Linear model with categorical variables (and constant variable) in R

Question

I'm trying to estimate days spent in hospital (length of stay, continuous variable) based on a clinical severity score (categorical, integer: 1, 2 or 3). The numbers reflect level of severity, so 1 is mild, 3 is severe.

I'm also interested to know if age (integer, continuous variable) confounds this as well.

In R, my code is as follows, but I'm unsure if I'm treating the categorical variable for severity score correctly.

df$scoreFac <- factor(df$score)
lm.model <- lm(lengthOfStay ~ scoreFac, data = df)

summary(lm.model)

The result coefficient is:

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   1.1705     0.1680   6.757  2.02e-10 ***
scoreFac2     0.4313     0.1768   2.429  0.02623 *  
scoreFac3     0.5340     0.1769   2.912  0.00383 ** 

If I want to add age onto this:

lm.modelB <- lm(lengthOfStay ~ scoreFac + age, data = df)
summary(lm.modelB)

Resulting in coefficient output:

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.753531   0.210627   3.631  0.00035 ***
scoreFac2   0.363182   0.175734   1.938  0.05595 .  
scoreFac3   0.434588   0.175463   2.485  0.01665 *  
age         0.008762   0.002147   3.158  0.00173 ** 

Should I be representing score differently (such as using score not scoreFac)? I'm not sure if I'm able to correctly interpret the esimtate when there's the dummy variables for score.

Answer 1

If you use score (the original variable) then you are assuming that severity is actually continuous. This may be a fine assumption. I know it's numbered 1, 2, 3, but surely those are just convenient measures. It could be between mild and moderate, or moderate and severe, or even vary within severe.

The problem would be that you are also assuming that it is interval level: That the differences between mild and moderate and between moderate and severe are the same. Even that may not be unreasonable, and you could do sensitivity analysis, using different numbers instead of 1, 2, and 3 and see what happens.

If you are not willing to make those assumptions, you can use ScoreFac, then each parameter estimate is comparing to the lowest level (by default).

Yet another possibility is to use a method like optimal scoring.

Finally, lm may not be right. LOS variables are typically very skewed, and, while lm does not make assumptions about the variable (only the residual), it may be better to use a robust method. And, if you have any censored observations (people still in the hospital when the study was done) you will need to use a survival method such as Cox.