bcoxph: Bayesian Cox Survial Models
In nyiuab/BhGLM: Bayesian hierarchical GLMs and survival models, with applications to Genomics and Epidemiology

Description Usage Arguments Details Value Author(s) References See Also Examples

This function is to set up Bayesian hierarchical Cox proportonal hazards model and to fit the model using the EM Newton-Raphson algorithm. As in bglm, several types of priors on the coefficients can be used. The Bayesian hierarchical Cox model includes classical Cox model and ridge Cox regression as special cases. It can be used for analyzing general survival data and large-scale and highly-correlated variables (for example, detecting disease-associated factors and predicting survival times).

    
bcoxph(formula, data, weights, subset, na.action, init, 
       control = coxph.control(eps = 1e-04, iter.max = 50), 
       ties = c("breslow", "efron"), tt,  
       prior = Student(0, 0.5, 1), group = NULL, method.coef, 
       Warning = FALSE, verbose = FALSE)

`formula, data, weights, subset, na.action, init, control, ties, tt`	These arguments are the same as in the function `coxph` in the package survival.
`prior, group, method.coef, Warning, verbose`	These arguments are the same as in the function `bglm`.

This function incorporates four types of prior distributions into the conventional Cox proportonal hazards model. It is an alteration of the standard function coxph for fitting classical Cox proportonal hazards model, and includes all the coxph arguments and also some new arguments for the hierarchical modeling. The standard procedure for fitting the conventional Cox proportonal hazards model is the Newton-Raphson algorithm, The function incorporates an EM algorithm for updating hyper-parameters into the standard Newton-Raphson procedure as implemented in the function coxph.

This function returns an object of class "coxph.penal" and "coxph", including all outputs from the function coxph and also results for the additional parameters in the hierarchical models.

Nengjun Yi, nyi@uab.edu

van Houwelinggen, H.G. & Putter, H. Dynamic Prediction in Clinical Survival Analysis, (CRC Press, 2012).

Yi, N. and Banerjee, S. (2009). Hierarchical generalized linear models for multiple quantitative trait locus mapping. Genetics 181, 1101-1113.

Yi, N., Kaklamani, V. G. and Pasche, B. (2011). Bayesian analysis of genetic interactions in case-control studies, with application to adiponectin genes and colorectal cancer risk. Ann Hum Genet 75, 90-104.

Yi, N. and Ma, S. (2012). Hierarchical Shrinkage Priors and Model Fitting Algorithms for High-dimensional Generalized Linear Models. Statistical Applications in Genetics and Molecular Biology 11 (6), 1544-6115.

Gelman, A., Jakulin, A., Pittau, M. G. and Su, Y. S. (2008). A weakly informative default prior distribution for logistic and other regression models. Annals of Applied Statistics 2, 1360-1383.

Rockova, V. and George, E. I. (2014) EMVS: The EM Approach to Bayesian Variable Selection. JASA 109: 828-846.

Zaixiang Tang, Yueping Shen, Xinyan Zhang, Nengjun Yi (2017) The Spike-and-Slab Lasso Cox Models for Survival Prediction and Associated Genes Detection. Bioinformatics, 33(18), 2799-2807.

Zaixiang Tang, Yueping Shen, Shu-Feng Lei, Xinyan Zhang, Zixuan Yi, Boyi Guo, Jake Chen, and Nengjun Yi (2019) Gsslasso Cox: a fast and efficient pathway-based framework for predicting survival and detecting associated genes. BMC Bioinformatics 20(94).

coxph, bglm

library(BhGLM)
library(survival)

N = 1000
K = 100
x = sim.x(n=N, m=K, corr=0.6) # simulate correlated continuous variables  
h = rep(0.1, 4) # assign four non-zero main effects to have the assumed heritabilty 
nz = as.integer(seq(5, K, by=K/length(h))); nz
yy = sim.y(x=x[, nz], mu=0, herit=h, p.neg=0.5) # simulate responses
yy$coefs

y = yy$y.surv
d = table(y[,2]); d[1]/sum(d) # cencoring proportion


# jointly update
# Compare with conventional and ridge Cox model
par(mfrow = c(2, 2), cex.axis = 1, mar = c(3, 4, 4, 4))
gap = 10

ps = 0.05
f1 = bcoxph(y ~ ., data = x, prior = De(0, ps))
# summary.bh(f1)
plot.bh(f1, threshold = 0.01, gap = gap, main = "Cox with double-exponential")

f2 = bcoxph(y ~ ., data = x, prior = Student(0, ps/1.4))
# summary.bh(f2)
plot.bh(f2, threshold = 0.01, gap = gap, main = "Cox with t")

ss = c(0.04, 0.5) 
f3 = bcoxph(y ~ ., data = x, prior = mde(0, ss[1], ss[2]))
# summary.bh(f3)
plot.bh(f3, threshold = 0.01, gap = gap, main = "Cox with mixture double exponential") 

# group-wise update
ps = 0.05
f1 = bcoxph(y ~ ., data = x, prior = De(0, ps), method.coef = 50)
#summary.bh(f1)
plot.bh(coefs = f2$coefficients, threshold = 10, gap = gap)