deriv_weight_estimator_BLH: A function that gives the derivative of the objective function of the model for gradient-based optimization algorithms.

Description

Given the necessary data, this function calculates the derivative of the objective function without a w.r.t. the baseline hazards and weights(regression coefficients) in the model to be used in gradient-based optimization algorithms.

Usage

deriv_weight_estimator_BLH(geDataT, survDataT, weights_baselineH, q, s, a, b, groups)

Arguments

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.

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.

weights_baselineH

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

One of the two parameters on the prior distribution used on the weights (regression coefficients) in the model.

The second of the two parameters on the prior distribution used on the weights (regression coefficients) in the model.

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 The prior on the regression coefficients was adopted from: Mazur, J., Ritter,D.,Reinelt, G. & Kaderali, L. (2009). Reconstructing Non-Linear dynamic Models of Gene Regulation using Stochastic Sampling. BMC Bioinformatics, 10(448).

Examples

Run this code

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