Fit semiparametric additive hazards model

Description

Fit a semiparametric additive hazards regression model. Right-censored and left-truncated survival data are supported.

Usage

ahaz(surv, X, weights, univariate=FALSE, robust=FALSE)  

Arguments

Details

The semiparametric additive hazards model specifies a hazard function of the form:

h(t) = h_0(t) + \beta' Z_i

for i=1,\ldots,n where Z_i is the vector of covariates, \beta the vector of regression coefficients and h_0 is an unspecified baseline hazard. The semiparametric additive hazards model can be viewed as an additive analogue of the well-known Cox proportional hazards regression model.

Estimation is based on the estimating equations of Lin & Ying (1994).

The option univariate is intended for screening purposes in data sets with a large number of covariates. It is substantially faster than the standard approach of combining ahaz with apply, see the examples.

Value

An object with S3 class "ahaz".

References

Lin, D.Y. & Ying, Z. (1994). Semiparametric analysis of the additive risk model. Biometrika; 81:61-71.

See Also

summary.ahaz, predict.ahaz, plot.ahaz. The functions coef, vcov, residuals.

Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,15:24])

# Fit additive hazards model
fit1 <- ahaz(surv, X)
summary(fit1)

# Univariate models
X <- as.matrix(sorlie[,3:ncol(sorlie)])
fit2 <- ahaz(surv, X, univariate = TRUE)
# Equivalent to the following (slower) solution
beta <- apply(X,2,function(x){coef(ahaz(surv,x))})
plot(beta,coef(fit2))

Adjusted univariate association measures from ahaz

Description

Fast calculation of univariate association measures in the semiparametric additive risk model, adjusted for user-specified covariates

Usage

ahaz.adjust(surv, X, weights, idx, method=c("coef", "z", "crit"))

Arguments

Details

The function is intended mainly for programming use and screening purposes, when a very large number of covariates are considered and direct application of ahaz is unfeasible.

Running this function is equivalent to running ahaz with design matrix cbind(X[,i],X[,idx]) for each column X[,i] in X. By utilizing basic matrix identities, ahaz.adjust runs many times faster.

The following univariate association measures are currently implemented:

• method="z", Z-statistics, obtained from a fitted ahaz model.

• method="coef", regression coefficients, obtained from a fitted ahaz model.

• method="crit", the increase in the natural loss function of the semiparametric additive hazards model when the covariate is included in the model.

Value

A list containing the following elements:

See Also

ahaz, ahaz.partial, ahazisis.

Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,3:ncol(sorlie)])

# Adjust for first 10 covariates
idx <- 1:10
a <- ahaz.adjust(surv,X,idx=idx)

# Compare with (slower) solution
b <- apply(X[,-idx],2,function(x){coef(ahaz(surv,cbind(x,X[,idx])))[1]})
plot(b,a$adj[-idx])

Partial calculation of estimating quantities used by ahaz

Description

Partial calculation of the quantities used in the estimating equations for ahaz.

Usage

ahaz.partial(surv, X, weights, idx)

Arguments

Details

The function is intended mainly for programming use when a very large number of covariates are considered and direct application of ahaz is unfeasible.

The estimating equations for the semiparametric additive hazards model are of the form D\beta=d with D a quadratic matrix with number of columns equal to the number of covariates. The present function returns d[idx], D[idx,], and B[idx,]; the latter a matrix such that D^{-1} B D^{-1} estimates the covariance matrix of the regression coefficients.

Value

A list containing the following elements:

See Also

ahaz, ahaz.adjust.

Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,3:ncol(sorlie)])

# Get D for the first 10 covariates only
a<-ahaz.partial(surv,X,idx=1:10)
pD1 <- a$D

# Equivalent to the (slower) solution
b <- ahaz(surv,X)
pD2 <- b$D[1:10,]
max(abs(pD1-pD2))

Tuning controls for regularization

Description

Define the type of tuning method used for regularization. Currently only used by tune.ahazpen.

Usage

# Cross-validation
cv.control(nfolds=5, reps=1, foldid=NULL, trace=FALSE)

# BIC-inspired
bic.control(factor = function(nobs){log(nobs)})

Arguments

Details

For examples of usage, see tune.ahazpen.

The regression coefficients of the semiparametric additive hazards model are estimated by solving a linear system of estimating equations of the form D\beta=d with respect to \beta. The natural loss function for such a linear function is of the least-squares type

L(\beta)=\beta' D \beta -2d'\beta.

