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.
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.
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.
- 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?
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"