomes were actually better in the intervention group than in the control. Applying QBA to a trial provides researchers with more confidence and insight into the conclusions that were produced and should be incorporated into the analysis plan at the design stages of the trial.