This loss function is used for cross-validation as described by Martinussen & Scheike (2008).

Penalty parameter selection via a BIC-inspired approach was described by Gorst-Rasmussen & Scheike (2011). With df is the degrees of freedom and n the number of observations, we consider a BIC inspired criterion of the form

BIC = \kappa L(\beta) + df\cdot factor(n)

where \kappa is a scaling constant included to remove dependency on the time scale and better mimick the behavior of a ‘real’ (likelihood) BIC. The default factor=function(n){log(n)} has desirable theoretical properties but may be conservative in practice.

Value

An object with S3 class "ahaz.tune.control".

References

Gorst-Rasmussen, A. & Scheike, T. H. (2011). Independent screening for single-index hazard rate models with ultra-high dimensional features. Technical report R-2011-06, Department of Mathematical Sciences, Aalborg University.

Martinussen, T. & Scheike, T. H. (2008). Covariate selection for the semiparametric additive risk model. Scandinavian Journal of Statistics; 36:602-619.

See Also

tune.ahazpen

Independent screening for the semiparametric additive hazards model

Description

Fast and scalable model selection for the semiparametric additive hazards model via univariate screening combined with penalized regression.

Usage

ahazisis(surv, X, weights, standardize=TRUE,
        nsis=floor(nobs/1.5/log(nobs)), do.isis=TRUE,
        maxloop=5, penalty=sscad.control(), tune=cv.control(),
        rank=c("FAST","coef","z","crit"))

Arguments

.

Details

The function is a basic implementation of the iterated sure independent screening method described in Gorst-Rasmussen & Scheike (2011). Briefly, the algorithm does the following:

1. Recruits the nsis most relevant covariates by ranking them according to the univariate ranking method described by rank.

2. Selects, using ahazpen with penalty function described in penalty, a model among the top two thirds of the nsis most relevant covariates. Call the size of this model m.

3. Recruits 'nsis minus m' new covariates among the non-selected covariates by ranking their relevance according to the univariate ranking method described in rank, adjusted for the already selected variables (using an unpenalized semiparametric additive hazards model).

Steps 2-3 are iterated for maxloop times, or until nsis covariates has been recruited, or until the set of selected covariate is stable between two iterations; whichever comes first.

The following choices of ranking method exist:

• rank="FAST" corresponds to ranking, in the initial recruitment step only, by the basic FAST- statistic described in Gorst-Rasmussen & Scheike (2011). If do.isis=TRUE then the algorithm sets rank="z" for subsequent rankings.

• rank="coef" corresponds to ranking by absolute value of (univariate) regression coefficients, obtained via ahaz

• rank="z" corresponds to ranking by the |Z|-statistic of the (univariate) regression coefficients, obtained via ahaz

• rank="crit" corresponds to ranking by the size of the decrease in the (univariate) natural loss function used for estimation by ahaz.

Value

An object with S3 class "ahazisis".

References

Gorst-Rasmussen, A. & Scheike, T. H. (2011). Independent screening for single-index hazard rate models with ultra-high dimensional features. Technical report R-2011-06, Department of Mathematical Sciences, Aalborg University.

See Also

print.ahazisis, ahazpen, ahaz.adjust

Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,3:ncol(sorlie)])

# Basic ISIS/SIS with a single step
set.seed(10101)
m1 <- ahazisis(surv,X,maxloop=1,rank="coef")
m1
# Indices of the variables from the initial recruitment step
m1$SISind
# Indices of selected variables
m1$ISISind
# Check fit
score <- X[,m1$ISISind]%*%m1$ISIScoef
plot(survfit(surv~I(score>median(score))))

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, 1e-4), lambda,
        penalty.wgt=NULL, keep=NULL, control=list())

Arguments

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".

References

Gorst-Rasmussen A., Scheike T. H. (2012). Coordinate Descent Methods for the Penalized Semiparametric Additive Hazards Model. Journal of Statistical Software, 47(9):1-17. https://www.jstatsoft.org/v47/i09/

Gorst-Rasmussen, A. & Scheike, T. H. (2011). Independent screening for single-index hazard rate models with ultra-high dimensional features. Technical report R-2011-06, Department of Mathematical Sciences, Aalborg University.

Leng, C. & Ma, S. (2007). Path consistent model selection in additive risk model via Lasso. Statistics in Medicine; 26:3753-3770.

