I have data for a cross-over randomized controlled trial. I wonder if I can use MANCOVA to compare my outcomes (they are continuous) while having paired data. If I can't, what would be an appropriate test here? I have some covariates that I want to account for. I already did some Wilcoxon tests, but it didn't account for covariates.
The design of the study is as follows:
There are two groups: Group is given treatment (a drug) and then control (Sequence AP). Another group is given control then treatment (the same drug) (PA sequence). Between the treatment and control, there is a washout period.
I have four DVs that are continuous. Each variable is measured two times. For example, the AP sequence had the variables measured one time after the intervention (t0) and another time after the place (t1). Same thing for the PA sequence. They had the placebo, then had the variables measured (t0), then a washout period, then the intervention, and then the DVs were measured again (t1). I have covariates that are measured at baseline (before the study starts). So think of my data as a dataframe with the following columns:
1- Sequence (AP vs PA)
2- t0 (DV1)
3- t1 (DV1)
4- Covariate 1
5- Covariate 2
and so on
I would like to:
1- Compare between t0 and t1 for each sequence while controlling for covariates. I started with Wilcoxon test to compare t0 and t1 considering that this is paired data and some of the DVs are not normally distributed. However, I know that Wilcoxon doesn't account for my covariates. I thought about using MANCOVA (but am not sure if it is the right one because some of my DVs are not normally distributed and my data is paired data). Ignoring the normality thing, can we use MANCOVA for this scenario? In case of Mancova, I will have to convert my wide data to long data (i.e., instead of having each DV presented as column t0 once and t1 once, I will put them on top of each other). My DVs would be my four continuous DVs, then we have an independent categorical variable (drug vs placebo) and continuous covariates. I can do that for each sequence separately, then combine them.
Btw, Wilcoxon didn't find any significant difference.
2- If MANCOVA is not valid, what would be a simple but robust solution?
The correlation method below would work? I assume if the difference between t0 and t1 is not correlated with my covariates, then it is unlikely that they might be confounding variables.
Update: I am thinking of using correlation between the difference in my DVs (t1-t0) with my covariates to create a correlation matrix. If they are not significant, then it is safe to say that these covariates are not confounding my results. Does that make sense?
Any advice?
I am suggesting my opinion for your question
1. MANCOVA:
MANCOVA (Multivariate Analysis of Covariance) is a viable option when you have multiple dependent variables (DVs), and you want to examine group differences while controlling for covariates. However, MANCOVA assumes multivariate normality, which might be a concern if some of your DVs are not normally distributed.
I am suggesting for your question normally distributed and you have paired data, you might consider using a mixed-effects model or a repeated measures ANOVA. These models can handle paired data and allow for the inclusion of covariates.
In R, the lme or nlme package might be useful for mixed-effects modeling.
2. Alternative Approach:
You mentioned the idea of using correlation between the difference in DVs (t1-t0) and covariates to create a correlation matrix. This approach is somewhat related to assessing the relationship between changes in DVs and covariates. It's not a direct substitute for MANCOVA, but it can provide insights into potential confounding.
Here's a simplified step-by-step process:
- Calculate the differences (t1-t0) for each DV.
- Examine the correlation between these differences and your covariates.
- If the correlations are not significant, it suggests that the covariates may not be confounding variables.
Remember, correlation does not imply causation, but it can provide useful information about associations.
3. Robustness Checks:
Considering your study design, it's good that you've performed Wilcoxon tests for non-normally distributed data. Additionally, you might want to explore bootstrapping as a robust resampling method to assess the stability of your results, especially if your sample size is limited.
In summary, for your specific scenario, mixed-effects models or repeated measures ANOVA may be more appropriate than MANCOVA. The correlation-based approach can offer additional insights into potential confounding. Always consider the assumptions of each method and choose the one that best fits your data and research questions. If in doubt, consulting with a statistician or data analyst with expertise in your specific field can be invaluable.
Why not use ANCOVA? Use the t0 DV as an additional covariate and t1 DV as the outcome. Its a simpler analysis and if the groups are randomized it should give a more precise estimate of the treatment effect than your proposed analysis.
I don't see the value of MANCOVA here as you end up analyzing a wierd weighted composite of the 4 DVs and to answer your research questions about each outcome you'd likely have to follow up with the ANCOVAs anyway. You can, if desired, apply a multiple comparison correction to the separate ANCOVAs for Type I error control (and that's superior than relying on the omnibus test from the MANCOVA). You can use a correction that accounts for the correlation between DVs like Hochberg. The MANCOVA is an unnecessary step in my view.
Alternatively you could use a multivariate regression that models the 4 DVs and their correlations directly rather than creating some wierd composite - but I'm not sure its necessary.
Thom Baguley I agree with you that Mancova will complicate things unnecessarily. I ended up doing linear mixed models (4 models since I have 4 DVs), and the results came out consistent with my Wilcoxon test but this time LMM accounted for covariates. I did with the lme4 package in R.
ANCOVA didn't work because I have DVs with only 2 strata levels.
What do you think?
I may have misunderstood, but if you treat t0 DV as a covariate (centered to aid interpretation) you may not need a linear mixed model. If you have additional random effects then a linear mixed model seems fine.
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