For parameter estimation, PEANUTS uses the partial likelihood
methods of Cox (1972). Suppose a cohort is of size 
. Let 
be the survival times and 
the censoring indicators; 
takes value 1 if the 
subject fails from the cause of
interest and takes value 0 otherwise. Further, let 
; 
is the relative risk (or
relative hazard) for the 
subject whose covariate
vector takes value 
at time 
and 
is a 
-vector of unknown parameters. In
PEANUTS, 
may be any member of the EPICURE
general class of models. The partial likelihood is
(A.1)
where 
is the set of all members of the
risk set at . The likelihood is the product over
all subjects in the cohort.
The maximum partial likelihood estimate, 
, for 
is the quantity that nullifies
the 
partial derivatives of the log
partial likelihood, namely,
(A.2)
where
The covariance matrix for 
is taken as the expected
information matrix, 
; the 
entry of 
is
(A.3)
where
and
In the case of ties in the failure times of non-censored cases, the methods given by Peto (1972) and Breslow (1974) for the partial likelihood are used:
where 
is the number of uncensored
events at time . Expressions for the score equations
and for the information matrix follow directly.