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I'll explain briefly the experimental set-up.

  • One gruop of subject measured in two conditions:

A: with treatment (Instrumented gait analysis with foot orthosis)

B: without treatment (Barefoot instrumented gait analysis)

Before testing, subjects used the treatment (foot orthosis) for different periods, this may have an impact on the results. I need to verify if there are differences between the two conditions using the treatment duration as a covariate.

Paolo Brasiliano
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    Do you just mean something like ANCOVA but extending the Wilcoxon test instead of the t-test (same as the ANOVA F-test with two groups)? – Dave Aug 27 '21 at 14:01
  • Questions solely about how software works are off-topic here, but you may have a real statistical question buried here. You may want to edit your question to clarify the underlying statistical issue. You may find that when you understand the statistical concepts involved, the software-specific elements are self-evident or at least easy to get from the documentation. --- so you might want to edit to title so this do not looks like a software only question! – kjetil b halvorsen Aug 27 '21 at 14:14
  • I am with @kjetilbhalvorsen that there is a statistical question hiding in here, and, if the answer to my question in the previous comment is in the affirmative, then there is a good statistical answer to be posted that culminates with, "Implement this with rms::orm." See here. – Dave Aug 27 '21 at 14:20
  • Thanks both for your advices, I am sorry for the form of my question but the first time I post something on this website. I edited the question as you suggested, hope it is fine now. Thank you again – Paolo Brasiliano Aug 27 '21 at 14:39
  • How would you do it if you had normal distributions? // What is not normally distributed? There is no assumption in linear regression that the pooled/marginal $y$ variable is normal. That assumption is about the error term (estimated by the residuals). – Dave Aug 27 '21 at 14:42
  • If i had normal distribution I would run a repeated measure ANCOVA. My dependent variables are not normally distributed. – Paolo Brasiliano Aug 27 '21 at 15:00
  • Dependent variables, as in plural? What do you mean by that? // It might be worth doing something Wilcoxon-like, even if there is a normal error term. In that case, the link I gave states which regression method extends the Wilcoxon Mann-Whitney U test the way that linear regression extends the t-test (it's proportional odds ordinal logistic regression, and the implementation, I think, is to take the exact same formula you'd use in lm and put it inside rms::orm.) – Dave Aug 27 '21 at 15:10
  • Do you just want to adjust for duration as a confounder? Or do you want a conditional effect using duration as a covariate? If the former, look up average treatment effect estimation (R package tmle) for estimating the effect difference between a binary treatment adjusting for arbitrary confounders nonparametrically. –  Aug 29 '21 at 06:04
  • @Lars I need to verify if there are differences between the conditions and if a significant interaction between the conditoin and the duration exists – Paolo Brasiliano Aug 31 '21 at 08:13

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You could use the a robust ANCOVA for two dependent groups and one covariate called Dancova from the WRS package in R. Uses by default 20% trimmed means. Assumptions for classic ANCOVA are not required.

# load the latest WRS package
> source("https://dornsife.usc.edu/assets/sites/239/docs/Rallfun-v38.txt")

> Dancova(x1, y1, x2 = x1, y2, tr = 0.2, plotit = TRUE)

x1 are covariate values for your first group, x2 for the second (should be the same as x1)

y1 are dependent variable values for your first group, y2 for the second

Jan
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  • How to intrepret output from Dancova function? Rows have no names – Paolo Brasiliano Aug 31 '21 at 10:47
  • Forgot to explain the output. So the function determines 5 points (values) of your covariate and then for each value performs a dependent yuen's t-test on 20% trimmed means (i.e. whether the DV for the two groups differs significantly). Due to multiple tests the function controls for keeping the type 1 error rate so you can conclude that you have a significant difference on each point only if p.value < p.crit. By the way you can set trimming to 0 (tr = 0) if your DV is not skewed and you do not have outliers -- increases power of your test. – Jan Aug 31 '21 at 11:12
  • Thank you again, one last question. Do you have any suggestion on how to report the results? – Paolo Brasiliano Aug 31 '21 at 12:40
  • Yes, a robust ANCOVA for two dependent groups has been deployed with the function Dancova the WRS package (Wilcox, 2017) in R. This function does not make parametric assumptions about the form of the regression line and uses a running interval smoother instead. The analysis revealed that for the treatment duration "x" the (20% trimmed) mean of DV was significantly higher in group 1 than in group 2 (p = .024). For the treatment duration "y" ... – Jan Aug 31 '21 at 13:10
  • You can also report the test statistic which is $T_y$ for trimmed means or $t$ respectively $W$ for no trimming (uses Welch's t-test instead). In case you don't need the confidence intervals or the test statistic you can also use the function DancovaV2 which uses bootstrap samples and is more powerful. Also if you don't like the chosen points (values) of the covariate you can determine their values and number manually for both functions. Like this: pts = c(4, 7, 10). – Jan Aug 31 '21 at 13:17