deriv_weight_estimator_BLH_noprior: A function that gives the derivative of the objective function of the model for gradient-based optimization algorithms without including the prior on the regression coefficients.

Description

Given the necessary data, this function calculates the derivative of the objective function without a prior on the regression coefficients w.r.t. the baseline hazards and weights(regression coefficients) in the model to be used in gradient-based optimization algorithms. This is sometimes necessary to get the optimization algorithm out of a peaked origin where it could start.

Usage

deriv_weight_estimator_BLH_noprior(survDataT, geDataT, weights_baselineH, a, b, groups)

Arguments

survDataT

The survival data of the patient set passed on by the user. It takes on the form of a data frame with at least have the following columns True_STs and censored, corresponding to the observed survival times and the censoring status of the subjects consecutively. Censored patients are assigned a 1 while patients who experience an event are assigned 1.

geDataT

The co-variate data (gene expression or aCGH, etc...) of the patient set passed on by the user. It is a matrix with the co-variates in the columns and the subjects in the rows. Each cell corresponds to that rowth subject's columnth co-variate's value.

weights_baselineH

A single vector with the initial values of the baseline hazards followed by the weights(regression coefficients) for the co-variates.

The shape parameter for the gamma distribution used as a prior on the baseline hazards.

The scale parameter for the gamma distribution used as a prior on the baseline hazards.

groups

The number of partitions along the time axis for which a different baseline hazard is to be assigned. This number should be the same as the number of initial values passed for the baseline hazards in the beginning of the weights_baselineH argument.

Value

A vector of the same length as the ``weights_baselineH'' argument corresponding to the calculated derivatives of the objective with respect to every component of ``weights_baselineH''.

References

The basic model is based on the Cox regression model as first introduced by Sir David Cox in: Cox,D.(1972).Regression models & life tables. Journal of the Royal Society of Statistics, 34(2), 187-220. The extension of the Cox model to its stepwise form was adapted from: Ibrahim, J.G, Chen, M.-H. & Sinha, D. (2005). Bayesian Survival Analysis (second ed.). NY: Springer. as well as Kaderali, Lars.(2006) A Hierarchial Bayesian Approach to Regression and its Application to Predicting Survival Times in Cancer Patients. Aachen: Shaker

Examples

Run this code

data(Bergamaschi)
data(survData)
deriv_weight_estimator_BLH_noprior(survDataT=survData[1:10, 9:10], geDataT=Bergamaschi[1:10, 1:2], weights_baselineH=c(0.1,0.2,0.3,rep(0,2)), a=1.5, b=0.3, groups=3)