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1、A comparison of nonparametric and parametric methods toadjust for baseline measuresMartin O. Carlssona,b, Kelly H. Zoua, Ching-Ray Yua, Kezhen Liub, Franklin W. SunaaPfizer Inc., New York, NY, USAbDepartment of Statistics, Rutgers, The State University of New Jersey, New Brunswick, NJ, USAa r t i c
2、l ei n f oa b s t r a c tArticle history:Received 13 July 2013Received in revised form 8 January 2014Accepted 13 January 2014Available online 21 January 2014When analyzing the randomized controlled trial, we may employ various statistical methodsto adjust for baseline measures. Depending on the meth
3、od chosen to adjust for baselinemeasures, inferential results can vary. We investigate the Type 1 error and statistical power oftests comparing treatment outcomes based on parametric and nonparametic methods. Wealso explore the increasing levels of correlation between baseline and changes from theba
4、seline, with or without underlying normality. These methods are illustrated and comparedvia simulations. 2014 Elsevier Inc. All rights reserved.Keywords:Randomized controlled trialsPercent change from baselineAnalysis of covarianceRobust regressionCovariate imbalance1. IntroductionForrandomizedcontr
5、olledtrials,inferentialresultsmayvarydepending on whether or not an individual subjects baselinedata are adjusted for, as well as the method chosen to adjust.Either the post-treatment value or change from baselinemay be analyzed to account for the effect of the baselinemeasures. Alternatively, the p
6、ercent change from baseline, ascale invariant method can also be used. It is a measure thatis easy to interpret although its distribution is complicated,especially when baseline and post-baseline measures arecorrelated.Lords paradox states that the relationship between acontinuousoutcomeandacategori
7、calexposuremaybereversedwhen an additional continuous covariate (e.g., baseline mea-sures) is introduced1.Thus, appropriate inferentialproceduresmust be employed to adjust for baseline measures. The analysisof covariance (ANCOVA) approach remains the most populartool in practice even with a set of s
8、tringent assumptions in-cluding linearity, parallelism, homoscedasticity, and normality.Previously, Vickers 2 has compared several parametrict-testandANCOVAbasedmethodsinalargesamplesetting.Herecommended the use of ANCOVA which had the greatestpower in the case of normally-distributed data, when bas
9、elineand post-baseline data are correlated. We aim to extend hiscomparisons by incorporating the strength of correlation anddistributional assumptions.The remainder of this manuscript is organized as follows. InSection 2, we review commonly-used nonparametric methodsand parametric univariate methods
10、 to compare change scoresand percent change from baseline. We also compare differentmultivariate regression methods to adjust for the baseline. InSection 3, we present Monte-Carlo simulation studies thatinvestigated Type 1 error and statistical power performance. InSection 4, we apply these methods
11、to two published examplescontaining laboratory assay data and dental caries data. Finally,Contemporary Clinical Trials 37 (2014) 225233 Corresponding author at: 235 East 42nd Street, Mail Stop: 219/7/1,New York, NY 10017, USA. Tel.: +1 212 733 0087; fax: +1 212 3094368.E-mail addresses: Martin.C (M.
12、O. Carlsson),Kelly.Z (K.H. Zou), Ching-Ray.Y (C.-R. Yu),LiuKeZ (K. Liu), Franklin.S (F.W. Sun).1551-7144/$ see front matter 2014 Elsevier Inc. All rights reserved.http:/dx.doi.org/10.1016/j.cct.2014.01.002Contents lists available at ScienceDirectContemporary Clinical Trialsjournal homepage: 5 presen
13、ts conclusions and discussion based on thisresearch.2. Univariate and multivariate adjustment methods2.1. NotationsLet the i-th bivariate measurements under each of treat-ment groups k(k = 1,K) have a bivariate joint distributionfunction, Hk(,).Xki;Yki ? i:i:d:Hkx;y;i 1;nk;1with baseline variable X
14、and post-baseline variable Y, respec-tively. The total sample size across all k treatment groups isN Ki1nk.The post-baseline scores are denoted by Yki. The changefrom the baseline is Dki= Yki Xki. The percent change fromthe baseline, (Dki/Xki) 100% 3, is recommended for labelclaim purposes based on
15、patient-reported outcomes 4. Thelatter may be easier to interpret since the percent changescore is a dimensionless measure.2.2. Univariate methodsThe commonly-used univariate nonparametric method iseither the Wilcoxons rank-sum test (for two samples) orKruskalWallis test (for more than two samples).
16、 Alterna-tively, a parametric method, the two-sample t-test or theone-way Analysis of Variance (ANOVA) may be conducted. Itis assumed here that the reader is familiar with the methodsbeing investigated and thus they are not described in detail.2.3. Multivariate methods2.3.1. Parametric ANCOVAThe ANCOVA is a commonly-used multivariable regres-sion method on a set of baseline covariates, which may alsobe conducted to adjust the baseline values. There are fiveassumptions for conducting the ANCOVA a