Martinussen, T. & Scheike, T. H. (2008). Covariate selection for the semiparametric additive risk model. Scandinavian Journal of Statistics; 36:602-619.

Zou, H. & Li, R. (2008). One-step sparse estimates in nonconcave penalized likelihood models, Annals of Statistics; 36:1509-1533.

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))*1e-2

# 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)

# User-specified 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)

Controls for ahazpen fitting algorithm

Description

Controls the numerical algorithm for fitting the penalized semiparametric additive hazards model. This is typically only used in a call to ahazpen.

Usage

ahazpen.fit.control(thresh=1e-5, maxit=100000, ...)

Arguments

Value

A list with elements named as the arguments.

See Also

ahazpen

Penalty controls for ahazpen

Description

Describe the penalty function to be used in the penalized semiparametric additive hazards model. Typically only used in a call to ahazpen or tune.ahazpen.

Usage

# (Adaptive) lasso/elasticnet
lasso.control(alpha=1, ada.wgt=NULL)

# Stepwise SCAD
sscad.control(a=3.7, nsteps=1, init.sol=NULL, c=NULL)

Arguments

Details

The lasso/elasticnet penalty function takes the form

p_\lambda(\beta)=\lambda((1-\alpha)\|\beta\|_2 + \alpha\|\beta\|_1)

where 0 <\alpha \leq 1. Choosing \alpha<1 encourages joint selection of correlated covariates and may improve the fit when there are substantial correlations among covariates.

The stepwise SCAD penalty function takes the form

p_\lambda(\beta)=w_\lambda(c|b_1|)|\beta_1|+\ldots+ w_\lambda(c|b_{nvars}|)|\beta_{nvars}|

where b is some initial estimate, c is a scaling factor, and for I the indicator function

w_\lambda(x)=\lambda I(x \le \lambda) + \frac{(a\lambda - x)_+}{a - 1}I(x>\lambda)

The scaling factor c controls how ‘different’ the stepwise SCAD penalty is from the standard lasso penalty (and is also used to remove dependency of the penalty on the scaling of the time axis).

The one-step SCAD method of Zou & Li (2008) corresponds to taking b equal to the estimator derived from ahaz. See Gorst-Rasmussen & Scheike (2011) for details. By iterating such one-step SCAD and updating the initial solution b accordingly, the algorithm approximates the solution obtained using full SCAD. Note that calculating the full SCAD solution generally leads to a nonconvex optimization problem: multiple solutions and erratic behavior of solution paths can be an issue.

The arguments ada.wgt and init.sol can be specified as functions of the observations. This is convenient, for example, when using cross-validation for tuning parameter selection. Such a function must be specified precisely with the arguments surv, X and weights and must output a numeric vector of length corresponding to the number of covariates. ahazpen will take care of scaling so the function should produce output on the original scale. See the examples here as well as the examples for tune.ahazpen for usage of this feature in practice.

Value

An object with S3 class "ahaz.pen.control".

References

Gorst-Rasmussen, A. & Scheike, T. H. (2011). Independent screening for single-index hazard rate models with ultra-high dimensional features. Technical report R-2011-06, Department of Mathematical Sciences, Aalborg University.

Leng, C. & Ma, S. (2007). Path consistent model selection in additive risk model via Lasso. Statistics in Medicine; 26:3753-3770.

Martinussen, T. & Scheike, T. H. (2008). Covariate selection for the semiparametric additive risk model. Scandinavian Journal of Statistics; 36:602-619.

Zou, H. & Li, R. (2008). One-step sparse estimates in nonconcave penalized likelihood models, Annals of Statistics; 36:1509-1533.

See Also

ahazpen, tune.ahazpen

Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,3:ncol(sorlie)])

# Fit additive hazards regression model with elasticnet penalty
model <- ahazpen(surv,X,penalty=lasso.control(alpha=0.1),dfmax=30)
plot(model)

# Adaptive lasso with weights 1/|beta_i|^0.5. Note that, although
# we do not use 'weights', it MUST be included as an argument
adafun <- function(surv,X,weights)
 return(1/abs(coef(ahaz(surv,X)))^.5)
model <- ahazpen(surv,X[,1:50],penalty=lasso.control(ada.wgt=adafun))
plot(model)

# One-step SCAD with initial solution derived from univariate regressions
scadfun <- function(surv,X,weights){
 fit <- ahaz(surv,X,univariate=TRUE)
 return(coef(fit))
}
set.seed(10101)
model.ssc <- tune.ahazpen(surv,X,dfmax=30,penalty=sscad.control(init.sol=scadfun))
plot(model.ssc)

Plot an ahaz object

Description

Plot method for a fitted semiparametric additive hazards model; plots the Breslow estimate of underlying cumulative hazard function.

