Is Tobit regression appropriate for ELISA data with out of range values?

[Mudit Agarwal]

My thesis is on analysing cytokine values across two groups (control and intervention) and I have two sets of observations - baseline and 1 week post intervention.
The cytokine levels were analysed using ELISA and a bunch of values are out of range (higher than highest standard).

1. Is it appropriate to use a Tobit regression model with right censoring to account for the out of range values?

2. To account for individual level variability, is it better to use a difference of the baseline and 1 week values, or to include the baseline values as a covariate in the tobit model?

Thank you for helping
Regards

[Jeff Wooldridge]

What is the logical range, and what range of measurements do you have? Is the idea to set the values outside the range to the largest or smallest logical value?

[Clyde Schechter]

The logical range for cytokine measurements is any non-negative real number. But actual assays used in clinical laboratories have an upper limit of measurement. Consequently, the most extreme high values are reported as > [fill in the lab's upper limit of measurement range for the particular cytokine]. Consequently the reported values are right censored. And, yes, tobit regression can be used--I have seen it done.

BUT, tobit assumes that the observed values are derived from an underlying latent variable and a normally distributed error term, which is then censored for observation. This normality of the error term is usually strongly violated in the case of cytokine measurements, where it is usually more like lognormal. (That is the measurement error is characterized by a constant coefficient of variation, rather than a constant variance.) So one approach is to first log-transform the cytokine variable and then apply tobit, with censoring at the log of the upper limit of measurement. Another approach that is, I think, actually better, but is extremely difficult to explain to non-statistical audiences because it is very counter-intuitive, is to use semi-parametric survival analysis, with the cytokine measurement (untransformed) serving as the "survival time" variable.

And although I have seen analyses in which the censored values are replaced by the upper limit of measurement range and then analyzed, this is a poor choice for cytokines because the true value may be one or even several orders of magnitude greater than the upper limit of measurement. Cytokine levels can be really wild! (In that regard, it is different from, say, a blood glucose value reported as > 500 mg/dl. There it would be somewhat reasonable to treat it as if it were 500 because glucose levels very seldom go very much higher than 500 mg/dl, and in the rare worst case you wouldn't be off by more than a factor of 2.)

[Mudit Agarwal]

Thank you for your reply! This was really helpful. Yes I have log transformed the cytokine values for the tobit model, apologies I didn't mention that.
I am not very well versed with survival analysis, but I will look into it. Thanks again!