Is using a questionnaire score (EuroQol's EQ-5D) with a bimodal distribution as outcome in linear regression a problem? There is currently a debate whether the EQ-5D score that has a ceiling problem and a bimodal distribution can be used in a linear regression model or not.
Background
The score is very simple and frequently used to assess patient's health related quality of life and consists out of five questions where each has 3 possible answers (there is a newer with 5 answers but it's less used).
The score is commonly used in national registries as a patient reported outcome measure (PROM) and is very convenient because the questions are easy to answer and the completeness is therefore good.
Continuous score
The score is created by using a "tariff" where unique combinations of the 5 variables translate into a continuous-like variable but with the above mentioned limitations. I'm not sure how they decide on the tariff score but the different combinations of the answers combine into a unique value, for instance if you have answered best health on all five categories you get a code of 11111 that gives the maximum of 1.000. If you've answered best on the first 2 question and worst on the last 3 you have a code of 11333 and get a score of -0.066. The score is country-adjusted and ranges between -0.594 to 1.000 in my Swedish tariff.
The Paretian calculation
In most orthopaedic studies we have a preoperative score and a postoperative score. By comparing the two models as the Paretian Classification of Health Change suggests we get four possible outcomes; no change, worse, improved, or mixed change. Mixed meaning that one category became improved while another one deteriorated. As I understand the Paretian outcome is best analyzed using a multinomial logistic model.
My questions

*

*When having large datasets of > 10 000 patients does it matter that the score is not normally distributed and is the Paretian way of analyzing the score better?

*Scores like this are very frequently used today - what are the limitations?

Update
After taking all these wise arguments and discussing them closer with our statistician I got some interesting input:

*

*In large sample the central limit theorem will kick in as long as the sample isn't heavily skewed

*If the score itself has a flaw (as the EQ-5D score) it might not be right to expect a normal distribution because the bimodality is not due to a subgroup but due to a score feature (I think this is a different way of putting what @whuber wrote: "... The residuals will closely reflect that error distribution"

*The normality of the sample helps in calculating the p-value/confidence interval and this could be circumvented by using bootstrapping

*Using ordinal regression and leaving out the mixed group we can validate the results from the linear regression - i.e. show that the predictors behave similarly when used "non-parametric"

 A: One question that you ought to ask first is whether or not using a weighted score is correct for the kind of analysis that you want to do.  There is a discussion of that in Parkin, D., Rice, N. and Devlin, N. (2010) Statistical analysis of EQ-5D profiles: Does the use of value sets bias inference? Medical Decision Making. 30(5), 556-565 doi: 10.1177/0272989X09357473 The Paretian classification is described and discussed in Devlin, N., Parkin, D. and Browne, J. (2010) Patient-reported outcomes in the NHS: New methods for analysing and reporting EQ-5D data. Health Economics. 19(8), 886-905.DOI: 10.1002/hec.1608
If using the score is OK, what really matters is the distribution of the regression residuals, not the score. If you are using the Paretian classification, you are correct that an ordered model can't be used.
'Tariff' is a slightly silly label, but for historical reasons has been used in this context. Just means a set of scores attached to categorical EQ-5D health states. 
A: First, categorizing continuous variables is generally a bad idea; Royston, Altman and Saurbrei wrote a good article on why dichotomizing is bad, and the same arguments apply to more categories. Altman wrote an article on categorizing variables, but only the abstract is freely available, and I have not read the whole article.
Second, the assumptions of linear regression are not that the dependent variable is normally distributed, but that the residuals from the model are. So, before you can see if your model violates the assumptions, you need to run it and look at the results.
Third, if the residuals are not normally distributed, you have several choices:


*

*Multinomial logistic regression with the four categories you list

*Ordinal logistic regression with "mixed" excluded.

*Looking at each category separately

*Some sort of robust regression


Before doing any of these, my impulse would be to look at the variables graphically, with density plots and possibly quantile normal plots.
A: if you have some predictor variables (which I'm assuming you have as you mention regression in your question), I'm wondering if an ordinal logistic regression, using the Paretian measure as the dependent variable (which appears to be ordered categories of pre- versus post- differences), is the best way forward. I love the UCLA websites for the clarity of their explanations of various methods, here is their outline of ordinal logistic regression using SPSS and  here is their example for Stata. As you can see from these sites, you will need to verify that the proportional odds assumption is met with your data. 
Ordinal logistic regression is an accepted statistical method, and Professor Agresti has written about it in his books on categorical data analysis. I recommend buying any of his books if your work is taking you down categorical data analysis paths.
