### Partial Likelihood Function for the Cox Model

Let denote the K distinct, ordered event times. Let denote the multiplicity of failures at ; that is, is the size of the set of individuals that fail at . Let be the weight associated with the jth observation unit in the ith cluster in stratum h. Using this notation, the pseudo-likelihood functions used in PROC SURVEYPHREG to estimate are described in the following sections.

#### Continuous Time Scale

Let denote the risk set just before the kth ordered event time .

The Breslow likelihood is expressed as

The Efron likelihood is expressed as

where is