Estimating the Baseline Hazard Function
Property 2: The following is an estimate for cj:
Proof: Using the first two terms of the Taylor series we see that
In general if y = ax, then ln y = x ln a, and so y = exp(x∙ lna), which proves that ax = exp(x∙lna). Thus
We can therefore represent the equation
by
which is equivalent to
Solving for cj, we have
Newton’s Method
Property 1 (Newton-Raphson): We can estimate the r × 1 coefficient matrix B = [bi] as Bpfor some large enough p, where B0 consists of all zeros (initial guess) and for all p
where 
In addition, Ip is the covariance matrix for Bp at each step p in the iteration.
Proof: We first consider the case where dj = 1 for all time periods tj. Thus
The only thing we need to prove is that the ui represent the first partial derivatives of LL and the vik represent the second partial derivatives. First, we note that
It then follows that
In the case where we use Breslow’s approximation
and so
In the case where we use Efron’s approximation
we first note that
and so
Dr, muchas gracias por responder, si respetuosamente que por favor adiciones a los resultados esa información.
Dr, thank you very much for responding, if you respectfully please add to the results that information.
Dr. Zaiontz, thank you very much for this page, really it is very useful and didactic.
Dr., please what probability do you have to add in the Cox Regression, the statistics and p-value, of Concordance, R squared, maximum likelihood test, and the test of the logrank ?
Thank you very much for your attention.
Dr. Zaiontz, muchas gracias por esta página, realmente como siempre lo he manifestado es muy útil y didáctica.
Dr. por favor que probabilidad hay de agregar en la Regresión Cox, los estadísticos y valor p, de Concordancia, R cuadrado, prueba de máxima verosimilitud, y la prueba de el puntaje logrank ?
Muchas gracias, por su atención.
Gerardo,
Are you asking me to enhance the existing capability by adding addition information (p-value, R^2, etc.) or are you requesting something else?
Charles
Dr. good morning, what a pity the delay in response, I could not find where I had written it.
If I’m asking you the possibility that you better the Real Statitsitics tool, adding the p value.
Doc, buenos días, que pena la demora en respuesta, no encontraba donde la había escrito.
Si te estoy pidiendo la posibilidad que mejores la herramienta de Real Statitsitics, agregando el valor p.
Hello Gerardo,
If you look at the following webpage, there is the p-value.
Cox Regression Tool
Perhaps you are referring to the p-value for a different test. If so, which test?
Charles
Ok Dr many thanks