Statistical methodology for analyzing ordinal outcomes of traumatic brain injury

Statistical methodology for analyzing ordinal outcomes
of traumatic brain injury

Statistical analysis of data for treatment of traumatic brain injury (TBI) from randomized clinical trials (RCTs) regularly fails to identify statistically significant changes in patient condition. Patient outcome is typically measured on an ordinal scale which is then analyzed with statistical methods that lack sensitivity to detect changes across all measured outcomes, have restrictive assumptions, or lack adequate statistical power. The conventional binary regression model, the proportional odds model, partial proportional odds model, and the continuation ratio model are four standard methods applied in the analysis of ordinal variables, traditionally deemed effective in a number of cases. To overcome their known deficiencies in some scenarios, the sliding dichotomy model was recently developed to accurately analyze the changes in patient condition across ordinal scales and has had several productive applications in specific cases.

This study compares the sample size, type I error rate and power among these models. This study attempts to detect the consistency among the contemporary models and also the weakness of the sliding dichotomy model in controlling the type I error rate. A few recommendations for handling ordinal variables in applied research are also proposed.

This study used data from Corticosteroid Randomisation after Significant Head Injury (CRASH), a baseline observed data set consisting of 10,008 patients, as the primary data set. Varying the sample sizes, the number of covariates, the band size of the sliding dichotomy approach and randomizing the treatment effect created different scenarios. A number of possible contexts that might occur in practical clinical trials was simulated to try and test the applicability of the models. For each scenario, the effect on statistical power and type I error rates of the models was assessed. Another supplementary primary data set, already collected from Bangladesh, was applied to compare the two data sets. Apart from these two, we tested two other non-clinical trial data sets to assess the models' application in the field of public health.

Although previous studies have suggested that smaller samples sizes can maintain desired power for some applications of the sliding dichotomy model, the results of this study indicate that consideration of the type I error rates does not encourage this approach, due to the risk of false-positive inferences from application of this method. The model could not even maintain the error rate even when the sample size was high (over 1000); often times the type I error rate were higher than 5%.

Inconsistent results were observed from all the models applied to different data sets. These inconsistencies across all the ordinal methods suggest that researchers may find value in evaluating multiple methods and using goodness of fit statistics to help report and interpret results, and also encourages use of meta-analysis in some studies. However, this is not the best or ultimate solution to inconsistent performance of methods. Specific problems with the current methods were detected as part of this research and some potential solutions were outlined. Empirical studies with both clinical and non-clinical data are required to devise a model that can adequately balance the errors and statistical power, and have less (or no) restrictive assumptions.