Use Of Analysis Of Covariance Research Articles

A Simulation-Based Comparison of Covariate Adjustment Methods for the Analysis of Randomized Controlled Trials.

Covariate adjustment methods are frequently used when baseline covariate information is available for randomized controlled trials. Using a simulation study, we compared the analysis of covariance (ANCOVA) with three nonparametric covariate adjustment methods with respect to point and interval estimation for the difference between means. The three alternative methods were based on important members of the generalized empirical likelihood (GEL) family, specifically on the empirical likelihood (EL) method, the exponential tilting (ET) method, and the continuous updated estimator (CUE) method. Two criteria were considered for the comparison of the four statistical methods: the root mean squared error and the empirical coverage of the nominal 95% confidence intervals for the difference between means. Based on the results of the simulation study, for sensitivity analysis purposes, we recommend the use of ANCOVA (with robust standard errors when heteroscedasticity is present) together with the CUE-based covariate adjustment method.

Método de Papadakis e tamanho de parcela em experimentos com a cultura da alface

RESUMO: O trabalho teve por objetivo testar a eficiência do método Papadakis na melhoria da qualidade de experimentos com a cultura da alface, determinar a melhor forma de estimativa da covariável e o tamanho ótimo de parcela para uso no método. A forma de estimativa da covariável que proporciona maior eficiência do método e o cálculo do tamanho de parcela ajustado para uso nesse método, foram determinados a partir de oito ensaios de uniformidade com a cultura da alface. A eficácia do uso de análise de covariância (ANCOVA) utilizando a covariável estimada pelo método Papadakis foi testada a partir de um experimento com tratamentos com a cultura da alface, em que a variável estudada foi a massa fresca da parte aérea das plantas. O uso de ANCOVA com a covariável estimada pelo método Papadakis melhora a qualidade de experimentos com a cultura da alface. A covariável que proporciona a maior eficiência da ANCOVA é aquela que considera uma parcela vizinha de cada lado da parcela de referência no sentido da linha de cultivo. O tamanho de parcela na linha de cultivo, ajustado para uso do método, é de quatro plantas (1,2 m) para estufa e túnel, e de cinco plantas (1,5 m) para o campo.

Empirical comparison of four baseline covariate adjustment methods in analysis of continuous outcomes in randomized controlled trials.

BackgroundAlthough seemingly straightforward, the statistical comparison of a continuous variable in a randomized controlled trial that has both a pre- and posttreatment score presents an interesting challenge for trialists. We present here empirical application of four statistical methods (posttreatment scores with analysis of variance, analysis of covariance, change in scores, and percent change in scores), using data from a randomized controlled trial of postoperative pain in patients following total joint arthroplasty (the Morphine COnsumption in Joint Replacement Patients, With and Without GaBapentin Treatment, a RandomIzed ControlLEd Study [MOBILE] trials).MethodsAnalysis of covariance (ANCOVA) was used to adjust for baseline measures and to provide an unbiased estimate of the mean group difference of the 1-year postoperative knee flexion scores in knee arthroplasty patients. Robustness tests were done by comparing ANCOVA with three comparative methods: the posttreatment scores, change in scores, and percentage change from baseline.ResultsAll four methods showed similar direction of effect; however, ANCOVA (−3.9; 95% confidence interval [CI]: −9.5, 1.6; P=0.15) and the posttreatment score (−4.3; 95% CI: −9.8, 1.2; P=0.12) method provided the highest precision of estimate compared with the change score (−3.0; 95% CI: −9.9, 3.8; P=0.38) and percent change (−0.019; 95% CI: −0.087, 0.050; P=0.58).ConclusionANCOVA, through both simulation and empirical studies, provides the best statistical estimation for analyzing continuous outcomes requiring covariate adjustment. Our empirical findings support the use of ANCOVA as an optimal method in both design and analysis of trials with a continuous primary outcome.

Inference following designs which adjust for imbalances in prognostic factors

When the minimisation method due to Taves is used to balance treatment groups across prognostic factors, a problem arises at the time of analysing the results. Since minimisation is essentially a deterministic method, any statistical test based on the assumption of complete randomisation should not be used in the analysis. Previous articles have shown that analysis of covariance (ANOCOVA) produces valid tests. In this article, these results are extended to trials with more than one prognostic factor and more than two treatments. An alternative design to minimisation which makes use of optimum design theory is also considered, with two choices of biased coin. Simulation is used to study the effect on the power and the coverage probabilities of the usual tests and confidence intervals when these different allocation methods are applied. The results are then illustrated using data from an actual clinical trial. Simulation shows that when ANOCOVA is used, it is sometimes more powerful with these designs than with minimisation and produces slightly conservative confidence intervals for the treatment mean differences. The increase in power and conservativeness is more pronounced when there are more prognostic factors. The possibility of treatment-covariate interactions is also addressed. Results are only given when treatment responses are normally distributed. Under the simulated situations considered, when a covariate-adaptive design is used, the use of ANOCOVA yields a test which preserves the nominal significance level as compared to the conservativeness of analysis of variance.

Analysis of covariance in agronomy and crop research

Yang, R.-C. and Juskiw, P. 2011. Analysis of covariance in agronomy and crop research. Can. J. Plant Sci. 91: 621–641. Analysis of covariance (ANCOVA) is a statistical technique that combines the methods of the analysis of variance (ANOVA) and regression analysis. However, ANCOVA is an advanced topic that often appears towards the end of many textbooks, and thus, it is either taught cursorily or ignored completely in many statistics classes. Additionally, many elaborated applications of ANCOVA to agronomy and crop research along with uses of the latest statistical software are rarely described in textbooks or classes. The objectives of this paper are to provide an overview on conventional ANCOVA and to introduce more advanced uses of ANCOVA under mixed models. We describe three elaborate applications including (i) the use of ANCOVA for dissecting dosage responses for different treatments, (ii) stability of treatments across multiple environments and (iii) removal of spatial variation that is not effectively controlled by blocking. These analyses illustrate that ANCOVA is either a simpler analysis or provides more information than conventional statistical methods. We provide a technical appendix ( Appendix A ) on principles and theory underlying mixed-model analysis of ANCOVA along with SAS programs ( Appendix B ) for more uses and in-depth understanding of this powerful technique in agronomy and crop research.

