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Hello,

I have read the manual "Modelling survival data in MLwiN 1.20".
http://www.bristol.ac.uk/media-library/ ... s/msdm.pdf
But, I could not have fully understood this manual.

I have a question about Proportional Hazard models in the Section 5.

Equation (15) is hi(tg)=dgi/(ngi x tg+Δ-tg),
where dgi=1 if the individual dies in the time period and 0 otherwise. The term ngi is
the total number of individuals at risk at time tg, i.e. the number of ties, and is unity
for a single subject at one time point.

Meanwhile, equation (6) shows the K-M estimator of the hazard rate as follows:
h(t)=dg/ng(tg+Δ-tg),
where dg is the number of individuals who died in the interval (tg+Δ-tg), and
dg is the total number of individuals alive at the start of the interval.

How could I prove the relationship between the hazard of death for the ith individual in the equation (15) and
the k-M estimator of the hazard rate in the equation (6).

For example, if there are 6 individuals in the time interval 3, and 2 people died in the interval,
equation (15) would be 1/(2 x 3)=0.166667 for individual died in the interval while equation (6) would be 2/(6 x 3)=0.111111.

In case there are any mistakes in my understanding, please let me know.

Thank you in advance for your help.
Sincerely yours,

Ryosuke Iida