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Laplace Regression
Survival percentiles represent important summary measures of a time variable of interest. For example, knowing that 50% of some patients die in a week while 10% of them survive one year may be of interest to researchers, clinicians, and patients alike. Laplace regression provides efficient estimates of survival percentiles and the effects of exposures on them. In the absence of censoring, Laplace regression is equivalent to ordinary quantile regression.
Bottai M, Zhang J. Laplace regression with censored data. Biom J, 52(4):487-503, 2010.

Bottai M, Zhang J. Authors' reply. Biom J, 53: 861-866, 2011.

Bottai M, Orsini N. A command for Laplace regression. Stata J, 13(2):302-314, 2013.

Bottai M, Orsini N, Geraci M. A Gradient Search Maximization Algorithm for the Asymmetric Laplace Likelihood. J Stat Comp Simulation. 85(10):1919-1925, 2015.

Frumento P, Bottai M. Laplace regression: a robust and computationally efficient estimator for censored quantiles. Working Paper, 2021.

Related Topics
An estimation equation for censored, truncated quantile regression implemented in the R package ctqr.

Frumento P, Bottai M. An estimating equation for censored and truncated quantile regression. Comput Stat Data An. 113: 53-63, 2017.


Stata command

Download with the following Stata commands:

net from http://www.imm.ki.se/biostatistics/stata
net install laplacereg, replace
net install laplace_surv, replace

Note: until Stata version 14, the "laplacereg" command was named "laplace". The name was changed after Stata version 15 was released, because it conflicted with the newly implemented set of functions for the Laplace distribution.

Worked-out examples in Stata

Example 1: Estimation of survival percentiles with data from a clinical trial on metastatic renal carcinoma

Example 2: Estimation of adjusted survival curves

R package

August 11-14, 2013
Incidence Percentiles
European Congress of Epidemiology. Aarhus, Denmark

June 10-12, 2013
A Percentile approach for time-to-event analysis
4th Nordic-Baltic Biometric Conference, Stockholm, Sweden

June 10-12, 2013
Quantile regression for censored data using flexible Laplace regression
4th Nordic-Baltic Biometric Conference, Stockholm, Sweden

July 14-17, 2012
Laplace regression: a novel method for modeling survival data
8th International Conference on Diet and Activity Methods. Rome, Italy

November 11, 2011
A command for Laplace regression
4th Nordic and Baltic Stata Users Group meeting. Stockholm, Sweden

Selected Applications
Bellavia A, Discacciati A, Bottai M, Wolk A, Orsini N. Using Laplace regression to model and predict percentiles of age at death, when age is the primary time-scale. Am J Epidemiol. 2015, 182(3):271-7.

Johannessen A, Skorge TD, Bottai M, Grydeland TB, Nilsen RM, Coxson H, Dirksen A, Omenaas E, Gulsvik A, Bakke P. Mortality by Level of Emphysema and Airway Wall Thickness. Am J Respir Crit Care Med, 2013, 187(6):602-8.

Rizzuto D, Orsini N, Qiu C, Wang H-X, Fratiglioni L. Lifestyle, social factors, and survival after age 75: population based study. A population based study. BMJ, 2012; 345:e5568

Orsini N., Wolk A, Bottai M. Evaluating percentiles of survival. Epidemiology, 2012, 23(5):770-1.

Unit of Biostatistics, Nobels väg 13, Karolinska Institutet, 17177 Stockholm, Sweden