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Cox partial likelihood function, how to solve?

• To: mathgroup at smc.vnet.net
• Subject: [mg38490] Cox partial likelihood function, how to solve?
• From: Søren Merser <merser at image.dk>
• Date: Fri, 20 Dec 2002 04:24:46 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hi there
I need a litle help here please

I've have the Mathematica expression below which is a Cox partial likelihood
function f  (for some survival data)
but I can't get Mathematica to solve the following problems:

Calculation of coefficient estimates of exp (-0.130) and age (0.611).
Results known from a statistical program (R)
    U=D[f, exp, age]
    NSolve[U==0, exp, age]

I'd then would like to calculate the information matrix which is the
negative second derivative of the log-likelihood function f
I've tried

    I = -D[f, {exp,2},{age,2}]

but the result isn't right  when i replace the exp and age like
se = Sqrt[Info]-1 /. exp-> -.130 /. age-> .611
(se should be .920 and .997)

the methods above works OK when there is only one (exposure) variable - but
not with additional covars

regards soren



likelihood function:



\!\(Log[\[ExponentialE]\^\(5\ age + 4\ exp\)\/\(\((1 +
\[ExponentialE]\^\(age \
+ exp\))\)\ \((1 + 2\ \[ExponentialE]\^\(age + exp\))\)\ \((3 + 2\ \
\[ExponentialE]\^age + \[ExponentialE]\^exp + 4\ \[ExponentialE]\^\(age +
exp\
\))\)\^5\)]\)

• Follow-Ups:
  • Re: Cox partial likelihood function, how to solve?
    • From: Daniel Lichtblau <danl@wolfram.com>