Detailed critique of the classical repeated measures ANOVA model. Its tests for main effects are diluted and difficult to interpret; the test for interaction is the main test of interest. Also they criticize the fact that the model allows separate baseline means for the different groups. They advocate ANACOVA as a superior approach, but propose the simple analysis of change from baseline scores as less confusing than a full blown repeated measures ANOVA. They do claim that ANACOVA assumes equal baseline means for all groups.
Argue that Huck & McLean's criticisms of repeated measures ANOVA overlook the possibility of using "differential effect" contrasts to provide the right analyses. They show that such contrasts are equivalent to the results of a simple analysis of change from baseline scores.
The authors compare t-tests on change from baseline scores to a classical repeated measures ANOVA (including subject-by-time random effect) and show the equivalence of the two methods. The ANOVA approach makes stronger assumptions and is more parsimonious, and also allows testing both within- and between-group differences. Analysis of covariance and its advantages are mentioned but dismissed since it assumes equal regression slopes for all groups.
Discusses Brogan & Kutner (1980) but with more elaboration of the role of analysis of covariance. It adjusts for regression to the mean, and when applied to the change from baseline scores instead of the raw responses, can be made to test for both within- and between-group differences. ANACOVA's applied to both raw responses and change from baseline scores are shown to be equivalent. A separate analysis for baseline group differences is recommended.
Discusses superiority of ANCOVA to t-tests on either raw scores or change from baseline scores, and ANOVA. However, also gives critiques of ANCOVA assumptions, including parallel line ANCOVA (assuming the same beta regardless of group).
Criticizes Egger et al. (1985). First, she states that when baseline balance is achieved, ANCOVA and t-test are both valid, but ANCOVA is more efficient. When baseline imbalance obtains, ANCOVA is invalid but t-test is not. Second, she disagrees that ANCOVA is inappropriate if the baseline has measurement error. Egger and Reading (1986) respond in the same issue, generally in agreement.
Compares a repeated measures ANOVA approach with ANACOVA and SUR (seemingly unrelated regression). Shows that the latter two are similar to each other. Recommends the latter two when the differences in baseline group means are due to measurement error; recommends repeated measures ANOVA when the baseline group means are truly different. Proposes a version of the latter model with baseline means constrained to be the same; this can be analyzed either conditional on baseline or unconditionally. Criticizes the test for group differences at baseline.
Follows tradition of Huck & McLean (1975) attacking repeated measures ANOVA and advocating ANCOVA. Considers eight different models for analyzing the data; all are variants of ANCOVA although some assume beta=1.
Compares multivariate analysis with 2-stage summary statistics approaches. Considers a model where the baseline group means are constrained to be the same.
This is a letter commenting on a paper by Caroll (1989) on covariance analysis with measurement error models. He considers the case of a response and a covariate (not necessarily the baseline) with a bivariate normal distribution. He shows that no bias occurs due to the measurement error in the covariate.
Attacks the classical repeated measures ANOVA approach due to its compound symmetric covariance structure. Accuses the method of being "dangerously wrong despite being often recommended" and says "the procedure should never be used" unless there is only one post-treatment time point.
They consider repeated measures designs with multiple pre and post randomization time points. They compare three estimators, t-tests on the post-randomization mean, t-tests on the change from baseline estimated by post-randomization mean minus pre-randomization mean, and ANCOVA with post-randomization mean as the response and pre-randomization mean as the covariate. They demonstrate that ANCOVA has the smallest variance of the three. For within-subject correlation > 0.5, they find that the change from baseline analysis has lower variance than the analysis that ignores baseline data. They assume a common baseline mean and use the compound symmetry assumption, despite Finney's objection. To combat regression to the mean, they argue that using the mean of multiple baselines will bring the variance of the change from baseline analysis close to that of ANCOVA. In this scenario, beta (the regression coefficient for baselines) approaches unity with an increase in the number of pre-treatment measures. Sample size calculations under compound symmetry are presented. They also consider the effect of measurement error on the baseline data. They find that all three estimators become biased, but the analysis ignoring baselines will be most severely affected. Senn (1994) disputes the bias for ANCOVA and the authors conceded the point.
Argue that there is a bias due to measurement error in the baseline covariate, or baseline imbalance. They introduce a Blomqvist bias correction for beta. They then consider baseline by treatment interaction.
This is a letter commenting on Frison & Pocock (1992). He disputes their claim that ANCOVA is biased. "ANCOVA is the best of the three methods considered and the only one which produces unbiased estimators in the presence of chance observed imbalance. It does this whether ornot the baselines are subject to measurement error." The authors reply conceding their error.
Disagree with Chambless & Roeback (1993) that intraindividual variation generates a bias in the ANCOVA estimator. Gives a compelling philosophical critique for why this is so. The authors replied, largely in disagreement. Senn replied yet again (1995) pressing his case.
First appears to uncover a generalization of Lord's paradox, comparing a repeated measures ANOVA with ANCOVA. Proposes instead a multiplicative regression model equivalent to taking log transform on the response and on the covariates.
Relies on causal inference machinery to discuss ANCOVA and SACS. Believes regression to the mean and measurement error in the baseline data are not reasons to avoid SACS.
Deploys the full machinery of mixed effects models. Proposes what LSTIC calls the constrained LDA model, when randomization allows assuming a common baseline mean. Shows that such a model is equivalent to the ANACOVA model. Discuss Lord's paradox as well.
Points out the repeated measures ANOVA has some technical difficulties when data are unbalanced. Also, its use of method of moments estimators is less efficient than maximum likelihood. Advocates mixed effects models which allow greater choice in covariance structures, and uses maximum likelihood estimation, although requires iterative computation and large sample approximation.
Writes ANCOVA and ANOVA in terms of repeated measures ANOVA model, and argues that ANCOVA is a special case of this model under the assumption of a common baseline mean. ANOVA of change scores is a special case of ANCOVA that assumes the pre-post correlation is unity. Discusses regression to the mean and Lord's paradox. Concludes that in randomized studies, ANCOVA is superior; in non-randomized studies, ANCOVA is biased and inefficient, and repeated measures ANOVA is preferred.
Criticizes alleged claim by Liang & Zeger (2000) that ANCOVA is biased unless the expected baseline difference is zero. He then derives general conditions under which ANCOVA is biased. If the bias in baseline difference is Bx and the bias in the post-treatment diference is By, then ANCOVA is unbiased when beta = By/Bx. If the variances at baseline and outcome are the same, beta is simply the correlation. He argues in this case that if By=Bx, ANCOVA is biased and SACS is unbiased! In a more general argument he says that if we assume "that despite the fact that grousp are different at basleine they would show the same evolution over time" then ANCOVA is biased unless the expected baseline means are the same. Finally, he argues that it is easy to design a trial where ANCOVA is unbiased and SACS is biased, but difficult to design a trial where the opposite is true. He attacks the random effects model approach in the Discussion, but he concedes that when treatment groups really are different at baseline, causal inference is a problem, a la Lord's paradox.
The most careful discussion of ANACOVA for longitudinal data analysis I have found. shows that it adjusts for regression to the mean. Shows that despite treating the baseline covariate as a fixed effect rather than a random effect, ANACOVA estimation is still unbiased and asymptotically normal (under bivariate normal assumption). Concedes that repeated measures ANOVA makes weaker assumptions than ANACOVA.
A well-written review of regression to the mean; provides many references to the literature. Shows how ANACOVA adjusts for the effect of regression to the mean. Claims that the ANACOVA estimator is biased because it treats the baseline covariate as fixed, not random (thus ignoring Crager's work).