ahazpen {ahaz}  R Documentation 
Fit penalized semiparametric additive hazards model
Description
Fit a semiparametric additive hazards model via penalized estimating equations using, for example, the lasso penalty. The complete regularization path is computed at a grid of values for the penalty parameter lambda via the method of cyclic coordinate descent.
Usage
ahazpen(surv, X, weights, standardize=TRUE, penalty=lasso.control(),
nlambda=100, dfmax=nvars, pmax=min(nvars, 2*dfmax),
lambda.minf=ifelse(nobs < nvars,0.05, 1e4), lambda,
penalty.wgt=NULL, keep=NULL, control=list())
Arguments
surv 
Response in the form of a survival object, as returned by the
function 
X 
Design matrix. Missing values are not supported. 
weights 
Optional vector of observation weights. Default is 1 for each observation. 
standardize 
Logical flag for variable standardization, prior to
model fitting. Estimates are always returned on
the original scale. Default is 
penalty 
A description of the penalty function to be used for
model fitting. This can be a character string naming a penalty
function (currently 
nlambda 
The number of 
dfmax 
Limit the maximum number of variables in the
model. Unless a complete
regularization path is needed, it is highly
recommended to initially choose a relatively smaller value of

pmax 
Limit the maximum number of variables to ever be considered by the coordinate descent algorithm. 
lambda.minf 
Smallest value of 
lambda 
An optional user supplied sequence of penalty parameters. Typical usage
is to have the
program compute its own 
penalty.wgt 
A vector of nonnegative penalty weights for each
regression coefficient. This is a number that multiplies 
keep 
A vector of indices of variables which should always be included in
the model (no penalization). Equivalent to specifying a 
control 
A list of parameters for controlling the
model fitting algorithm. The list is passed to 
Details
Fits the sequence of models implied by the penalty function
penalty
, the sequence of penalty parameters lambda
by
using the very efficient method of cyclic coordinate descent.
For data sets with a very large number of covariates, it is recommended
to only calculate partial paths by specifying a smallish value of
dmax
.
The sequence lambda
is computed automatically by the algorithm
but can also be set (semi)manually by specifying nlambda
or
lambda
. The stability and efficiency of the algorithm is highly
dependent on the grid lambda
values being reasonably dense, and
lambda
(and nlambda
) should be specified accordingly. In
particular, it is not recommended to specify a single or a few lambda
values. Instead, a partial regularization path should be calculated and
the functions predict.ahazpen
or
coef.ahazpen
should be used to extract coefficient
estimates at specific lambda values.
Value
An object with S3 class "ahazpen"
.
call 
The call that produced this object 
beta 
An 
lambda 
The sequence of actual 
df 
The number of nonzero coefficients for each value of

nobs 
Number of observations. 
nvars 
Number of covariates. 
surv 
A copy of the argument 
npasses 
Total number of passes by the fitting algorithm over the data, for all lambda values. 
penalty.wgt 
The actually used 
penalty 
An object of class 
dfmax 
A copy of 
penalty 
A copy of 
References
GorstRasmussen A., Scheike T. H. (2012). Coordinate Descent Methods for the Penalized Semiparametric Additive Hazards Model. Journal of Statistical Software, 47(9):117. https://www.jstatsoft.org/v47/i09/
GorstRasmussen, A. & Scheike, T. H. (2011). Independent screening for singleindex hazard rate models with ultrahigh dimensional features. Technical report R201106, Department of Mathematical Sciences, Aalborg University.
Leng, C. & Ma, S. (2007). Path consistent model selection in additive risk model via Lasso. Statistics in Medicine; 26:37533770.
Martinussen, T. & Scheike, T. H. (2008). Covariate selection for the semiparametric additive risk model. Scandinavian Journal of Statistics; 36:602619.
Zou, H. & Li, R. (2008). Onestep sparse estimates in nonconcave penalized likelihood models, Annals of Statistics; 36:15091533.
See Also
print.ahazpen
, predict.ahazpen
,
coef.ahazpen
, plot.ahazpen
,
tune.ahazpen
.
Examples
data(sorlie)
# Break ties
set.seed(10101)
time < sorlie$time+runif(nrow(sorlie))*1e2
# Survival data + covariates
surv < Surv(time,sorlie$status)
X < as.matrix(sorlie[,3:ncol(sorlie)])
# Fit additive hazards regression model
fit1 < ahazpen(surv, X,penalty="lasso", dfmax=30)
fit1
plot(fit1)
# Extend the grid to contain exactly 100 lambda values
lrange < range(fit1$lambda)
fit2 < ahazpen(surv, X,penalty="lasso", lambda.minf=lrange[1]/lrange[2])
plot(fit2)
# Userspecified lambda sequence
lambda < exp(seq(log(0.30), log(0.1), length = 100))
fit2 < ahazpen(surv, X, penalty="lasso", lambda = lambda)
plot(fit2)
# Advanced usage  specify details of the penalty function
fit4 < ahazpen(surv, X,penalty=sscad.control(nsteps=2))
fit4
fit5 < ahazpen(surv, X,penalty=lasso.control(alpha=0.1))
plot(fit5)