*! version 1.0.0 10aug12
help laplace

Title

laplace -- Laplace regression

Syntax

laplace depvar [indepvars] [if] [in]
[, laplace_options]

laplace_options

Model
quantiles(numlist) specifies the quantiles; default is quantiles(.5)

failure(varname) specifies the failure variable

sigma(varlist) specifies the variables to be included in the scale parameter model; default is constant only

Estimation
reps(#) perform # bootstrap replications; default is reps(20)

seed(#) set random-number seed to #

tolerance(#) tolerance for the log-likelihood; default is tolerance(1e-10)

maxiter(#) perform maximum of # iterations; default is maxiter(2000)

Reporting
level(#) set confidence level; default is level(95)

by, statsby, and xi are allowed with
laplace; see prefix.

See [R] sqreg postestimation for features
available after estimation.

Description

laplace estimates Laplace regression models for percentiles of a response variable with possibly censored data.
Typical applications are in time-to-event or survival analysis. For example, Laplace regression can estimate and
compare median survival across treatment or exposure groups.

Options for laplace

Model

quantiles(numlist) specifies the quantiles as numbers between 0 and 1;
numbers larger than 1 are interpreted as percentages. The default value is 0.5, which corresponds to the median.

failure(varname) specifies the failure event;
the value 0 indicates censored observations. If failure() is not specified, all observations are assumed to be uncensored.

sigma(varlist) specifies the variables to be included in the scale parameter model. Default is constant only.

Estimation

reps(#) specifies the number of bootstrap replications for estimating
variance-covariance matrix and standard errors of the regression coefficients.

seed(#) sets the initial value of the random-number seed used by the bootstrap. If seed(#) is specified the bootstrapped estimates are reproducible (see set seed).

tolerance(#) specifies the tolerance for the coefficient vector. When the absolute change in the log-likelihood from
one iteration to the next is less than or equal to tolerance(), the tolerance() convergence criterion is satisfied.
tolerance(1e-10) is the default.

maxiter(#) specifies the maximum number of iterations. When the number of iterations equals maxiter(), the optimizer stops,
displays an "x" and presents the current results. maxiter(2000) is the default.

Reporting

level(#); see
[R] estimation options.

Examples

Use the cancer trial dataset

sysuse cancer, clear

Estimate median survival by drug assuming no censored observations

xi: laplace studytime i.drug

Estimate median survival by drug with censored observations

xi: laplace studytime i.drug, fail(died)

Estimate the 25th, 50th (i.e. median), and 75th percentile

xi: laplace studytime i.drug, q(.25 .5 .75) fail(died)

Estimate the 50th percentile in drug groups 2 and 3

lincom [q50]_cons + [q50]_Idrug_2

lincom [q50]_cons + [q50]_Idrug_3

Test equality of median survival across drug groups

testparm _Idrug_2 _Idrug_3, eq(q50)

Adjust for age

xi: laplace studytime i.drug age, q(.25 .5 .75) fail(died)

Reference

Bottai, M. and Zhang, J. (2010), Laplace regression with censored data. Biometrical Journal, 52: 487-503

Authors

Matteo Bottai

Unit of Biostatistics

Institute of Environmental Medicine, Karolinska Institutet

Stockholm, Sweden

Nicola Orsini

Unit of Nutritional Epidemiology

Unit of Biostatistics

Institute of Environmental Medicine, Karolinska Institutet

Stockholm, Sweden

Saved results

laplace saves the following in e():

Scalars

e(N) number of observations

e(N_fail) number of failures

e(n_q) number of estimated quantiles

e(reps) number of bootstrap replications

Macros

e(cmd) laplace

e(cmdline) command as typed

e(depvar) name of dependent variable

e(eqnames) names of equations

e(qlist) requested quantiles

e(vcetype) title used to label Std. Err.

e(properties) b V

e(predict) program used to implement predict

Matrices

e(b) coefficient vector

e(V) variance-covariance matrix of the estimators

Functions

e(sample) marks estimation sample

Also see

Manual: [R] qreg

Online: [R] qreg postestimation;

[R] bootstrap