Usage

## S3 method for class 'ahaz'
plot(x, ...)

Arguments

Details

Calling plot.ahaz is equivalent to first calling ahaz, then calling predict with type="cumhaz", and finally calling plot.

See Also

ahaz, predict.ahaz, plot.cumahaz

Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,15:24])

# Fit additive hazards model
fit <- ahaz(surv, X)
plot(fit)

Plot an ahazpen object

Description

Plots regularization paths for fitted penalized semiparametric additive hazards model.

Usage

## S3 method for class 'ahazpen'
plot(x, xvar=c("norm","lambda"), labels=FALSE, df=TRUE,
                ylab="Regression coefficients", xlab=xname,...)

Arguments

See Also

ahazpen, print.ahazpen, predict.ahazpen, coef.ahazpen.

Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,3:ncol(sorlie)])

# Fit additive hazards regression model
fit <- ahazpen(surv, X, dfmax=50)
par(mfrow=c(1,2)); plot(fit); plot(fit,xvar="lambda")

# With labels only
plot(fit,labels=TRUE,df=FALSE)

Plot a cumahaz object

Description

Plots the Breslow estimate of cumulative hazard function, as obtained from the predict.ahaz

Usage

## S3 method for class 'cumahaz'
plot(x, ...)  

Arguments

See Also

predict.ahaz, predict.ahazpen

Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,15:24])

# Fit additive hazards regression model
fit <- ahaz(surv, X)

# Cumulative hazard
cumhaz <- predict(fit, type="cumhaz")
plot(cumhaz)

Plot a tune.ahazpen object

Description

Plot, as a function of the penalty parameter, the curve of tuning scores produced when tuning a penalized semiparametric additive hazards model.

Usage

## S3 method for class 'tune.ahazpen'
plot(x, df = TRUE, ...)  

Arguments

Details

A plot is produced displaying the tuning score for each value of penalty parameter (alongside upper and lower standard deviation curves, if cross-validation has been used). The value of lambda which minimizes the estimated tuning score is indicated with a dashed vertical line.

See Also

ahazpen, tune.ahazpen, print.tune.ahazpen.

Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,3:ncol(sorlie)])

# Do 10 fold cross-validation
set.seed(10101)
tune.fit <- tune.ahazpen(surv, X, penalty="lasso",
              dfmax=50, tune = cv.control(nfolds=10))
plot(tune.fit)

Prediction methods for ahaz

Description

Compute regression coefficients, linear predictor, cumulative hazard function, or integrated martingale residuals for a fitted semiparametric additive hazards model.

Usage

## S3 method for class 'ahaz'
predict(object, newX, type=c("coef", "lp",
       "residuals", "cumhaz"), beta=NULL, ...)
## S3 method for class 'ahaz'
coef(object, ...)
## S3 method for class 'ahaz'
vcov(object, ...)
## S3 method for class 'ahaz'
residuals(object, ...)

Arguments

Details

The Breslow estimator of the baseline cumulative hazard is described in Lin & Ying (1994).

The regression coefficients \beta_0 in the semiparametric additive hazards model are obtained as the solution \hat{\beta} to a quadratic system of linear equations D\beta=d. The (integrated) martingale residuals \epsilon_i for i=1,...,n are vectors, of length corresponding to the number of covariates, so that

D(\hat{\beta}-\beta_0) -d \approx \epsilon_1+\cdots+\epsilon_n

The residuals estimate integrated martingales and are asymptotically distributed as mean-zero IID multivariate Gaussian. They can be used to derive a sandwich-type variance estimator for regression coefficients (implemented in summary.ahaz when robust=TRUE is specified). They can moreover be used for implementing consistent standard error estimation under clustering; or for implementing resampling-based inferential methods.

See Martinussen & Scheike (2006), Chapter 5.4 for details.

Value

For type="coef" and type="lp", a vector of predictions.

For type="coef", a matrix of (integrated) martingale residuals, with number of columns corresponding to the number of covariates.

For type="cumhaz", an object with S3 class "cumahaz" consisting of:

References

Martinussen, T. & Scheike, T. H. & (2006). Dynamic Regression Models for Survival Data. Springer.

See Also

ahaz, summary.ahaz, plot.cumahaz.

