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How to analyse this data?

The percentage of wound closure was determined for 4 different substrates + control group over 4 different time points (18, 24, 48 72 h). Each substrate had 3-4 replicates, with a total of 68 observations.

I want to determine whether substrate type has an effect on wound closure, comparing it to the control group and taking into consideration that wound closure is expected to increase over time for all substrates.

I think a linear mixed effects model with a dunnett's post-hoc test might be appropriate, but I am new to this and am unsure about it.

Edit: yes, this is an in vitro wound healing assay using a multi-well plate. I have looked at alternative ways to compare the data and it seems to be more appropriate to determine the rate of wound closure through linear regression using the areas and then the cell front velocity for each substrate followed by a one-way ANOVA to check for significance. Is this correct?

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  • $\begingroup$ What are your hypotheses? $\endgroup$ Commented Apr 8 at 10:15
  • $\begingroup$ The hypothesis is that there a significant difference in the percentage of wound closure between the groups compared to the control group. It is expected that some substrates improve wound healing. $\endgroup$ Commented Apr 8 at 10:37
  • $\begingroup$ Is this in vitro wound closure after scratching a confluent cell culture in wells of a multi-well tissue culture plate? If so, what are typical starting and ending wound sizes? It's probably better to work in the actual wound size scale instead of jumping immediately to percentage changes. Please provide extra information by editing the question directly, as comments are easy to overlook and can be deleted. $\endgroup$
    – EdM
    Commented Apr 8 at 15:05
  • $\begingroup$ I would second @EdM's suggestion to use wound size scale. Your percent change is a ratio distribution, where both the numerator and denominator are random variables. These are very messy to use; the wiki article gives, as its first example of a ration distribution the Cauchy distribution (probably one of the most pathological distribution there is), and says :*Often the ratio distributions are heavy-tailed, and it may be difficult to work with such distributions and develop an associated statistical test*". $\endgroup$
    – jginestet
    Commented Apr 8 at 17:21

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The answer depends in part on the rate of wound healing. If yours is typical of experiments of this type, I suspect that there will be almost complete healing before 72 hours. See Radstake et al., Biochem Biophys Rep 2023 Jan 12;33:101423, for example. In that case there probably won't be a constant healing rate over the course of the experiment, so you will have to model time explicitly.

Unless you decide to focus only on a single early time point, you thus need to go beyond a simple one-way ANOVA. I'd recommend modeling wound width over time, unless you know that all wounds have the same observed length under the microscope so that area and width are measuring the same thing.

Chapter 7 of Frank Harrell's Regression Modeling Strategies goes into some detail about this type of longitudinal data. A simple way to proceed with only 4 time points (after the time 0 measurements presumably taken soon after the scratching) would be to model time as a multi-level unordered factor in a linear regression model. I'd be reluctant to code time as an ordered factor, as the time points aren't evenly spaced. See this UCLA web page on how an ordered factor should be restricted to evenly spaced values.

Alternatively, you might code time as a numeric variable and allow the model to fit it flexibly with a regression spline, but with only 4 time points that might not provide much advantage over treating time as a factor.

However you model time, include it in an interaction with a multi-level factor representing the substrates. Set the reference level of that factor to the control substrate. Post-modeling tools like those in the emmeans package in R can take the results of the regression model and show them as the wound width for each combination of substrate and time. Tools in that package also can do comparisons of all treatments against a control, with a "trt.vs.ctrl" contrast method, that's essentially the same as a Dunnett test. That test can be run on any combination of times or differences between times that best illustrate your results.

Your analysis also should take into account correlations of observations within wells over time. See the Harrell reference for suggestions. A generalized least squares model could be a good choice, as (unlike repeated-measures ANOVA) it allows you to include the width measured at time 0 as a predictor in the model for all subsequent time points from the same well (the best way to handle initial observations before treatments can have an effect) and it's able to handle some missing values. A mixed model treating wells as random effects would also be possible, with similar advantages over repeated-measures ANOVA.

Finally, a single multi-well plate only provides technical replicates. This experiment should be repeated on multiple biological replicates. See the Technical Perspective by the Pollards, Molecular Biology of the Cell 30: 1359-1368, 2019.

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