Alternative to tobit regression for left-censored biomarker variable

[Claire Sweeney]

Hi,

I'm a novice when it comes to stats so apologies if the question is a bit stupid!

I'm currently trying to do multivariate analysis on a biomarker variable, which is my DV. This variable is left-censored due to the limit of detection on the assay. The variable is non-normal, even after log-transformation. For these reasons, linear regression is inappropriate. I have explored tobit regression but due to a high degree of heteroscedasticity, the model is very inconsistent. I've also tried quartile regression with ordinal regression, however, the test for parallel lines is significant so I don't feel this method is appropriate either. Could anyone advise me on an alternative method? I'm currently using SPSS but also have access to STATA.

Thanks,

Claire

[Nick Cox]

There is an entire book on this problem -- start at https://www.practicalstats.com/nada/nadatext.html -- which I own but have only glanced at. I don't get a clear picture of how the problematic measurements are coded, whether as zeros with an understanding that observed zeros may well mean a little more, or conversely as detection limits with the understanding that the unobserved values may well be less.

Setting that aside, normality is an ideal condition only for errors perturbing a linear functional form; it sounds as if you may be focusing on the marginal distribution.

If this were my problem I would first read Helsel's book, but I haven't got enough time to do that right now. Either way, my strong impression with concentration data -- particularly if upper limits do not bite at all, which is the implication here -- is that i would considering work on logarithmic scale, using a generalised linear model.

I don't get a clear picture of what is happening for you with quantile (not quartile) regression.

[Joao Santos Silva]

Dear Claire Sweeney,

Further to Nick's very helpful advice, you may want to consider symmetrically censored least squares (the command scls is available form SSC) or censored quantile regression; I do not understand what you say about parallel lines.

Best wishes,

Joao

[Phil Bromiley]

Let me restate Nick's important point - regression only assumes normality of the errors (i.e., it does not assume normality of the dv or rhs variables) and that largely for getting test statistics. So, non-normal dv's do not inherently rule out regression.

Your mention of parallel lines suggests you're thinking about something and have run a model that you have not explained to us. Stata's tobit has an option for robust standard errors that take care of heteroscedasticity.

[Joao Santos Silva]

Dear Phil Bromiley,

I may be missing something, but the consistency of the Tobit estimator depends on the homoskedasticity assumption, so robust standard errors will not help at all. Hence my suggestion of regression methods that do not require homoskedasticity.

Best wishes,

Joao