Examples

data(sorlie)

set.seed(10101)

# Break ties
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,15:24])

# Fit additive hazards regression model
fit <- ahaz(surv, X)

# Parameter estimates
coef(fit)

# Linear predictor, equivalent to X%*%coef(fit)
predict(fit,type="lp")

# Cumulative baseline hazard
cumahaz <- predict(fit, type="cumhaz")

# Residuals - model fit
resid <- predict(fit, type = "residuals")
# Decorrelate, standardize, and check QQ-plots
stdres <- apply(princomp(resid)$scores,2,function(x){x/sd(x)})
par(mfrow = c(2,2))
for(i in 1:4){
  qqnorm(stdres[,i])
  abline(c(0,1))
}

# Residuals - alternative variance estimation
resid <- residuals(fit)
cov1 <- summary(fit)$coef[,2]
invD <- solve(fit$D)
Best<-t(resid)%*%resid
cov2 <- invD %*% Best %*% invD
# Compare with (nonrobust) SEs from 'summary.ahaz'
plot(cov1, sqrt(diag(cov2)),xlab="Nonrobust",ylab="Robust")
abline(c(0,1))

Prediction methods for ahazpen

Description

Compute regression coefficient estimates, linear predictor, cumulative hazard function, or integrated martingale residuals for a fitted penalized semiparametric additive hazards model.

Usage

## S3 method for class 'ahazpen'
predict(object, newX, type=c("coef","lp","residuals","cumhaz"),
        lambda=NULL, ...)
## S3 method for class 'ahazpen'
coef(object, ...)

Arguments

Details

See the details in predict.ahaz for information on the different types of predictions.

Value

For type="coef" and type="lp", a matrix of regression coefficients, respectively linear predictions for each value of the penalty parameter.

For type="residuals", a matrix of (integrated) martingale residuals associated with the nonzero penalized regression coefficients for a regularization parameter equal to lambda.

For type="cumhaz", an object with S3 class "cumahaz" based on the regression coefficients estimated for a regularization parameter equal to lambda, the object containing:

See Also

ahazpen, print.ahazpen, plot.ahazpen, predict.ahaz, plot.cumahaz.

Examples

data(sorlie)

set.seed(10101)

# Break ties
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,3:ncol(sorlie)])

# Fit additive hazards regression model w/lasso penalty
fit <- ahazpen(surv, X, dfmax=100)

# Coefficients
beta <- predict(fit,X,lambda=0.08,type="coef")
barplot(as.numeric(beta))

# Linear predictions
linpred <- predict(fit,X,lambda=0.1,type="lp")
riskgrp <- factor(linpred < median(linpred))
plot(survfit(surv~riskgrp))

# Residuals
resid <- predict(fit, X, lambda=0.1, type = "residuals")
par(mfrow = c(1,2))
hist(resid[,1],main=colnames(resid)[1])
hist(resid[,2],main=colnames(resid)[2])

# Cumulative hazard
cumhaz <- predict(fit,X,lambda=0.1,type="cumhaz")
plot(cumhaz)

Prediction methods for tune.ahazpen

Description

Compute regression coefficient estimates, linear predictor, cumulative hazard function, or integrated martingale residuals for a fitted and tuned penalized semiparametric additive hazards model.

Usage

## S3 method for class 'tune.ahazpen'
predict(object, newX,  lambda="lambda.min", ...)
## S3 method for class 'tune.ahazpen'
coef(object, ...)

Arguments

Details

See the details in predict.ahazpen for information on the available types of predictions.

Value

The obejct returned depends on the details in the argument ... passed to predict.ahazpen.

See Also

predict.ahazpen, ahazpen, print.ahazpen, plot.ahazpen, predict.ahaz, plot.cumahaz.

Examples

data(sorlie)

set.seed(10101)

# Break ties
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,3:ncol(sorlie)])

# Fit additive hazards regression model w/lasso penalty
cv.fit <- tune.ahazpen(surv, X, dfmax=100, tune="cv")

# Predict coefficients at cv.fit$lambda.min
coef(cv.fit)

# Predict risk score at cv.fit$lambda.min
predict(cv.fit,newX=X,type="lp")

Print an ahazisis object

Description

Print method for sure independence screening based on the semiparametric additive hazards model.

Usage

## S3 method for class 'ahazisis'
print(x, digits=max(3, getOption("digits") - 3), ...)

Arguments

Details

The call that produced x is printed, alongside the number of covariates initially recruited, the number of covariates finally recruited (if applicable) and the number of iterations (if applicable).

