I am using R to build a model. My outcome variable is the number of patients with specific disease of interest (Call it X) in health facilities over the past 7 days. I converted the count data to proportion by: Number of patients with x in past 7 days/number of total patients past 7 daysX100 %. I used Poisson regression but since there is overdispersion, I moved to Negative Binomial Poisson regression. One point I should mention is both the count data and the proportion are not normally distributed. I read that converting count data to percentages isn't advisable. But we want to appreciate the count of patients for the disease we are studying regarding the total number of patients visiting the facility for any illness. Is Negative binomial regression a best approach? do you suggest better approach?
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$\begingroup$ Have you considered Binomial regression? It sounds very much as if you are modeling something binomial. $\endgroup$– BernhardCommented May 1, 2023 at 9:38
3 Answers
This does not really make sense to me. Modelling a count of things (e.g. patients) as Poisson, Negative binomial or a version of these with overdispersion, and possibly with an offset for number of days or the like (these are, after all, distributions for counts - you could also truncate them, if you want to reflect that the total number of beds is limited). Modeling a percentage as Poisson (NegBin etc.) when you know the denominator makes no sense to me (your model doesn't even respect that a proportion needs to be in [0,1] / percentage in [0, 100]). If a known denominator, a percentage is better modelled as a binomial outcome (e.g. using a form of logistic regression) e.g. as X out of available bed-days (=number of beds times days). If you didn't know the denominator, something like beta-regression is an option.
Also, there's presumably some correlation (patients likely rarely stay one night, which you are not modeling, which you could try to do). It can often be a good idea to write down the data generating process and describe all of it using distributions that make sense.
I have a count data converted to proportion which test to use?
I read that converting count data to percentages isn't advisable. But we want to appreciate the count of patients for the disease we are studying regarding the total number of patients visiting the facility for any illness.
You can convert the data for the purpose of presentation, but that doesn't restrict you to perform any of the analysis on the raw non-converted count data. Converting to proportions doesn't make that you need to change the test that you use (but of course, you shouldn't enter the converted numbers directly into your test algorithm).
One point I should mention is both the count data and the proportion are not normally distributed.
Is Negative binomial regression a best approach?
It is difficult to make an assessment of this without more details. There are many ways to analyse count data.
In any case, the fact that some data is not normally distributed doesn't mean a lot. And, how much does it differ from normal distributed data?
- Poisson and binomial distributed data is in any case not normally distributed and discrepancies are to be expected. How bad does the distribution look like? Is it like several outliers, multiple modes, or is it just a shape of the distribution that's not very close to the typical bell shape?
- Even if a normal distribution would be theoretically expected for some analytical method (instead of Poisson, binomial or generalized versions of them), then discrepancies from the theory do not directly make that the application of the model is bad. A lot of models are still consistent and/or efficiënt even if some of the assumptions are not fulfilled. See also: Is normality testing 'essentially useless'? and Regression when the OLS residuals are not normally distributed
- Another aspect with the statement is that it is more precisely the conditional distribution that matters, and not the distribution of the total marginal data (it is not clear which one you are referring to). See also: Where does the misconception that Y must be normally distributed come from?
What matters is that you use a model that closely resembles your situation. Those models will typically give more accurate estimates.
It seems like you could remove the multiplication by 100 and model this outcome using a binomial or quasibinomial (if there’s overdispersion) regression model. You can model proportions or percentages with this model but you have to state the total number of possible counts. They are two ways you can express this model. See below:
prop.m1 <- glm(cbind(Successes, Total - Successes) ~ X1,
data = df,
family = binomial)
prop.m2 <- glm(Proportion ~ X1,
data = df,
family = binomial,
weights = Total) # provide prior weights
