# Comparing the difference in change in repeated measures ordinal variables between two groups

I have two groups of patients, those with (OSA) and those without (nOSA) sleep apnoea. Patients were scheduled to undergo a surgical procedure (Sx). Each patient completed a type of quality of life survey before (pre-Sx) and after (post-Sx) surgery. Each question in the quality of life survey is scored 0, 1, 2, 3 (with 0 being the "best" and 3 being the "worst").

I want to find answer a specific question, but am unsure which test is most appropriate - Was the change in quality of life (change in the ordinal variable) following the surgery different for OSA versus nOSA patients? We suspect that the OSA group has a greater change in quality of life after surgery, compared with the nOSA group.

So I need some kind of test which can compare the change in the distribution of the scores between the two groups?

Or would it make sense to some kind of multivariate analysis and use "OSA/nOSA" as a variable and see if it significantly contributes to the change in quality of life after surgery. Could I do a multivariate regression model of some kind?

Using SPSS...

Any insights most welcome!

• Summated scale scores from health-related quality of life questionnaires are generally treated as numerical variables, so that parametric and non-parametric tests for continuous data are used. If, on the contrary, you are interested in responses to a particular Likert-type item, then treating those responses as ordinal make sense (although many authors would still rely on statistical tests for continuous data, provided the distribution of responses does not exhibit a high skewness). – chl Sep 28 '14 at 19:22
• I would strongly advise against treating ordinal data as numeric on an interval or ratio scale. It's a hack, and just because it's commonly done doesn't make it valid. You should look into ordinal mixed regression, which handles the repeated-measures design nicely. Beware that this will take you some time to get acquainted to, as both the theory and the correct model specification can be difficult to grasp at first. – coanil Sep 29 '14 at 12:10
• Your design seems to be quite simple. There is one fixed between-group factor (OSA vs nOSA) and one fixed repeated-measures factor (pre-Sx vs post-Sx). The model is Y = RMfactor + BGfactor + RMfactor*BGfactor where the significance of the last term, the interaction, is what interests you. The only dilemma is whether to treat Y as interval or as ordinal. If interval - simply use linear model (usual ANOVA). If ordinal - use generalized linear model (in a form of GEE, "generalized estimating equations") with cumulative logit or probit link function (i.e. "ordinal ANOVA"). – ttnphns Sep 30 '14 at 2:31

If you are familiar with ordinal logistic regression models and mixed-effects models with lmer in the lme4 package in R, you may want to check out the clmm (cumulative link mixed models) function in the ordinal package. This function, built on lmer, may prove especially useful if you have covariates to control for.

I suppose this answer may be more relevant to Brian's problem than that of @user45094; I am not sure if SPSS has something like cumulative link mixed models.

I believe the Wilcoxon signed-rank test is the one that fits your situation the best. Check here or reference  for more detailed explanation about the test.

The Wilcoxon signed-rank test is used to compare two paired samples when data are either interval scale but assumptions for the paired t-test (normality of within-pair differences) are not satisfied or ordinal (ranked) scale. The hypothesis being tested is whether the median difference is zero (as opposed to mean difference in the paired t-test). 

Moreover, one assumption about the test is that "the distribution of the differences between the two related groups (i.e., the distribution of differences between the scores of both groups of the independent variable; for example, the reaction time in a room with "blue lighting" and a room with "red lighting") needs to be symmetrical in shape" 

If the above assumption doesn't hold in your real data, another suitable test is the Sign test 

The reference  and  are tutorials of using SPSS to conduct the two tests, which I think exactly fits your case.You can find the step-by-step explanations through the two links.

Hope this helps.

Reference:

 Evie McCrum-Gardner, 2008, "Which is the correct statistical test to use?"