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When analyzing a lognormal data with left-censored values using a regression model, I have read that you can use methods that fit right-censored data but “flip” the data by subtracting from some large constant. Why does this work? Why are the coefficients the same?

This link describes the NADA package: "The routines in NADA for R internally flip the original data by subtraction from a large constant, in order to produce right-censored values that can be input to survival analysis routines."

The survreg library in R has the option for "type=left", but I am not clear on the correspondence, and I would like to see the equations and make survreg match NADA.

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  • $\begingroup$ I would be surprised if this worked. Do you have a reference? What software are you hoping to use? $\endgroup$
    – Cam.Davidson.Pilon
    Commented Mar 27, 2022 at 20:08
  • $\begingroup$ Are you talking about a parametric regression model? If so, you can use the likelihood contribution from left-censored observations directly. I don't see how that time-reversal trick will work for a fully parametric AFT (e.g., lognormal) model. Also, how sure are you that the data are actually left censored? Klein and Moeschberger suggest this method in Section 5.2 for getting product-limit estimates with left censoring, but continue to say "Examples of pure left censoring are rare." $\endgroup$
    – EdM
    Commented Mar 27, 2022 at 20:35
  • $\begingroup$ Yes, I was referring to a lognormal parametric regression for left-censored observations. In some fields, these are called "non-detects" and there are a few textbooks devoted to this topic, such as Dennis Helsel's "Nondetects and data analysis". This book is often cited as a reference for the reversal trick, but I don't have access to the book. $\endgroup$
    – julieth
    Commented Mar 27, 2022 at 21:07

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If the only censoring is left censoring, as you can have with chemical concentrations that are below a detection limit, that "time"-reversal (here, concentration-reversal) method will work for getting nonparametric, Kaplan-Meier-type curves. With left censoring, Klein and Moeschberger suggest in Section 5.2

instead of measuring time from the origin we fix a large time 􏱣$\tau$ and define new times by $\tau$􏱣 minus the original times. The data set based on these reverse times is now right-censored and the estimators in sections 4.2–4.4 can be applied directly.

That's not, however, the way that the NADA package handles parametric regression models. For that, according to the manual page for cenlme():

This routine is a front end to the survreg routine in the survival package

which directly uses the appropriate contributions to the likelihood from left-censored observations in a parametric model.

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  • $\begingroup$ Looking at the source link, it appears there is subtraction from a constant and then it is passed to survreg. $\endgroup$
    – julieth
    Commented Mar 27, 2022 at 21:22
  • $\begingroup$ @julieth see this page, line 224 to see what happens with a regression model. Even if your define the outcome in the NADA package's Cen() format, for a regression model it just puts it back into a standard Surv() object for survreg() via the NADA package's asSurv() function. That Cen() format seems only to be used for models where it makes sense. $\endgroup$
    – EdM
    Commented Mar 27, 2022 at 23:04

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