[R] Random effects and level 1 censoring

From: John Logsdon <j.logsdon_at_quantex-research.com>
Date: Tue 09 Jan 2007 - 10:23:09 GMT


I have a question about constructing the likelihood function where there is censoring at level 1 in a two-level random effects sum.

In a conventional solution, the likelihood function is constructed using the density for failures and the survivor function for (in this case, right) censored results. Within (for example) an R environment, this is easy to do and gives the same solution as survreg even if it is a little heavy.

But where there is an hierarchical situation, we need to consider the contributions at level 2.

y_ij=X_ij.beta'+err2_i+err1_ij

If all the units at level 1 for a given level 2 are censored, then the information we have for the level 2 is itself censored and we should presumably use the survivor function. Conversely if none of the units at level 1 are censored, then the information at level 2 is complete and the density should be used.

But what do we do if only some of the level 1 units for a given level 2 are censored? My instinct is to weight the density and survivor functions for that given level 2 case according to the proportion of level 1 failures.

Am I right?

For a number of reasons I don't want to code for specific distributions and I am quite happy to use a sledge hammer to crack a walnut with optim().:)

Best wishes

John

John Logsdon                               "Try to make things as simple
Quantex Research Ltd, Manchester UK         as possible but not simpler"
j.logsdon@quantex-research.com              a.einstein@relativity.org
+44(0)161 445 4951/G:+44(0)7717758675       www.quantex-research.com

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