See Also

ahazisis

Print an ahazpen object

Description

Print method for fitted penalized semiparametric additive hazards model.

Usage

## S3 method for class 'ahazpen'
print(x, digits=max(3, getOption("digits") - 3), ...)

Arguments

Details

The call that produced x is printed, alongside the number of observations, the number of covariates, and details on the sequence of penalty parameters.

See Also

ahazpen, predict.ahazpen, coef.ahazpen.

Print a summary.ahaz object

Description

Produces a printed summary of a fitted semiparametric additive hazards model.

Usage

## S3 method for class 'summary.ahaz'
print(x, digits=max(getOption("digits") - 3, 3),
      signif.stars=getOption("show.signif.stars"), ...)  

Arguments

See Also

summary.ahaz, ahaz, plot.ahaz.

Print a tune.ahazpen object

Description

Print method for tune.ahazpen objects.

Usage

## S3 method for class 'tune.ahazpen'
print(x, digits=max(3, getOption("digits") - 3), ...) 

Arguments

Details

The call that produced x is printed, alongside the number of penalty parameters used, the value of the optimal penalty and the number of non-zero regression coefficients at the optimal penalty parameter.

See Also

ahazpen, tune.ahazpen, plot.tune.ahazpen.

Sorlie gene expressions

Description

Dataset containing 549 gene expression measurement, exit time and exit status in a study of breast cancer among 115 women.

Usage

data(sorlie)

Format

time

Time to exit.

status

Status at exit (censoring = 0, event = 1).

X1,...,X549

Gene expression measurements.

References

Soerlie T., et al. (2003). Repeated observation of breast tumor subtypes in independent gene expression data sets. Proc Natl Acad Sci 100:8418-8423

Examples

  data(sorlie)

Summarize an ahaz object

Description

Produces a summary of a fitted semiparametric additive hazards model.

Usage

## S3 method for class 'ahaz'
summary(object, ...)  

Arguments

Value

An object with S3 class "summary.ahaz".

See Also

ahaz, plot.ahaz

Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,15:25])

# Fit additive hazards model
fit1 <- ahaz(surv, X)
summary(fit1)

Choice of penalty parameter in ahazpen

Description

Tuning of penalty parameters for the penalized semiparametric additive hazards model via cross-validation - or via non-stochastic procedures, akin to BIC for likelihood-based models.

Usage

tune.ahazpen(surv, X, weights, standardize=TRUE, penalty=lasso.control(),
             tune=cv.control(), dfmax=nvars, lambda, ...)

Arguments

Details

The function performs an initial penalized fit based on the penalty supplied in penalty to obtain a sequence of penalty parameters. Subsequently, it selects among these an optimal penalty parameter based on the tuning control function described in tune, see ahaz.tune.control.

Value

An object with S3 class "tune.ahazpen".

References

Gorst-Rasmussen, A. & Scheike, T. H. (2011). Independent screening for single-index hazard rate models with ultra-high dimensional features. Technical report R-2011-06, Department of Mathematical Sciences, Aalborg University.

See Also

ahaz.tune.control, plot.tune.ahazpen, ahazpen.

Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2

# Survival data + covariates
surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,3:ncol(sorlie)])

# Training/test data
set.seed(20202)
train <- sample(1:nrow(sorlie),76)
test <- setdiff(1:nrow(sorlie),train)

# Run cross validation on training data
set.seed(10101)
cv.las <- tune.ahazpen(surv[train,], X[train,],dfmax=30)
plot(cv.las)

# Check fit on the test data
testrisk <- predict(cv.las,X[test,],type="lp")
plot(survfit(surv[test,]~I(testrisk<median(testrisk))),main="Low versus high risk")

# Advanced example, cross-validation of one-step SCAD
# with initial solution derived from univariate models.
# Since init.sol is specified as a function, it is
# automatically cross-validated as well
scadfun<-function(surv,X,weights){coef(ahaz(surv,X,univariate=TRUE))}
set.seed(10101)
cv.ssc<-tune.ahazpen(surv[train,],X[train,],
                     penalty=sscad.control(init.sol=scadfun),
                     tune=cv.control(rep=5),dfmax=30)
# Check fit on test data
testrisk <- predict(cv.ssc,X[test,],type="lp")
plot(survfit(surv[test,]~I(testrisk<median(testrisk))),main="Low versus high risk")