Abstract
Some randomized clinical trials are conducted to compare test treatment, an active reference control, and placebo with the objectives of demonstrating that test treatment is not inferior to reference control, and to show that both test treatment and reference control are better than placebo. We typically want to adjust for covariables that are strongly associated with the response of interest in order to gain variance reduction, to adjust for random imbalances of covariables, and to clarify the degree to which differences between randomized groups are due to treatments rather than other factors associated with response.
Parametric modeling is often used to evaluate the relationship between covariables and the conditional distributions of response given the covariables. There can be concerns, however, about model assumptions, and they are not always straightforward to assess. An alternative is to use a nonparametric method for the primary evaluation of treatment comparisons. The nonparametric method is performed through linear models for (unconditional) differences between treatment groups for means of response criteria (or functions of such means) and covariables jointly with specifications that adjust random differences for means of covariables to zero. This paper discusses the role of nonparametric analysis of covariance in clinical trials to compare test treatment, an active reference control, and placebo with three examples.
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Koch GG, Davis SM, Anderson RL. Methodological advances and plans for improving regulatory success for confirmatory studies. Stat Med. 1998;17:1675–1690.
Koch GG, Gansky SA. Statistical considerations for multiplicity in confirmatory protocols. Drug Inf J. 1996;30:523–534.
Koch GG, Amara IA, Davis GW, Gillings DB. A review of some statistical methods for covariance analysis of categorical data. Biometrics. 1982;38(3);563–595.
Koch GG, Tangen CM, Jung JW, Amara IA. Issues for covariance analysis of dichotomous and ordered categorical data from randomized clinical trials and nonparametric strategies for addressing them. Stat Med. 1998;17:1863–1892.
Stokes ME, Davis CS, Koch GG. Categorical Data Analysis Using the SAS System. Cary, NC: SAS Institute Inc.; 1995.
Robinson LD, Jewell NP. Some surprising results about covariate adjustment in logistic regression models. Int Stat Rev. 1991;59(2):227–240.
Gail MH, Wieand S, Piantadosi S. Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates. Biometrika. 1984;71(3):431–444.
Chastang C, Byar D, Piantadosi S. A quantitative study of the bias in estimating the treatment effect caused by omitting a balanced covariate in survival models. Stat Med. 1988;7:1243–1255.
Simpson EG. The interpretation of interaction in contingency tables. J Roy Stat Soc: Series B. 1951;13:238–241.
Koch GG, Carr GJ, Amara IA, Stokes ME, Uryniak TJ. Categorical Data Analysis. Statistical Methodology in the Pharmaceutical Sciences. Berry DA, ed. New York: Marcel Dekker: 1990:291–475.
Carr GJ, Hafner KB, Koch GG. Analysis of rank measures of association for ordinal data from longitudinal studies. J Am Stat Assoc. 1989;84(407):797–804.
Koch GG, Gillings DB, Stokes ME. Biostatistical implications of design, sampling, and measurement to health science data analysis. Ann Rev Pub Health. 1980;1:163–225.
Senn SJ. Covariate imbalance and random allocation in clinical trials. Stat Med. 1989;8:467–475.
Senn SJ. Testing for baseline balance in clinical trials. Stat Med. 1994;13:1715–1726.
Beach ML, Meier P. Choosing covariates in the analysis of clinical trials. Control Clin Trials. 1989;10:161S–175S.
Canner PL. Covariate adjustment of treatment effects in clinical trials. Control Clin Trials. 1991;12:359–366.
Hwang AK, Morikawa T. Design issues in noninferiority/equivalence trials. Drug Inf J. 1999;33:(in press)
Fieller EC. The distribution of the index in a normal bivariate population. Biometrika. 1932;24:428–440.
Hadgu A, Koch GG. Application of generalized estimating equations to a dental randomized clinical trial. J Biopharm Stat. 1999;9:161–178.
O’Brien PC. Procedures for comparing samples with multiple endpoints. Biometrics. 1984,40:1079–1087.
Lehmacher W, Wassmer G, Reitmeir P. Procedures for two-sample comparisons with multiple endpoints controlling the experimentwise error rate. Biometrics. 1991;47:511–521.
Gansky S, Koch GG, Wilson J. Statistical evaluation of relationships between analgesic dose and ordered ratings of pain relief over an eight-hour period. J Biopharm Stat. 1994;4:233–265.
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Koch, G.G., Tangen, C.M. Nonparametric Analysis of Covariance and Its Role in Noninferiority Clinical Trials. Ther Innov Regul Sci 33, 1145–1159 (1999). https://doi.org/10.1177/009286159903300419
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DOI: https://doi.org/10.1177/009286159903300419