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: rvaradhan@jhmi.edu<mailto:rvaradhan@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: rvaradhan@jhmi.edu<mailto:rvaradhan@jhmi.edu>


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