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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. 

Papers
Bottai M, Zhang J. Laplace regression with censored data. Biom J, 52(4):487503, 2010. Bottai M, Zhang J. Authors' reply. Biom J, 53: 861866, 2011. Bottai M, Orsini N. A command for Laplace regression. Stata J, 13(2):302314, 2013. Bottai M, Orsini N, Geraci M. A Gradient Search Maximization Algorithm for the Asymmetric Laplace Likelihood. J Stat Comp Simulation. 85(10):19191925, 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: 5363, 2017. Software Stata command Download with the following Stata commands:
net from http://www.imm.ki.se/biostatistics/stata Workedout 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 ctqr 
Presentations
August 1114, 2013 Incidence Percentiles European Congress of Epidemiology. Aarhus, Denmark June 1012, 2013 A Percentile approach for timetoevent analysis 4th NordicBaltic Biometric Conference, Stockholm, Sweden June 1012, 2013 Quantile regression for censored data using flexible Laplace regression 4th NordicBaltic Biometric Conference, Stockholm, Sweden July 1417, 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 timescale. Am J Epidemiol. 2015, 182(3):2717. 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):6028. Rizzuto D, Orsini N, Qiu C, Wang HX, 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):7701. 
Unit of Biostatistics, Nobels väg 13, Karolinska Institutet, 17177 Stockholm, Sweden 