[R] estimating survival times with glmnet and coxph

[Damjan Krstajic]

Dear all,

I am using glmnet (Coxnet) for building a Cox Model and
to make actual prediction, i.e. to estimate the survival function S(t,Xn) for a
new subject Xn. If I am not mistaken, glmnet (coxnet) returns beta, beta*X and
exp(beta*X), which on its own cannot generate S(t,Xn). We miss baseline
survival function So(t).

Below is my code which takes beta coefficients from
glmnet and creates coxph object (iter=0, init=beta) in order to later calculate
survival estimates with survfit.

I would be grateful if someone could confirm that my
solution with coxph object (iter=0, init=beta) is correct and that the warning
I get 'X matrix deemed to be singular' when creating a coxph object is of no
concern. Below is my code which uses example from "Coxnet: Regularized Cox
Regression".

Thanks in advance.
DK

library(survival)
library(glmnet)
load(system.file("doc","VignetteExample.rdata",package="glmnet"))
attach(patient.data)

# leave the first patient for testing
# and train glmnet on all other patients
trainX      <-x[-1,]
trainTime   <-time[-1]
trainStatus <- status[-1]

# fit Coxnet
fit <- glmnet(trainX,Surv(trainTime,trainStatus),family="cox",alpha=0.5,maxit=10000)

# find lambda for which dev.ratio is max
max.dev.index     <- which.max(fit$dev.ratio)
optimal.lambda <- fit$lambda[max.dev.index]

# take beta for optimal lambda
optimal.beta  <- fit$beta[,max.dev.index]

# find non zero beta coef
nonzero.coef <- abs(optimal.beta)>0
selectedBeta <- optimal.beta[nonzero.coef]

# take only covariates for which beta is not zero
selectedTrainX   <- trainX[,nonzero.coef]

# create coxph object with pre-defined coefficients
coxph.model<- coxph(Surv(trainTime,trainStatus) ~selectedTrainX,init=selectedBeta,iter=0)

Warning message:
In coxph(Surv(trainTime, trainStatus) ~ selectedTrainX,
init = selectedBeta,  :
X matrix deemed to be singular; variable 99 100 101 102 103 104 105
106 107 108 109 110 111 112 113 114 115 116 117 118 119
120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137
138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155
156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173
174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192
193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209
210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227
228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245
246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263
264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281
282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299
300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317
318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335
336 337 338 [... truncated]

# take test covariates for which beta is not zero
selectedTestX <- x[1,nonzero.coef]

# find survival curve for test subject
sfit<- survfit(coxph.model,newdata=selectedTestX)
cat("\ntime ")
cat(sfit$time)
cat("\nsurvival ")
cat(sfit$surv)