The added value of ordinal analysis in clinical trials: an example in traumatic brain injury
 Bob Roozenbeek^{1, 2}Email author,
 Hester F Lingsma^{2},
 Pablo Perel^{3},
 Phil Edwards^{3},
 Ian Roberts^{3},
 Gordon D Murray^{4},
 Andrew IR Maas^{1},
 Ewout W Steyerberg^{2} and
 the IMPACT (International Mission on Prognosis and Clinical Trial Design in Traumatic Brain Injury) Study Group and the CRASH (Corticosteroid Randomisation After Significant Head Injury) Trial Collaborators
DOI: 10.1186/cc10240
© Roozenbeek et al.; licensee BioMed Central Ltd. 2011
Received: 1 December 2010
Accepted: 17 May 2011
Published: 17 May 2011
Abstract
Introduction
In clinical trials, ordinal outcome measures are often dichotomized into two categories. In traumatic brain injury (TBI) the 5point Glasgow outcome scale (GOS) is collapsed into unfavourable versus favourable outcome. Simulation studies have shown that exploiting the ordinal nature of the GOS increases chances of detecting treatment effects. The objective of this study is to quantify the benefits of ordinal analysis in the reallife situation of a large TBI trial.
Methods
We used data from the CRASH trial that investigated the efficacy of corticosteroids in TBI patients (n = 9,554). We applied two techniques for ordinal analysis: proportional odds analysis and the sliding dichotomy approach, where the GOS is dichotomized at different cutoffs according to baseline prognostic risk. These approaches were compared to dichotomous analysis. The information density in each analysis was indicated by a Wald statistic. All analyses were adjusted for baseline characteristics.
Results
Dichotomous analysis of the sixmonth GOS showed a nonsignificant treatment effect (OR = 1.09, 95% CI 0.98 to 1.21, P = 0.096). Ordinal analysis with proportional odds regression or sliding dichotomy showed highly statistically significant treatment effects (OR 1.15, 95% CI 1.06 to 1.25, P = 0.0007 and 1.19, 95% CI 1.08 to 1.30, P = 0.0002), with 2.05fold and 2.56fold higher information density compared to the dichotomous approach respectively.
Conclusions
Analysis of the CRASH trial data confirmed that ordinal analysis of outcome substantially increases statistical power. We expect these results to hold for other fields of critical care medicine that use ordinal outcome measures and recommend that future trials adopt ordinal analyses. This will permit detection of smaller treatment effects.
Introduction
Traumatic brain injury (TBI) is a major health and socioeconomic problem throughout the world. Basic research has elucidated many of the pathophysiological mechanisms underpinning secondary damage and many neuroprotective agents have been developed to counteract these mechanisms. Since the 1980s, at least 33 randomized controlled phase III trials have been performed to investigate the effectiveness of new therapeutic interventions in TBI, but none has convincingly demonstrated benefit in the overall population [1]. Heterogeneity of the population and limitations of the conventional statistical analysis of TBI trials contribute to this lack of success [2, 3]. We recently published a set of recommendations for improving the design and analysis of future TBI trials [4]. These recommendations were mainly derived from simulation studies and include the use of relatively broad enrolment criteria, covariate adjustment and ordinal rather than dichotomous outcome analysis.
The Glasgow Outcome Scale and its traditional dichotomy in favourable versus unfavourable outcome
Dead  
Vegetative State  Unfavourable 
Severe Disability  
Moderate Disability  Favourable 
Good Recovery 
Materials and methods
Data
We used the individual patient data of the MRC CRASH trial into which 10,008 patients were enrolled.
The CRASH trial (Corticosteroid Randomisation After Significant Head Injury) was an international, randomised, placebocontrolled trial designed to investigate the effect of early administration of methylprednisolone on the risk of death and disability after head injury. Full results have been reported [6, 7]. Enrolment was stopped in May 2004, following demonstration of a higher 14day mortality rate in the active treatment arm (21.1% versus 17.9% deaths; P = 0.0001). Outcome at six months was available for 9,554 patients. The current study was exempt from institutional review board approval.
