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st: Correlations for censored data

From   "Seed, Paul" <>
To   "" <>
Subject   st: Correlations for censored data
Date   Wed, 23 Oct 2013 11:29:05 +0000

Dear Statalist, 
I have data for a group of subjects on a large number of biomarkers that are sometimes measured, 
sometimes only recorded as "below the limit of detection", and sometimes even "above the limit of accuracy".

Apart from the censoring, I anticipate that the values will be Normally distributed after log transformation.
So the (transformed) data is censored multivariate Normal, with some underlying distribution _N_(_Mu_, _Sigma_),
where _Mu_ is a vector of means, and _Sigma_ is a matrix of covariances. 


Subject		Marker1	Marker2	Marker 3
1		<12		20		37
2		144		< 5		28
3		>3000		44		87
4		.		.		.
5		.		.		.

I want to reduce the number of biomarkers via factor analysis.
Is it possible to estimate the true (Pearson's product moment) correlation 
between each pair of biomarkers (i.e. what I would get if I had the actual values).  
I am hoping for something like the -tetrachoric-  command; or at least some 
advice about how to handle the maximum likelihood calculations.

Paul T Seed, Senior Lecturer in Medical Statistics, 
Division of Women's Health, King's College London
Women's Health Academic Centre, King's Health Partners 
(+44) (0) 20 7188 3642.

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