R glm for censored data

Question

I want to know if there is a significant difference in a blood biomarker concentration between 2 populations (population 1 = healthy individuals - population 2 = sick individuals). I need to control for the factor 'region'.

My issue is that the distribution of population 2 is not normal (data are censored following the upper detection limit by the lab device) as shown on these plots:

With a normal distribution I would use this model in R:

m <- glm(blood.biomarker ~ status + region + status*region, data=f, family="gausian") # status = healthy or sick
summary(m)
emmeans(m, list(pairwise ~ status), adjust = "tukey")

I am a bit confused regarding the model or the glm family I should use in this case.

I also have a similar situation but with 3 groups (1 group has a normal distribution and 2 groups have a censored distribution). How to deal with this?

If you have censored data then you need survival analysis. vanilla linear models will not do. — user2974951, Feb 16 '23 at 08:56
In survival analysis we assume that censoring is independent which is not the case here — Wael, Feb 17 '23 at 12:56

score 3 · Accepted Answer · answered Mar 18 '23 at 15:24

The blood biomarker concentration measurements are censored because of the upper detection limit (at 2,500 judging from the plots).

You can use ordinal regression (aka proportional odds regression) to model the data. You can also do a Wilcoxon rank-sum test to compare populations 1 and 2 or the Kruskal-Wallis test to compare more than two populations. But with the tests you cannot include additional covariates (such as region) and in any case ordinal regression generalizes these tests.

Alternatively, you can use tobit regression.

Keep in mind that the censoring implies some loss of information. For example, you can't learn much about the upper quantiles of the blood biomaker in population 2, other than they are ≥ 2,500. Similarly, you cannot do precise inference (say a 95% two-sided confidence interval) for the population 2 mean.

Here are some relevant threads/links:

Biostatistics for Biomedical Research Sections 7.3.1 and 7.6.2 analyze data censored at an upper detection limit of 2,5000, just as in your case.
Tobit models and Ordinal logistic regression by the UCLA Stats Help.
What regression approach would suit zero-inflated data that is censored at a fuzzy threshold?
Explanation of a censored regression model

Or search for censored regression on Cross Validated.

score 1 · Answer 2 · answered Mar 18 '23 at 15:43

1

Possibly you might figure out some distribution and apply some censurized estimation method.

But, in this case, a single regressor (the groups), it might be easier to perform a permutation test.

answered Mar 18 '23 at 15:43

Sextus Empiricus

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R glm for censored data

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