# Which statistical analyses should I use?

I want to compare data from a treatment group vs a control group over time (baseline, 1 yr, 2 yr).

The measurements are repeated for all subjects across all time points (i.e., all participants complete the same set of questionnaires at all time points).

Some participants have missing data (some did not complete questionnaires at certain time points).

Control group has more subjects than treatment group (unequal sample sizes).

I am not sure whether I should use mixed models analyses to handle missing data because I am not sure whether mixed models can be used for unequal sample sizes. Or should I use Scheffe's method (non-parametric variant of anova) to handle the unequal sample sizes.

I am interested to investigate whether scores on a questionnaire (that measures severity of symptoms) differ between the treatment group (given medication) and the control group (not on medication) across the different time points.

I was thinking of using repeated measures mixed model analysis (specified as 'Linear Mixed Models analysis' in SPSS which involves selecting the appropriate covariance structure [e.g.compound symmetry and 1st order auto regressive]) because all subjects undergo the same questionnaire across all time points and also due to incomplete data from some participants.

The only issue is that I have 300+ participants in the control group and 30+ participants in the treatment group. (very unequal group sizes).

In this case, will the repeated measures mixed model analysis still be appropriate?

I agree with Peter that performing multiple t-tests will not be advisable in this case as it also increases family-wise error (hence increases tendency of committing a type 1 error).

If by "mixed model" you mean a multilevel model (which is known by a variety of terms) that is, a model of the form

$Y = X\beta + Z\gamma + \epsilon$

then, yes, they can deal with unequal sample sizes.

Given that the same set of subjects took tests multiple times, you violate the assumption of independent data and so the simpler models will not be appropriate.

These methods also deal well with missing data, provided it is missing at random. There are no really good methods for dealing with data that is missing not at random.

• (+1) To clarify, multilevel modeling software handle missing data on the dependent-variable side, but typically not on the predictors side (though this seems to be irrelevant here--just wanted to make sure this didn't go unnoticed in case the OP has missing data on predictor variables as well). – Patrick Coulombe Jan 20 '14 at 1:23

A little more context about your data and missing info would be nice, but here goes nothing:

First, check out the Two Sample t-test for equal means. The two data sets can either have a one-to-one map or not. This tests if the means are equal or not. With unequal sample sizes and (possibly) unequal variances, you can use a more specific model known as Welch's t test. You can do this at each point in time, and then test the three models to see if there are significant model differences.

These models are easy to understand and helpful when you are just looking for mean and variance comparisons. Are there other stats you are trying to compare?

Also, there are various options for dealing with mssing data. Either ignore them, or fill them in using various methods. Here is a short list of popular methods in R.

• A two sample t-test or Welch's t-test could compare the means at each time point, but it would not be appropriate for tests that used multiple time points. – Peter Flom Nov 20 '13 at 15:59
• @Peter Flom - True, I was just thinking about one point in time at first. Can't you do it at each point in time, and than do a test comparison on the three models to see if they are statistically different? – Stu Nov 20 '13 at 16:03