Covariates imbalance

Berger, V.W., 2005, Selection bias and covariate imbalances in randomized clinical trials, John Wiley Sons. 

This point was discussed in Chapter 3, where it was shown that balance is not necessary for correct Inference. Stratification as illustrated in section 7.1 and/or analysis of covariance can be used to deal with the distribution of observed covariates. The point is rather that the standard methods of statistical analysis make an average allowance for covariate imbalance. This average allowance is not perfect but it is logically adequate where no further information is available (Senn, 2005a). 

Berger VW (2005a) Quantifying the magnitude of baseline covariate imbalances resulting from selection bias in randomized clinical trials. Biometrical Journal 47 119-12 7. 

Berger VW (2005b) Selection Bias and Covariate Imbalances in Randomized Clinical Trials. John Wiley Sons, Ltd, Chichester. 

Senn SJ (1989) Covariate imbalance and random allocation in clinical trials [see comments]. Statistics in Medicine 8 467-475. [Comment in Statistics in Medicine 10(5) 797-799 (1991)]. Senn SJ (1994) Testing for baseline balance in clinical trials. Statistics in Medicine 13 1715-1726. Senn SJ (2000) Consensus and controversy in pharmaceutical statistics (with discussion). The Statistician 49 135-176. 

Berger Selectioii Bias and Covariate Imbalances in Randomized Clinical Trials Brown and Prescott Applied Mixed Models in Medicine, Second Edition Chevret (Ed) Statistical Methods for Dose-Finding Experiments Ellenberg, Fleming and DeMets - Data Monitoring Committees in Clinical Trials A Practical Perspective... 

Adjusted analyses presented earlier in this chapter also share some of these advantages and provide improvements in efficiency, can also account for baseline imbalances and allow the evaluation of the homogeneity of the treatment effect. On this final point, however, adjusted analyses are less able to identify the nature of those interactions. With ANCOVA it is possible to say which particular covariates are causing such interactions. A further point to note here and, as mentioned... 

Baseline imbalance in itself should not be considered an appropriate reason to include a baseline measure as a covariate. ... 

When there is some imbalance between the treatment groups in a baseline covariate that is solely due to chance then adjusted treatment effects may account for this observed imbalance when unadjusted analyses may not. If the imbalance is such that the experimental group has a better prognosis than the control group, then adjusting for the imbalance is particularly important. Sensitivity analyses should be provided to demonstrate that any observed positive treatment effect is not solely explained by imbalances at baseline in any of the covariates. ... 

Non-parametric procedures tend to be simple two group comparisons. In particular, a general non-parametric version of analysis of covariance does not exist. So the advantages of ANCOVA, correcting for baseline imbalances, increasing precision, looking for treatment-by-covariate interactions, are essentially lost within a non-parametric framework. 

The first attempt at estimating interindividual pharmacokinetic variability without neglecting the difficulties (data imbalance, sparse data, subject-specific dosing history, etc.) associated with data from patients undergoing drug therapy was made by Sheiner et al. " using the Non-linear Mixed-effects Model Approach. The vector 9 of population characteristics is composed of all quantities of the first two moments of the distribution of the parameters the mean values (fixed effects), and the elements of the variance-covariance matrix that characterize random effects.f " " ... 

It is also possible in an analysis of covariance to adjust outcomes using individual slopes rather than a postulated common slope. This is not my usual habit in analysing trials and unless I state so specifically I shall not include this further refinement under the heading of analysis of covariance. This point is discussed in section 7.2.7 below. Stratification and analysis of covariance, when carried out on strongly prognostic factors, not only adjust for observed imbalances but even where (in fact especially where) such factors are balanced, bring with them a strong reduction in variance of the estimated treatment effect and a consequent increase in power. 

As with other approaches, the propensity score model is only as good as the covariates selected to provide the adjustment. A propensity score is a single metric that is intended to account for all of the explanatory variables that predict who will receive treatment. Propensity scores generally balance observed confounders but do not necessarily produce balance on factors not incorporated into the model. Such imbalances represent a particular problem... 

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