# Penalised Maximum Likelihood for Survival Analysis Models

### Description

Simultaneously estimate the regression coefficients and provide a 'non-parametric' smooth estimate of the baseline hazard function for proportional hazard Cox models using maximum penalised likelihood (MPL).

### Details

This package allows to perform simultaneous estimation of the regression coefficients and baseline hazard function in Cox proportional hazard models, with right censored data and independent censoring, by maximising a penalised likelihood, in which a penalty function is used to smooth the baseline hazard estimate.

Optimisation is achieved using a new iterative algorithm, which combines Newton's method and the multiplicative iterative algorithm by Ma (2010), and respects the non-negativity constraints on the baseline hazard estimate (refer to Ma, Heritier and Lo (2014)).

Valid inferences for the regression coefficients and the baseline hazard, cumulative baseline hazard and survival functions as well as for their predictions are available.

This software is accepted by users "as is" and without warranties or guarantees of any kind.

### Author(s)

Dominique-Laurent Couturier, Jun Ma, Stephane Heritier.

Maintainer: Dominique-Laurent Couturier dlc48@medschl.cam.ac.uk.

### References

Ma, J. and Heritier, S. and Lo, S. (2014), On the Maximum Penalised
Likelihood Approach for Proportional Hazard Models with Right Censored
Survival Data. *Computational Statistics and Data Analysis* **74**, 142-156.

Ma, J. (2010), Positively constrained multiplicative iterative algorithm for
maximum penalised likelihood tomographic reconstruction.
*IEEE Transactions On Signal Processing* **57**, 181-192.