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Survival Analysis Using SAS®: A Practical Guide by Paul D. Allison

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Partial Likelihood

What’s remarkable about partial likelihood is that you can estimate the β coefficients of the proportional hazards model without having to specify the baseline hazard function λ0(t). In this section, we will

  • consider some general properties of partial likelihood

  • look at two simple examples using PROC PHREG

  • examine the mathematics of the method in some detail.

The likelihood function for the proportional hazards model of equation (5.1) can be factored into two parts:

  • one part depends on both λ0(t) and β (the vector of coefficients)

  • the other part depends on β alone.

What partial likelihood does, in effect, is discard the first part and treat the second part—the partial likelihood function—as though it were an ordinary likelihood ...

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