Change from baseline and analysis of covariance revisited

The case for preferring analysis of covariance (ANCOVA) to the simple analysis of change scores (SACS) has often been made. Nevertheless, claims continue to be made that analysis of covariance is biased if the groups are not equal at baseline. If the required equality were in expectation only, this would permit the use of ANCOVA in randomized clinical trials but not in observational studies. The discussion is related to Lord's paradox. In this note, it is shown, however that it is not a necessary condition for groups to be equal at baseline, not even in expectation, for ANCOVA to provide unbiased estimates of treatment effects. It is also shown that although many situations can be envisaged where ANCOVA is biased it is very difficult to imagine circumstances under which SACS would then be unbiased and a causal interpretation could be made.

Analysis of covariance (ANCOVA) with difference scores

When comparing pretest to posttest changes in non-randomized groups, most researchers are correctly avoiding ANCOVA with posttest as the dependent variable and pretest as the covariate. However, there is a widespread use of ANCOVA in which the difference score (posttest minus pretest) is used as the dependent variable, and pretest as the covariate. A computer simulation study is presented which shows that measurement error causes identical, biased conclusions when comparing changes using either the posttest score or the posttest minus pretest difference score as the dependent variable. The reasons for this bias are explained and illustrated.

How to reduce the number of patients needed for randomized trials: a basic introduction

Complementary therapies are often used to treat patients with persisting conditions. In a typical randomized trial, patients are assessed for symptom severity at baseline, randomized to treatment or control and then reassessed after a suitable follow-up period. It can be shown that the number of patients required for such trials can be reduced by the use of two methods: repeat measurement and analysis of co-variance (ANCOVA). An example is given of a trial of acupuncture for back pain. Administering the pain questionnaire twice at baseline and four times at follow-up reduces the number of patients by approximately 20% compared to single questionnaire administration. Use of ANCOVA decreases the number of patients by approximately a further 10%. There are considerable economic and ethical advantages to reducing sample size by a third; however, ANCOVA is statistically complex and expert statistical help is required.

Comparison of Two Procedures to Estimate the Hospital Stay Attributable to Nosocomial Infection: Matched Cohort Study versus Analysis of Covariance of the Total Unmatched Cohort

We compare the results of a matched cohort study with those yielded by analysis of covariance (ANCOVA) in the cohort where the matched study was nested to assess whether the matching design underestimates (as it has been assumed) the extra length of hospitalization due to nosocomial infection. A total of 218 patients developed hospital infection in a cohort of 1483 general surgery patients; 161 were successfully matched 1:1 for surgical procedure, ASA score, age (±10 years), emergency-scheduled surgery, preoperative stay, and, whenever possible, number of diagnoses and sex. Unmatched infected patients (57, 23.1%) were different from matched ones. There were no differences for the variables between matched infected patients and their pairs. The matched cohort study overestimates the extra LOH due to hospital infection. The use of ANCOVA in the total cohort obviates the selection bias of the matched cohort design.

Analysis of Covariance: A Proposed Algorithm

Many researchers erroneously think that analysis of covariance (ANCOVA) should be performed only when there are pre-existing significant differences between the groups on the potential covariate. It has been shown however that, when correctly applied, ANCOVA offers two major advantages over simple analysis of variance (ANOVA): (a) greater statistical power due to a reduction in error variance; and (b) a reduction in bias in experiments where differences between groups exist at the beginning of an experiment. An algorithm has been proposed where the use of ANCOVA is conditional upon (a) a test of homogeneity of within-group regression slopes; (b) a Pearson correlation coefficient 2 0.3 between the covariate (X) and the dependent variable (1) in the case of a randomized study; in a non-randomized study (e.g. intact groups), the use of ANCOVA is not conditional on r5? 0.3 because, in this case, critical adjustments can be obtained with correlation lower than 0.3; and (c) a linear relationship between X and Y

Correction for the influence of background muscle activity on stretch reflex amplitudes

Background muscle activity (BGR) exerts a strong influence on stretch reflex amplitudes. While it is considered important to correct for this influence, which method best able to eliminate the effects of BGR remains unknown. We have therefore compared one previously described and one novel correction method which respectively consisted of calculating (1) the difference between reflex amplitude and BGR, and (2) the ratio of reflex amplitude to BGR. These correction methods were evaluated in a group of 23 healthy individuals. BGR and stretch reflexes were recorded from the gastrocnemius muscle of standing subjects who received sudden toe-up perturbations of a supporting platform upon which they were standing. Calculation of differences markedly reduced the influence of BGR on stretch reflex amplitudes in most, although not all, subjects. Calculation of ratios failed to correct for BGR in most subjects and caused a net increase in the influence of BGR on stretch reflex amplitudes. Because both correction methods insufficiently corrected for BGR in normal subjects, we introduce the use of analysis of covariance (ANCOVA) to reliably remove the influence of BGR on stretch reflex amplitudes. The use of ANCOVA is exemplified by showing that stretch reflex amplitudes are enhanced in patients with Parkinson's disease even if the influence of high BGR is completely taken into account.