This paper presents and compares several methods of measuring continuous baseline covariate imbalance in clinical trial data. Simulations illustrate that though the t-test is an inappropriate method of assessing continuous baseline covariate imbalance, the test statistic itself is a robust measure in capturing imbalance in continuous covariate distributions. Guidelines to assess effects of imbalance on bias, type I error rate and power for hypothesis test for treatment effect on continuous outcomes are presented, and the benefit of covariate-adjusted analysis (ANCOVA) is also illustrated.
FriedmanLMFurbergCDDeMetsDL. Fundamentals of clinical trials, 2nd edn. New York: Springer Science + Business Media, LLC, 1998.
2.
HarringtonDP. The randomized clinical trial. J Am Stat Assoc2000; 95: 312–315.
3.
GreenS. Design of randomized trials. Epidemiol Rev2002; 24: 4–11.
4.
McEntegartDJ. The pursuit of balance using stratified and dynamic randomization techniques: An overview. Drug Inf J2005; 37: 293–308.
5.
RosenbergerWFLachinJM. Randomization in clinical trials: Theory and practice, New York: Wiley Interscience, 2002.
6.
PocockSJAssmannSEEnosLEKastenLE. Subgroup analysis, covariate adjustment and baseline comparisons in clinical trial reporting: Current practice and problems. Stat Med2002; 21: 2917–2930.
7.
AustinPCMancaAZwarensteinMJuurlinkDNStanbrookMB. A substantial and confusing variation exists in handling of baseline covariates in randomized controlled trials: A review of trials published in leading medical journals. J Clin Epidemiol2010; 63: 142–153.
8.
AltmanDG. Comparabilty of randomised groups. Statistician1985; 34: 125–136.
9.
SennSJ. Covariate imbalance and random allocation in clinical trials. Stat Med1989; 8: 467–475.
10.
StigsbyBTavesD. Rank-minimization for balanced assignment of subjects in clinical trials. Contemp Clin Trials2010; 31: 147–150.
11.
GreevyRLuBSilberJHRosenbaumP. Optimal multivariate matching before randomization. Biostatistics2004; 5: 263–275.
12.
RosenbaumPRubinD. Constructing a control group using multivariate matched sampling methods that incorporate the propensity score. Amer Stat1985; 39: 33–38.
13.
BeggCBIglewiczB. A treatment allocation procedure for sequential clinical trials. Biometrics1980; 36: 81–90.
14.
AtkinsonAC. Optimum biased coin designs for sequential clinical trials with prognostic factors. Biometrika1982; 69: 61–67.
15.
AtkinsonAC. The comparison of designs for sequential clinical trials with covariate information. J R Stat Soc A Sta2002; 165: 349–373.
16.
GailMHWeiandSPiantadosiS. Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates. Biometrika1984; 71: 431–444.
17.
RobinsonLDJewellNP. Some surprising results about covariate adjustment in logistic regression models. Int Stat Rev1991; 58: 227–240.
18.
HauckWHAndersoneSMarcusS. Should we adjust for covariates in nonlinear regression analyses of randomized trials?Control Clin Trials1998; 19: 249–256.
19.
HernandezAVSteyerbergEWHabbemaJDF. Covariate adjustment in randomized controlled trials with dichotomous outcomes increases statistical power and reduces sample size requirements. J Clin Epidemiol2004; 57: 454–460.
20.
HollanderMWolfeDA. Nonparametric statistical methods, 2nd edn. New York: Wiley-Interscience, 1999.
21.
CiolinoJDZhaoWMartinRHPaleschYY. Quantifying the cost in power of ignoring continuous baseline covariate imbalances in clinical trial randomization. Contemp Clin Trials2010. (In Press.
22.
Huber M. Testing for covariate balance using nonparametric quantile regression and resampling methods. Unpublished Working and Discussion Papers, 2009.
23.
Sekhon JS. Alternative balance metrics for bias reduction in matching methods for causal inference. Unpublished Papers for Download, 2007.
24.
RosenbergerWFSverdlovO. Handling covariates in the design of clinical trials. Stat Sci2008; 23: 404–419.
25.
AgrestiA. Categorical data analysis, 2nd edn. Hoboken, New Jersey: John Wiley & Sons, Inc., 2002.
26.
HosmerDWLemeshowSS. Goodness-of-fit tests for the multiple logistic regression model. Commun Stat A-Theor1980; 9: 1043–1069.
27.
McFaddenD. Frontiers in econometrics, New York: Academic Press, 1974.
28.
The National Institute of Neurological Disorders and Stroke rt-PA Stroke Study Group. Tissue plasminogen activator for acute ischemic stroke. NEJM 1995; 333: 1581–1587.
29.
SennSJ. Testing for baseline balance in clinical trials. Stat Med1994; 13: 1715–1726.
30.
RobertsCTorgersonDJ. Baseline imbalance in randomised controlled trials. Brit Medl J1999; 319: 185–185.
31.
FayersPKingM. The baseline characteristics did not differ significantly. Qual Life Res2008; 17: 1047–1048.
IngallTJO'FallonWMAsplundKGoldfrankLRHertzbergVSLouisTA. Findings from the reanalysis of the ninds tissue plasminogen activator for acute ischemic stroke treatment trial. Stroke2004; 35: 2418–2424.
34.
FreyJL. Recombinant tissue plasminogen activator (rtpa) for stroke: The perspective at 8 years. Neurologist2005; 11: 123–133.
35.
HertzbergVIngallTO'FallonWAsplundKGoldfrankLLouisT. Methods and processes for the reanalysis of the ninds tissue plasminogen activator for acute ischemic stroke treatment trial. Clin Trials2008; 5: 308–315.
36.
ICH E9 Expert Working Group. Statisticl principles for clinical trials: ICH harmonized tripartite guideline. Stat Med 1999; 18: 1905–1942.
37.
TrowmanRDumvilleDTorgersonDJCrannyG. The impact of trial baseline imbalances should be considered in systematic reviews: A methodological case study. J Clin Epidemiol2007; 60: 1229–1233.
38.
RaabGDayS. How to select covariates to include in the analysis of a clinical trial. Control Clin Trials2000; 21: 330–342.
39.
FordINorrieJ. The role of covariates in estimating treatment effect and risk in long-term clincial trials. Stat Med2002; 21: 2899–2908.