Conventional dichotomous outcome analysis
We first estimated the effect of the treatment on the sixmonth GOS, dichotomized as unfavourable versus favourable, with binary logistic regression. The treatment effect was adjusted for four baseline covariates: age, Glasgow Coma Scale (GCS), pupillary reactivity and presence of major extracranial injury. Age was handled as a continuous variable and GCS as a categorical variable (range 3 to 15). Pupillary reactivity was grouped into three categories: both pupils reactive, one reactive and none reactive to light. The presence of major extracranial injury was included as a binary variable, having a positive value when patients had an extracranial injury that required hospital admission on its own.
Subsequently, we used two approaches exploiting the ordinal nature of the GOS: a proportional odds logistic regression model and the sliding dichotomy approach.
Proportional odds logistic regression
A proportional odds logistic regression model was fitted with the GOS collapsed to a 4point ordinal scale (Severe Disability and Vegetative State were taken together) as the outcome variable. The proportional odds model has the same structure as the binary logistic regression model, but uses an ordinal outcome variable with more than two possible categories. It estimates a common odds ratio over all possible cutoffs of the outcome scale. The common odds ratio is formally valid if the odds ratios for each cutoff are the same (the proportional odds assumption). We can, however, interpret the common odds ratio as a summary measure of treatment effect, even if the odds ratios differ by cutoff [8]. The common odds ratio can also be interpreted as the average shift over the total ordinal outcome scale caused by the treatment under study [5, 9, 10].
Sliding dichotomy
The sliding dichotomy approach dichotomizes the GOS into a binary measure, but the point of dichotomy is tailored to each individual patient's baseline prognosis [11]. For example, for a patient with an excellent prognosis only good recovery may be considered as a favourable outcome, whereas for a patient with a very poor prognosis, survival may be regarded as a favourable outcome. First, the baseline prognostic risk of each patient was estimated by calculating the probability of unfavourable outcome with a prediction model including the following variables: age, GCS, pupillary reactivity, and presence of major extracranial injury [12]. Subsequently, patients were divided into three prognostic bands of equal size, that is, for the best, intermediate and worst prognosis. For each band a separate cutoff on the GOS was defined and a new outcome variable was generated. For example, in the best prognosis band we only considered Good Recovery as a favourable outcome. The effect of treatment on this newly constructed dichotomous outcome was then estimated with binary logistic regression, with stratification by prognostic band and adjustment for the four covariates mentioned above. The pooled sliding dichotomy odds ratio can be interpreted as the effect of treatment on outcomes being worse than expected [11].
Comparison of the different approaches
We calculated Wald statistics, based on the coefficients of the treatment effect and the corresponding standard error for each analysis. The ratio of the Wald statistics can be interpreted as the gain in information density and is, therefore, a suitable measure for the efficiency of the different approaches.
We adjusted the treatment effect for four baseline covariates in all analyses (age, GCS, pupillary reactivity, major extracranial injury) [12, 13]. Missing data occurred for 509 patients on pupillary reactivity and 196 on the presence of extracranial injury. These missing covariates were imputed with a multiple imputation model. Statistical analyses were performed in R Statistical Software version 2.7.2 using the Design library (R Foundation for Statistical Computation, Vienna, Austria).
Results
Baseline characteristics of patients enrolled in the CRASH trial with Glasgow Outcome Scale score available
Corticosteroid (n= 4,800)  Placebo (n= 4,754)  

