Hi,
This is a follow-up of my last post about how to generate multivariate
survival times. I haven't recieved any answer or suggestion so far.
Instead, I heard from several people who are confronted with the same
question. The following are my naive approaches that I would like to share
with those who asked for a copy of the answers that I possibly recieved.
Approach (1): Use Truncated Multivariate Normal Distribution
-------------
This is rather easy to be implemented. The dependence will be controlled
using the covariance matrix or correlation matrix. After generate
data from a multivaraite normal distribution based on some desired
correlation matrix, simply taking the absolute values of nonzero numbers
should do.
> X <- abs(X[X!=0])
Approach (2): Use Multivariate Exponential Distribution, which is due to a
------------
friend of mine, Xin Yan, who is working in Smith-Klein (Maybe Wrongly
spelled).
The approach can simulate recurrent times or multiple times data, while
the previous approach gives usual multivaraite time type data. The key
difference between recurrent times and multivarite tiems is, in a multiple
time vector (Ti1, Ti2, ....Tik) for a particuler unit i, it is required
that Tik > Ti(k-1) > ... > Ti2 > Ti1. By introducing appropraite
coefficients, this requirement can be easily satisfied.
To simulate, more specific details involve specifying a marginal for Ti1,
kind of arbitrarily but with exponential marginal preferred, and then
getting Ti2 from some chosen marginal distribution after conditioning on
Ti1, and so on. This is the usual way of simulating multivaraite data
when the density is given. By the way, for the density of multivariate
exponential, one might refer to the following paper,
Gumbel, E. J. 'Bivaraite Exponential DIstributions' JASA 698-707(1960)
Also, following Xin's suggestion, it's better to set a upper bound M for
the simulated times to make the data more real, which is same as in
simulating univaraite failure times.
I'm currently working on it. I'll be happy if someone who is doing
the same job wants to share codes.
Good Luck to all,
Xiao-Gang Su
My Previous Post:
=================
> Subject: How to Generate Multivariate Survival Times?
>
>
> Hi, I'm currently working on some projects in which I need to simulate
> multivariate survival times of dimentionality at least 3. It's best to
> have control on the inherent dependence using some indicators, which could
> be a matrix or soemthing else. Are there any people who have done similar
> work before?
>
> Thanks for your help,
>
> Xiao-Gang Su
>
> ******************************************************************************
> Xiao-Gang Su
> Division of Statistics Phone: (530) 752-6103 (Office)
> the University of California (530) 752-4243 (Lab)
> One Shields Avenue E-mail: xgsu@wald.ucdavis.edu
> Davis, CA 95616 Web: http://anson.ucdavis.edu/users/xgsu
> *******************************************************************************
>
>
******************************************************************************
Xiao-Gang Su
Division of Statistics Phone: (530) 752-6103 (Office)
the University of California (530) 752-4243 (Lab)
One Shields Avenue E-mail: xgsu@wald.ucdavis.edu
Davis, CA 95616 Web: http://anson.ucdavis.edu/users/xgsu
*******************************************************************************
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