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.

A randomized, double-blind, crossover clinical trial of diclofenac plus misoprostol versus acetaminophen in patients with osteoarthritis of the hip or knee

“…Similar results were seen with the conservative assumptions of 0 change for the 8 patients with no data after visit 2 and the same change for visit 3 Ϫ visit 2 as was seen for visit 5 Ϫ visit 4 for the 1 patient missing visit 3 and with data for visits 4 and 5; therefore, missing data for 9 patients at visit 3 (6 in group I and 3 in group II) was not an issue for the primary analyses. The results from analyses for period 2 and for both periods were also robust to such methods for managing missing data at visit 5, and the P values from the primary analyses for period 1 and their supportive counterparts for period 2 were confirmed with analogous nonparametric methods (31).…”

Inhibition of the Sodium-Hydrogen Exchanger With Cariporide to Prevent Myocardial Infarction in High-Risk Ischemic Situations

“…13 Predefined covariates were age, sex, entry MI, ST-segment depression, congestive heart failure, diabetes, previous MI, and cerebrovascular or peripheral vascular disease. The homogeneity of these covariates was tested with Fisher and Wilcoxon tests.…”

Efficacy and Safety of Tenecteplase in Combination With the Low-Molecular-Weight Heparin Enoxaparin or Unfractionated Heparin in the Prehospital Setting

“…In addition, nonparametric, covariate-adjusted rates were calculated using Koch's method. 26 Covariates used were gender, age, weight, infarct location, previous infarct, Killip class, heart rate, time to tenecteplase, and systolic blood pressure. Because the results of the adjusted and nonadjusted analyses were very similar, only nonadjusted results are presented.…”