[R] How to generate a random variate that is correlated with a given right-censored random variate?

[Dimitris Rizopoulos]

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: rvaradhan at jhmi.edu<mailto:rvaradhan at jhmi.edu>
>
> From: Ravi Varadhan
> Sent: Friday, August 26, 2011 2:56 PM
> To: r-help at 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 at jhmi.edu<mailto:rvaradhan at jhmi.edu>
>
>
> 	[[alternative HTML version deleted]]
>
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-- 
Dimitris Rizopoulos
Assistant Professor
Department of Biostatistics
Erasmus University Medical Center

Address: PO Box 2040, 3000 CA Rotterdam, the Netherlands
Tel: +31/(0)10/7043478
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