Perhaps it could help if you could assume a more flexible model for [T];
for instance, a PH model with a piecewise-constant baseline hazard,
which you can simulate as a Poisson variable.
Best,
Dimitris
On 8/26/2011 10:45 PM, Ravi Varadhan wrote:
Hi,
Here is an update. I implemented this bivariate lognormal approach. It works
well in simulations when I generated the marginal [T] from a lognormal
distribution and independently censored it. It, however, does not do well when
I generate from a marginal [T] that is Weibull or a distribution not well
approximated by a lognormal. How to make the approach more robust to
distributional assumptions on the marginal of [T]?
I am thinking that a bivariate copula approach is called for. The [U] margin
can be standard lognormal as before, and the [T] margin needs to be a flexible
distribution. What kind of bivariate coupla might work? Then, how to
generate from the conditional distribution [U | T]? Any thoughts?
Thanks,
Ravi.
-------------------------------------------------------
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology School of Medicine Johns Hopkins
University
Ph. (410) 502-2619
email: rvarad...@jhmi.edu<mailto:rvarad...@jhmi.edu>
From: Ravi Varadhan
Sent: Friday, August 26, 2011 2:56 PM
To: r-help@r-project.org
Subject: How to generate a random variate that is correlated with a given
right-censored random variate?
Hi,
I have a right-censored (positive) random variable (e.g. failure times subject
to right censoring) that is observed for N subjects: Y_i, I = 1, 2, ..., N.
Note that Y_i = min(T_i, C_i), where T_i is the true failure time and C_i is
the censored time. Let us assume that C_i is independent of T_i. Now, I would
like to generate another random variable U_i, I = 1, 2, ..., N, which is
correlated with T. In other words, I would like to generate U from the
conditional distribution [U | T=t].
One approach might be to assume that the joint distn [T, U] is bivariate
lognormal. So, the marginals [T] and [U], as well as the conditional [U | T]
are also lognormal. I can estimate the marginal [T] using the right-censored
data Y (assuming independent censoring). For example, I might use
survival::survreg to do this. Then, I assume that U is standard lognormal
(mean = 0, var = 1). Now, I only need to assume a value for correlation
parameter, r, and I can then sample from the conditional [U | T=t] which is
also a lognormal (parametrized by r).
Does this sound right? Are there better/simpler ways to do this?
Thanks very much for any hints.
Best,
Ravi.
-------------------------------------------------------
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology School of Medicine Johns Hopkins
University
Ph. (410) 502-2619
email: rvarad...@jhmi.edu<mailto:rvarad...@jhmi.edu>
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Erasmus University Medical Center
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