Repeated Measure ANOVA, GLM,GEE, Linear mixed model, Generalized linear mixed model?

Question

I have a table like below (it is a small subset of my data. In this table, I measured one variable over 4 different time points (T1,..., T4), now I would like to check is there any significant difference between time points for each sample? then based on that I will select those samples that have variability in different time points.

My assumption for the data is:

• non-normal distribution.
• unequal variance.
• the same sample size for each dependent group.

I have reviewed several methods (like, Repeated Measure ANOVA, GLM, GEE, linear mixed model, Kruskal Wallis test and GLMM), but I am confused about which one is more appropriate for my data?

 sample                                T1                       T2                        T3                       T4

1:824850-825300                 0.00000000                0.0000000                0.0000000                0.0000000        
1:894445-894831                 5.39848590                3.9919398                5.8171244                3.4732853         
1:902180-902369                 5.30856403                4.7035677                1.6972109                4.0094193
1:911400-911969                 3.93351892                8.6449756                3.9462391                5.9417675
1:912000-912125                 3.08713416                3.7929570                0.5132366                2.7979578
1:919425-920025                 4.37344006                6.4203699                3.5285015                3.4974473
1:934044-934294                 9.87882930               11.3788710                7.4419304                6.0622420
1:948960-949100                 1.65382187               11.0063484                5.4989633               12.4908832

Answer 1

Your data is setup in a "wide" format, which means that you have separate variables associated with each time point. This is fine if you want to use something like structural equation modeling or certain classical tests (ANOVA). But to use GEE or GLMM, you want to set your data up in a long format. For example, using just the first two samples, it would look something like this:

sample         time  outcome 
824850-825300   0    0.00000
824850-825300   1    0.00000
824850-825300   2    0.00000
824850-825300   3    0.00000
894445-894831   0    5.39848590
894445-894831   1    3.9919398
894445-894831   2    5.8171244
894445-894831   3    3.4732853

Once your data is setup like this, you can use GLMM or GEE to estimate a model that uses data from all samples. However, it seems like you want to do some sort of selection of samples to analyze beforehand, and that is confusing to me. First of all, all the methods you have identified operate on the entire collection of samples in your data. They don't identify whether any one sample within the collection of samples in your data are somehow different from one another.

An example of a very basic mixed model you could use on your data, and using a linear (Gaussian) mixed model in R, is the following:

m <- lmer(outcome ~ 1 + (1|sample), data=df)

This model allows for unique intercepts (mean value on the outcome) for each sample. The idea is that values within samples are likely to be correlated and you want to allow for such correlation. From this model you get a variance estimate for sample ($\sigma^2_j$) and the residual ($\sigma^2_i$), representing between- and within-sample variation, respectively. You can quantify the average correlation between outcome values within a sample by calculating an intraclass correlation coefficient (ICC): $\sigma^2_j$/($\sigma^2_j$ + $\sigma^2_i$). Again, this would be a correlation at the whole sample level.

Typically, you would want to use predictors to explain variation between and within samples, including predictors that are constant within a sample (time-invariant) and predictors that are unique to each time point within a sample (time-varying). Perhaps this is not the answer you are looking for. If that is the case, then provide greater detail on what you want to do.