Analysis of the MRC CRASH trial data showed that ordinal analysis of the GOS resulted in substantially greater statistical power to detect a treatment effect with equal sample size. Whilst results obtained with the conventional analysis of the dichotomized GOS were non-significant, those obtained with ordinal analysis were highly significant. With ordinal analysis, a 2- to 2.5-fold gain in information density was demonstrated, compared to the dichotomized analysis. Simulation studies had already suggested the potential for ordinal analysis to increase statistical power in TBI trials, but our current study has proven the value of this approach in the empirical data of a large trial with a true treatment effect.
Earlier research has demonstrated that adjustment for strong predictors of outcome (covariate adjustment) may result in a substantial increase in statistical power and trial efficiency [13
]. In the IMPACT database, we found that the required sample size for a RCT could potentially be reduced by around 25% when covariate adjustment would be applied with seven strong predictors [13
]. We, therefore, incorporated covariate adjustment in all analyses in the present study.
Why is the use of ordinal outcome analysis beneficial? The common practice of collapsing an ordinal outcome measure to a binary scale results in a loss of information [16
]. Moreover, dichotomization gives priority to one particular transition in the outcome scale: in the case of the GOS this is the change from severe disability to moderate disability. Patients with a relatively extreme prognosis have little potential to contribute to the detection of a treatment effect on an ordinal functional outcome scale, when this scale is dichotomized for the analysis [17
]. A patient with a very good prognosis will almost inevitably have a favourable outcome, even without the benefits of a new effective therapy. In contrast, for patients with a very poor prognosis it is extremely unlikely to have a favourable outcome at six months, even with a very beneficial new treatment. This does not mean that these patients may not benefit from the treatment, but simply that the fixed split for dichotomising the outcome measure is not appropriate for these situations. When the outcome is analysed in an ordinal way, all patients can contribute to the detection of a treatment effect.
The idea of exploiting the ordinal nature of ordered outcome scales is far from a new concept in the statistical community [18
]. Nevertheless, this approach has not been applied to the analysis of clinical trials on a regular basis. The sliding dichotomy approach was recently applied for the primary efficacy in a number of trials: the PAIS trial in stroke [19
], the STICH trial in spontaneous intracerebral hemorrhage [20
], and the Pharmos trial in TBI [21
]. The proportional odds model was used in several neurological trials, for example, in the GAIN International trial [22
] and the SAINT I trial [23
Inherent to the proportional odds model is the proportional odds assumption, that is, that the treatment effect is constant across all cut-offs of the outcome scale. This assumption may partly be violated in empirical data. We, therefore, recommend reporting the odds ratios per cut-off if a common odds ratio is reported as the summary measure of the treatment effect. Indeed, we found that the odds ratios were not identical across all cut-offs for the GOS (Table ). Also, some variation was seen in the odds ratios across prognostic bands for the sliding dichotomy (Table ). The proportional odds assumption was formally tested with the 'PROC LOGISTIC' test from the SAS software package (SAS Institute Inc., Cary, NC, USA) and was found to be violated. This was confirmed by a graphical test in R software (the 'residuals' function from the Design
library) to test for parallelism. In a previous study we simulated a non-proportional treatment effect, that is, a treatment that only affected mortality and did not cause a shift for the other categories of the GOS. We found to our surprise that the statistical power of ordinal analyses (proportional odds or sliding dichotomy) remained higher than a dichotomous analysis at the 'correct' cut-off (mortality vs. survival) [11
]. This robust gain in statistical power is a clear advantage of ordinal analysis, even if one were to object to interpretation of a summary odds ratio when underlying assumptions are violated [8
The choice between the two ordinal approaches involves primarily a value judgement. The sliding dichotomy approach and its explanation (the effect of treatment on outcomes being worse than expected) may be particularly appealing for clinicians, but it requires a (validated) prognostic model to identify each patient's baseline prognostic risk. The proportional odds method does not necessarily require such a model, but may not have a proper interpretation if effect estimates vary substantially by cut-off (a violation of the proportional odds assumption). A pragmatic approach is to focus more on the underlying concept of 'shift analysis', instead of emphasizing the formal assumptions of this model.
Both approaches to ordinal outcome analysis that were investigated in the present study resulted in substantial power increase. Therefore, we strongly recommend incorporating ordinal methods in the analysis of future trials when an ordered outcome measure is considered. We do not advocate that this power increase should motivate reduced sample sizes for future trials. Since most TBI trials that were published in the past decades have been underpowered [24
], the power increase that results from ordinal analysis can thus be used to increase the chance of detecting smaller, but clinically relevant, treatment effects with the same sample size.
The use of ordinal outcome scales is not unique to TBI, but is common to many fields of clinical research. Equally common is the practice of dichotomising ordinal outcome measures. In the field of stroke research, the modified Rankin Scale and the Barthel Index are often used as primary efficacy endpoints - and are also dichotomized [25
]. The Optimising Analysis of Stroke Trials (OAST) Collaboration has shown the benefit of ordinal analysis in the field of stroke [27
]. Other examples of ordinal outcome scales can be found in cardiology (for example, NYHA Functional Classification for heart failure), vascular surgery (for example, Rutherford Classification for peripheral artery disease) and pain management (for example, Visual Analogue Scale). The widespread use of ordinal outcome measures and the persisting practice of collapsing these measures into a binary outcome indicate that our findings in this case study on TBI have much broader implications than for TBI alone. We consider our results directly relevant to clinical trials in other fields of medicine that use ordinal outcome measures, especially if outcomes occur over the full range of the scale.