PROC PHREG: Newton-Raphson Method :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The PHREG Procedure

Newton-Raphson Method

Let $\text{[math]}$ be one of the likelihood functions described in the previous subsections. Let $\text{[math]}$ . Finding $\text{[math]}$ such that $\text{[math]}$ is maximized is equivalent to finding the solution $\text{[math]}$ to the likelihood equations

$\text{[math]}$

With $\text{[math]}$ as the initial solution, the iterative scheme is expressed as

$\text{[math]}$

The term after the minus sign is the Newton-Raphson step. If the likelihood function evaluated at $\text{[math]}$ is less than that evaluated at $\text{[math]}$ , then $\text{[math]}$ is recomputed using half the step size. The iterative scheme continues until convergence is obtained—that is, until $\text{[math]}$ is sufficiently close to $\text{[math]}$ . Then the maximum likelihood estimate of $\text{[math]}$ is $\text{[math]}$ .

The model-based variance estimate of $\text{[math]}$ is obtained by inverting the information matrix $\text{[math]}$

$\text{[math]}$

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