st: Interval censoring using intcens

[<S.Jenkins@lse.ac.uk>]

Steve Samuels provided very good advice. Some other reflections from me:

-intcens- (on SSC) is a program that fits parametric _continuous_
survival time distributions to interval-censored survival time data
(a.k.a. as grouped or discrete time data). The program doesn't allow
time-varying covariates. It has one row per spell/obs -- convenient for
the maximisation by -ml-.

I'm not sure that -stpm- (which you ask about) is appropriate for
interval-censored data. I would check further if I were you. (If it is,
then also check out -stpm2- which is more flexible and faster. Use
-findit- to get latest version -- it's from SJ or SSC.)

You could think more generally about models for interval-censored data
-- see the MS and lessons off my survival analysis webpages (URL below)
for discussion and references.  This shows how you can fit models which
make no assumption about the shape of the underlying survival time
distribution. (You can assume shapes for the interval-hazard if you
wish; but can also assume interval-specific values if you wish and your
data allow it.) And time-varying covariates can be easily incorporated.

More complicated is what to do with multiple spells. (You don't mention
them explicitly, but it sounds as if you have them according to your
description.)   The key issue is non-independence across spells from the
same person. Steve Samuels remarked on this and suggested clustering the
standard errors (persons as clusters). An alternative is to assume some
parametric form for the individual-specific effect that generates the
non-independence across spells from the same person -- this is 'frailty'
a.k.a. 'unobserved heterogeneity'. The most straightforward of handling
this would be:
* Reorganise (expand) your data so that you have one row in data set for
each interval that each person is at risk of infection, and create an
event occurrence indicator y_it for person i and interval t (see my
Lessons)
* Create any time-varying covariates required. At minimum, this will be
some specification for the duration dependence of the interval hazard
* fit a -xtcloglog- model with the binary outcome variable being y_it.
This assumes that the person-specific frailty is normal (Gaussian). Or
just fit a -cloglog- model if you want to ignore frailty. Either way,
you would be fitting the interval-censored model corresponding to an
underlying continuous time model that satisfies the proportional hazards
assumption. (That assumption can be tested using interactions between
explanatory variables and the variables summarising duration
dependence.)  An alternative would be -xtlogit- and -logit- to data
organised in the same way.

[Cf. -pgmhaz8- and -hshaz- (on SSC) which also fit discrete time
proportional hazards models with frailty (Gamma, and discrete mass
point, respectively), but only to single spell data.  -xtcloglog- and
-xtlogit- work with multiple spell data because the frailty is
integrated out numerically.] 

Stephen
-------------------------------------
Professor Stephen P. Jenkins <s.jenkins@lse.ac.uk>
Department of Social Policy 
London School of Economics and Political Science
Houghton Street, London WC2A 2AE, U.K.
Tel: +44 (0)20 7955 6527
Changing Fortunes: Income Mobility and Poverty Dynamics in Britain, OUP
2011, http://ukcatalogue.oup.com/product/9780199226436.do
Survival Analysis using Stata:
http://www.iser.essex.ac.uk/survival-analysis  
Downloadable papers and software: http://ideas.repec.org/e/pje7.html 

----------------------------------------------------------------------

Date: Sat, 28 Jul 2012 09:29:15 +0100
From: Patrick Munywoki <pmunywoki@gmail.com>
Subject: st: Interval censoring using intcens

Hi,
I have been attempting to analyse interval censored time-to-event data
with 'intcens' ado (Griffin et al 2006). My data arise from a
longitudinal household-based study with nasal swab collections
twice-a-week for a duration of 26 weeks regardless of their any
symptoms. I want to be able to estimate the duration of infectious
period for one of the viruses we detected. I have reduced the data  to
one observation per infection episode in order to use the 'intcens'
command with t0 being the date last positive sample while t1 is the
date of the next negative sample. I hope this data conversion to
single observation per infection episode data is alright?

My questions?
1. How do i interpret the coefficient given in the results below?

intcens t0 t1 male, dist(exp) time nolog

stata output
Exponential distribution -      log acceleration factors

Uncensored               0
Right-censored           0
Left-censored            0
Interval-censored      188

        Number of obs   =       188
        Wald chi2(1)    =       0.00
Log likelihood =  -1796.982     Prob > chi2     =       0.9990


Coef.   Std. Err.      z    P>z     [95% Conf.  Interval]

male   -.0001871        .1470683    -0.00   0.999    -.2884356  .2880615
_cons    9.817517       .2234524    43.94   0.000     9.379558  10.25548

Note the actual interval between the dates t0 and t1 is on average(sd)
3.6 (0.98) days; median(IQR) 4 (3-4) days; and range 2-7 days.


2. Whenever i try using any other distribution this error message pops
up. What could be the problem here?
intcens t0 t1 male, dist(weib) time nolog
initial values not feasible
r(1400);

3. Is there an alternative method to the interval censoring which
allows me to use the multiple records per person accounting for the
interval censoring. I have tried stpm but not sure whether it allows
for this.

I would greatly appreciate your help ,

Many thanks,

- --
Patrick Munywoki

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