Censored regression (Tobit-style)

Shown in the app as censored_regression. Part of the method reference, under Survival and censored data.

When to use

Model a censored continuous outcome from predictors without substituting detection limits (lognormal or gaussian error distribution).

What you provide

• Outcome: one numeric column.
• Predictors: one or more columns.

Options

Missing data

• Complete case (listwise deletion)

Multiple comparisons

• Not adjustable for this method. Where it makes post-hoc comparisons, the procedure applies its own correction.

Related methods

Other methods under Survival and censored data:

• Peto-Peto generalized Wilcoxon test
• Kaplan-Meier (log-rank test)
• Cox proportional-hazards regression
• Weibull accelerated failure time regression
• Factors associated with outcome (time-to-event outcome)

Guides that discuss this method

• How to analyse values below the detection limit

Worked example

Celeus's result on a published or illustrative dataset, next to an independent computation and, where one exists, a published value. The data themselves are not reproduced here.

synthetic left-censored lab example (censored regression)

• Source: Illustrative or synthetic example data
• Licence: synthetic (no third-party content)
• Reference: Hand-authored synthetic fixture for censored regression; not published data

Quantity	Celeus	Independent computation	Published value	Agrees
Number of observations	32	32	-	Yes
Distribution for the censored outcome	lognormal	lognormal	-	Yes

Validation report

References

1. Tobin, J. (1958). Estimation of Relationships for Limited Dependent Variables. Econometrica 26: 24-36. doi:10.2307/1907382 doi:10.2307/1907382
2. Helsel, D. R. (2012). Statistics for Censored Environmental Data Using Minitab and R. John Wiley & Sons, 2nd edition.
3. Therneau, T. M., Grambsch, P. M. (2000). Modeling Survival Data: Extending the Cox Model. Springer, New York. doi:10.1007/978-1-4757-3294-8 doi:10.1007/978-1-4757-3294-8