there is indeed a difference.
In contrast, the difficulty with analysing a trial by the treatment patients actually received is that we do not know the direction of the bias. Clearly if there are relatively few patients who do not receive their allocated intervention, then this is not likely to be a major issue. Conversely, if the numbers are large, then this would be a major concern and may render the trial results untrustworthy.
One procedure that was once in widespread use was for the investigating team to review the trial data in detail after the protocol treatment and follow‐up were complete and all the trial‐specific information collected so as to decide which patients should be in the final comparison. This review would, for example, retrospectively check that all the patient eligibility criteria were satisfied and that there had been no important protocol deviations whilst on treatment. Only if eligibility and compliance to protocol (however defined) were confirmed would the subject be deemed eligible for the analysis. Usually, this review would not be blind to the treatment received, and even if the trial were double‐blind, there may still be clues once the data are examined in detail as to which treatment is which.
One problem is that this process tends to selectively exclude patients with the more severe disease. Evidence for selective exclusion of patients following such reviews is provided by Machin, Stenning, Parmar, et al. (1997) who examined the published and pioneering portfolio of the early randomised trials conducted by the UK Medical Research Council in patients with cancer. They showed that the earlier publications systematically excluded patients from analysis and hence reported on fewer patients in the more aggressive treatment arm, despite a 1 : 1 randomisation. Thus, for example, any patient who had difficulties with this treatment, perhaps the sicker patients, were not included in the assessment of its efficacy and this systematic exclusion would tend to bias the results in its favour.
2.9.1.2 Per‐protocol
However, in certain circumstances, a per‐protocol summary of the trial results may be more relevant. In such an analysis, the comparison is made only in those patients who comply (which has to be carefully defined in advance) with the treatment allocated. One example of a per‐protocol analysis is if the toxicity and/or side effects profile of a new agent are to be compared. In this circumstance, an ITT analysis including those patients who were randomised to the drug but then did not receive it (for whatever reason) could seriously underestimate the true scale of the relative safety profiles. If a per‐protocol analysis is appropriate for such endpoints, then the trial protocol should state that such an analysis is intended from the onset. One situation where a per‐protocol analysis is important is when reporting the results of non‐inferiority trials that we discuss in Chapter 15.
2.9.2 Trial publication
Once it is clear which patients are to be included in the final analysis, any exclusions after randomisation should be accounted for, described and justified in concordance with the CONSORT statement. Only then can work on the analysis and the trial publication be started. However, it is usually expedient to plan and prepare preliminary analyses prior to the final endpoint analysis, so that the results of the trial can be disseminated with the minimum of delay. Since the structure of research publications often takes a familiar format (indeed investigators should have a target clinical journal in mind even at the design stage), key items can be prepared in advance and some of these will be based on sections of the trial protocol itself as we will list in Figure 3.1. If nothing else, the protocol will provide much of the text outlining the background and purpose of the trial, the details of eligible patients, the interventions studied, the randomisation process, a sample size justification, key elements of the analytical methods and a list of some important references. Further, if the trial progress is monitored regularly with feed‐back reports to the investigating team, then these reports can form the basis for some tabular and graphical presentations that will be included in the final publication. Clearly, the responsible writing committee will have to amend and update some of these details as appropriate and the eventual presentation of results and ultimate discussion will depend on the trial findings.
2.10 Technical details
2.10.1 Statistical models
Whatever the type of trial, it is usually convenient to think of the underlying structure of the design in terms of a statistical model. This model encapsulates the question we are intending to answer. Once the model is specified, the object of the corresponding clinical trial (and hence the eventual analysis) is to estimate the parameters of this model as precisely as is reasonable.
Suppose in a particular trial, we wish to compare two treatments, Standard (S) and Test (T). We can use an indicator variable to identify the treatment received by a patient, by setting x = 0 and x = 1 for the two treatments respectively. If the outcome of interest is a continuous variable, y, then this is related to the treatment or intervention by the linear regression equation
In this equation, β0 and βTreat are constants and are termed the parameters of the model. Here, βTreat is the coefficient which represents the magnitude of the difference between the treatments and so to determine its value is the major focus for the clinical trials. In contrast, ε represents the noise (or error) and this is assumed to be random and have an independent Normal distribution with mean value 0 across all subjects recruited to the trial and standard deviation (SD), σ. The object of a trial would be to estimate β0 and βTreat, and we write such estimates as b0 and bTreat to distinguish them from the corresponding parameters.
2.10.2 Fitting the model
Given a set of pairs of observations (x1, y1), (x2, y2), …, (xn, yn) from n individuals, the regression coefficient of βTreat is estimated by
(2.2)
and the intercept by
(2.3)
The corresponding SD is estimated by
(2.4)
