Issues for covariance analysis of dichotomous and ordered categorical data from randomized clinical trials and non‐parametric strategies for addressing them

Abstract

Analysis of covariance is an effective method for addressing two considerations for randomized clinical trials. One is reduction of variance for estimates of treatment effects and thereby the production of narrower confidence intervals and more powerful statistical tests. The other is the clarification of the magnitude of treatment effects through adjustment of corresponding estimates for any random imbalances between the treatment groups with respect to the covariables. The statistical basis of covariance analysis can be either non-parametric, with reliance only on the randomization in the study design, or parametric through a statistical model for a postulated sampling process. For non-parametric methods, there are no formal assumptions for how a response variable is related to the covariables, but strong correlation between response and covariables is necessary for variance reduction. Computations for these methods are straightforward through the application of weighted least squares to fit linear models to the differences between treatment groups for the means of the response variable and the covariables jointly with a specification that has null values for the differences that correspond to the covariables. Moreover, such analysis is similarly applicable to dichotomous indicators, ranks or integers for ordered categories, and continuous measurements. Since non-parametric covariance analysis can have many forms, the ones which are planned for a clinical trial need careful specification in its protocol. A limitation of non-parametric analysis is that it does not directly address the magnitude of treatment effects within subgroups based on the covariables or the homogeneity of such effects. For this purpose, a statistical model is needed. When the response criterion is dichotomous or has ordered categories, such a model may have a non-linear nature which determines how covariance adjustment modifies results for treatment effects. Insight concerning such modifications can be gained through their evaluation relative to non-parametric counterparts. Such evaluation usually indicates that alternative ways to compare treatments for a response criterion with adjustment for a set of covariables mutually support the same conclusion about the strength of treatment effects. This robustness is noteworthy since the alternative methods for covariance analysis have substantially different rationales and assumptions. Since findings can differ in important ways across alternative choices for covariables (as opposed to methods for covariance adjustment), the critical consideration for studies with covariance analyses planned as the primary method for comparing treatments is the specification of the covariables in the protocol (or in an amendment or formal plan prior to any unmasking of the study).

Energy intake and expenditure during sedentary screen time and motion-controlled video gaming

“…Nonparametric ANCOVAs were performed to test hypotheses (22,23). This method needed only minimal assumptions beyond randomization in the study design.…”

Treatment of shoulder pain in spastic hemiplegia by reducing spasticity of the subscapular muscle: a randomised, double blind, placebo controlled study of botulinum toxin A

“…However, it appeared that the longer the time after stroke, the better was the effect. Thus taking into account the time elapsed since the cerebral lesion, covariance analysis 22 showed stronger statistical results, with pain being significantly reduced at week 2 (p = 0.042) and at week 4 (p = 0.007), and improvement in lateral rotation being significant at week 2 (p = 0.019) and at week 4 (p = 0.002).…”

“…Covariance analyses adjusted on values at baseline were used to compare pain reduction and change in range of motion between the two groups at each visit. 22 A x 2 test was used for comparisons of differences in MAS scores.…”

Design of a trial evaluating myocardial cell protection with cariporide, an inhibitor of the transmembrane sodium-hydrogen exchanger: the Guard During Ischemia Against Necrosis (GUARDIAN) trial

“…For the primary composite end-point of all-cause mortality and MI at day 36 after randomization, a nonparametric covariance adjustment analysis method [17] was used to calculate the P value and the 98% confidence limits. This analysis requires only the randomization assumption, maintains the same interpretation for the estimators of the event rate differences across different specifications of covariates, and reduces variance of these estimators compared with an unadjusted analysis.…”