Calculate the Score vector or the Hessian matrix for the Cox proportional hazards model with inputs of covariates, survival outcomes and the relative risks
coxScoreHess(X, y, exb, hess = FALSE)
coxpl(X, y, beta, sorted = FALSE)An p by 1 vector of the score of the function calculated at the point relative exp(X*beta). If hess = TRUE, then a list with the following three components is returned:
a 1 x p score vector.
a p x p matrix for the empirical varaince of the score.
a p x p hessian matrix.
the covariate matrix from model.matrix, without the interecpt term.
y is a survival object, y = Surv(time, event).
exb is the relative risks with exb = exp(X*beta).
output the Hessian matrix, with hess = FALSE as the default, which outputs the score vector only.
the p x 1 regression coefficient to be used in calculation of the partial likelihood.
data were sorted by time from the largest to the smallest, to speed up the algorithm, default is sorted = FALSE, sort by time is recommand when the function will be called multiple times for the same y.
The survival time shall be sorted from the largest to the smallest, an error will occur if y is not sorted.
partial likelihood = sum(event(exp(X*beta)/S0))
score = sum(event*(X - S1/S0))
Sigma = sum(S1*t(S1))
H = sum(event*(S2/S0 - S1*t(S1)/S0))
the robust varaince can be calculated by inv(H)*Sigma*inv(H).
numHessian
numScore
multiRoot