Interval-censored survival analysis
intcens depvar1 depvar2 [indepvars] [weight] [if exp] [in range] , distribution(distname) [time odds eform robust cluster(varname) cwien(varlist) small(#) level(#) init(matname) maximize_options] Description
intcens fits various distributions to a non-negative outcome y which is known to be in the interval [depvar1,depvar2] and which depends on indepvars. y for each observation is either point data, interval-censored, left-censored or right-censored. depvar1 and depvar2 should have the following form:
Type of data depvar1 depvar2 ---------------------------------------------- point data a = [a,a] a a interval-censored [a,b] a < b left-censored (0,b] . b or 0 b right-censored [a,inf) a . ----------------------------------------------
Any st settings are ignored.
Options
distribution(distname) is not optional. Available distributions are:
Distribution syntax remarks ---------------------------------------- Exponential exp Weibull weib Gompertz gomp Log-logistic logl or llo Log-normal logn or ln 2 parameter gamma gam note difference from streg Generalized gamma gen 3 parameter gamma Inverse Gaussian invg Inverse Gaussian wien Alternative parameterisation Time to endpoint of wienran See below for parameterisations Wiener process with random drift
time requests that exponential or Weibull results be reported in accelerated failure form.
odds requests that log-logistic estimates be presented as log odds ratios. The default is accelerated failure form.
If eform is specified then exponentiated coefficients are reported. The default is to report log hazard ratios etc.
cwien(varlist) is only valid with distributions wien or wienran. It allows the initial distance from the endpoint of the Wiener process to be modelled as a function of covariates (see below).
robust specifies that the sandwich estimator of variance is to be used in place of the conventional MLE variance estimator. robust combined with cluster() further allows observations which are not independent within cluster (although they must be independent between clusters).
cluster(varname) specifies that the observations are independent across groups (clusters) but not necessarily independent within groups. varname specifies to which group each observation belongs. cluster() implies robust; that is, specifying robust cluster() is equivalent to typing cluster() by itself.
small(#) specifies a tolerance within which interval-censored observations are treated as point data. The default is 1E-6. level(#) specifies the confidence level, in percent, for the confidence intervals of the coefficients; see help level.
maximize_options control the maximization process; see help maximize.
init(matname) supplies a matrix of inital values. They must be in the correct order but the columns do not need to be labelled. Use this option rather than from(), which is one of the maximize_options.
Parameterisations
The exponential, Weibull, Gompertz, log-logistic, log-normal and generalized gamma distributions are parameterised as in streg. The log-likelihoods reported for the distributions which are special cases of the generalized gamma are calculated so as to be comparable to the generalized gamma using likelihood ratio tests.
The log-logistic results can also be shown as odds ratios, in which case the survivor function is: S(t) = 1/(1+lambda*t^(1/gamma)), lambda=exp(X*B) The other densities are:
Two parameter gamma gam f(t) = (lambda*alpha)^alpha*t^(alpha-1)*exp(-lambda*alpha*t)/gamma(alpha), lambda = exp(-X*B)
Inverse Gaussian invg f(t) = 1/sqrt(2*pi*phi*t^3)*exp(-(t-eta)^2/(2*eta^2*phi*t)), eta = exp(X*B)
Inverse Gaussian wien f(t) = c/sqrt(2*pi*t^3)*exp(-(mu*t-c)^2/(2*t)), mu = exp(X*B), c = exp(X1*B1)
This is the time to first reach a distance c from the starting point for a Wiener process with drift rate mu and variance parameter 1. The two parameterisations are related by eta = c/mu, phi = 1/c^2.
Allowing the drift rate to have a normal distribution between subjects with mean mu and standard deviation tau gives the following density for time to reach c (not a proper density because the event may never happen). There may be convergence problems with this model: wienran f(t) = c/(sqrt(2*pi)*t*sqrt(t^2*tau^2+t))*exp(-(mu*t-c)^2/(2*(t^2*tau^2+t))), mu = exp(X*B), c = exp(X1*B1)
With the distributions wien or wienran, X is indepvars, the covariates listed before the comma, and X1 is the covariates in the option cwien( ). X would be factors which affect the rate of movement towards the endpoint, while X1 would be factors which reflect the initial distance from the endpoint.
See: Aalen O.O. & Gjessing H.K. (2001) Understanding the shape of the hazard rate: A process point of view. Statistical Science, 16, 1.
Examples
. intcens t0 t1 age trt, dist(weib) . intcens t0 t1 age trt, dist(weib) time . intcens t0 t1 age trt, dist(logl) odds . intcens t0 t1 age trt, dist(invg) . intcens t0 t1 trt, dist(wien) cwien(age)
Author Jamie Griffin Infectious Disease Epidemiology Unit London School of Hygiene and Tropical Medicine jamie.griffin@lshtm.ac.uk Updated 11th October 2005
Manual: [ST] streg Online: help for streg