Age (median, IQR)  33, 23 to 47  32, 23 to 48 
Gender  
Male  3,892 (81.1%)  3,824 (80.4%) 
Glasgow Coma Scale  
Severe (3 to 8)  1,925 (40.1%)  1,890 (39.8%) 
Moderate (9 to 12)  1,477 (30.8%)  1,405 (29.6%) 
Mild (13 to 14)  1,398 (29.1%)  1,459 (30.7%) 
Pupillary reactivity  
Both reactive to light  3,860 (80.4%)  3,822 (80.4%) 
One reactive to light  270 (5.6%)  294 (6.2%) 
Both not reactive to light  412 (8.6%)  387 (8.1%) 
Missing  258 (5.4%)  251 (5.3%) 
Major extracranial injury  
Yes  1,106 (23.0%)  1,039 (21.9%) 
No  3,600 (75.0%)  3,613 (76.0%) 
Missing  94 (2.0%)  102 (2.1%) 
Analysis of the treatment effect according to different dichotomizations and proportional odds logistic regression
Adjusted odds ratio^ (95% CI)  Wald statistic  Pvalue  

Dichotomous odds ratios  
Less than good vs. good recovery  1.12 (1.01 to 1.23)  2.26  0.024 
Unfavourable vs. favourable outcome  1.09 (0.98 to 1.21)  1.66  0.096 
Death vs. survival  1.27 (1.13 to 1.43)  4.16  < 0.0001 
Common odds ratio (proportional odds model)  1.15 (1.06 to 1.25)  3.41  0.0007 
Analysis of the Glasgow Outcome Scale with the sliding dichotomy approach
Dead  SD  MD  GR  Worse than expected  Better than expected  Odds ratio (95% CI)  Wald statistic  Pvalue  

Best prognosis  Corticosteroid  67  86  274  1,162  427  1,162  1.22 (1.03 to 1.43)  0.017  
Placebo  59  84  228  1,227  371  1,227  
Intermediate prognosis  Corticosteroid  282  215  365  748  497  1,113  1.06 (0.91 to 1.23)  0.45  
Placebo  225  241  357  749  466  1106  
Worst prognosis  Corticosteroid  899  280  212  210  899  702  1.28 (1.11 to 1.47)  0.0006  
Placebo  791  328  228  237  791  793  
Pooled odds ratio, unadjusted  1.17 (1.07 to 1.27)  3.67  0.0003  
Pooled odds ratio, adjusted^  1.19 (1.08 to 1.30)  3.69  0.0002 
The logistic regression analysis with dichotomized GOS resulted in a Wald statistic for the treatment effect of 1.66 (P = 0.096). Ordinal analysis with a proportional odds model gave a 2.05fold higher Wald statistic (3.41, P = 0.0007). The sliding dichotomy approach resulted in an even larger Wald statistic of 3.69 (P = 0.0002), indicating a 2.56fold increase in information density.
Discussion
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 nonsignificant, those obtained with ordinal analysis were highly significant. With ordinal analysis, a 2 to 2.5fold 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 [13–15]. 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 cutoffs of the outcome scale. This assumption may partly be violated in empirical data. We, therefore, recommend reporting the odds ratios per cutoff 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 cutoffs for the GOS (Table 2). Also, some variation was seen in the odds ratios across prognostic bands for the sliding dichotomy (Table 3). 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 nonproportional 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' cutoff (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 cutoff (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, 26]. 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.
Conclusions
We conclude that the application of ordinal outcome analysis substantially increases the power of a clinical trial. We recommend that future randomized trials, which use an ordinal outcome measure as efficacy parameter, adopt ordinal outcome analysis in order to facilitate detection of smaller treatment effects.
Key messages

None of the phase III clinical trials for Traumatic Brain Injury (TBI) has shown an overall significant treatment effect. Inefficient analysis of trials may contribute this the failure.

Dichotomous analysis of an ordinal outcome scale in clinical trials results in loss of information. Previous simulation studies suggested that ordinal outcome analysis could substantially improve statistical power of a clinical TBI trial.

The present study gives a reallife example of the benefit two approaches to ordinal outcome analysis in a large TBI trial (the CRASH trial).

Both approaches to ordinal analysis showed highly significant treatment effects, increased statistical power and a 2.1 to 2.6fold increase in information density.

We recommend that future trials adopt ordinal outcome analysis, in order to facilitate detection of smaller treatment effects.
Abbreviations
 CI:

confidence interval
 CRASH:

Corticosteroid Randomisation After Significant Head Injury
 GCS:

Glasgow Coma Scale
 GOS:

Glasgow Outcome Scale
 IMPACT:

International Mission on Prognosis and Clinical trial design in TBI
 MRC:

Medical Research Council
 NYHA:

New York Heart Association
 OAST:

Optimizing Analysis of Stroke Trials
 OR:

odds ratio
 PAIS:

Paracetamol (Acetaminophen) Ischemic Stroke
 RCT:

randomized controlled trial
 SAINT:

StrokeAcute Ischemic NXY Treatment
 STICH:

Surgical Trial in Intracerebral Haemorrhage
 TBI:

traumatic brain injury
Declarations
Acknowledgements
This study was performed as a part of the IMPACT Study in collaboration with the MRC CRASH Trial Collaborators. The IMPACT study was funded by the US National Institutes of Health (Clinical Trial Design and Analysis in TBI Project: R01 NS042691). The CRASH trial was funded by the UK Medical Research Council.
Authors’ Affiliations
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