R: Fit the additive trend filtering Cox model with a range of...

tfCox {tfCox}

R Documentation

Fit the additive trend filtering Cox model with a range of tuning parameters

Description

Fit additive trend filtering Cox model where each component function is estimated to be piecewise constant or polynomial.

Usage

tfCox(dat, ord=0, alpha=1, lambda.seq=NULL, discrete=NULL, n.lambda=30,
lambda.min.ratio = 0.01, tol=1e-6, niter=1000, stepSize=25, backtracking=0)

Arguments

`dat`	A list that contains `time`, `status` and `X`. `time` is failure or censoring time, `status` is failure indicator with 1 indicating failure and 0 indicating censoring, and `X` is n x p design matrix and may have p > n. Missing data are not allowed in `time`, `status` and `X`. `X` should be numeric.
`ord`	The polynomial order of the trend filtering fit; a non-negative interger (`ord>= 3` is not recommended). For instance, `ord=0` will produce piewise constant fit, `ord=1` will produce piewise linear fit, and `ord=2` will produce piewise quadratic fit.
`alpha`	The trade-off between trend filtering penalty and group lasso penalty. It must be in [0,1]. `alpha=1` corresponds to the case with only trend filtering penalty to produce piecewise polynomial, and `alpha=0` corresponds to the case with only group lasso penalty to produce sparsity of the functions. `alpha` between 0 and 1 is the tradeoff between the strength of these two penalties. For p < n, we suggest using 1.
`lambda.seq`	A vector of non-negative tuning parameters. If provided, `lambda.seq` should be a decreasing sequence of values since `tfCox` uses warm starts for speed. If `lambda.seq=NULL`, the default will calculate `lambda.seq` using `lambda.min.ratio` and `n.lambda`.
`discrete`	A vector of covariate/feature indice that are discrete. Discrete covariates are not penalized in the model. Default `NULL` means that none of the covariates are discrete thus all covariates will be penalized in the model.
`n.lambda`	The number of lambda values to consider and the default is 30.
`lambda.min.ratio`	Smallest value for lambda.seq, as a fraction of the maximum lambda value, which is the smallest value such that the penalty term is zero. The default is 0.01.
`tol`	Convergence criterion for estimates.
`niter`	Maximum number of iterations.
`stepSize`	Initial step size. Default is 25.
`backtracking`	Whether backtracking should be used 1 (TRUE) or 0 (FALSE). Default is 0 (FALSE).

Details

The optimization problem has the form

l(\theta)+\alpha\lambda\sum_{j=1}^p |D_jP_j\theta_j|_1+(1-\alpha)\lambda\sum_{j=1}^p|\theta_j|_2

where l is the loss function defined as the negative log partial likelihood divided by n, and \alpha provides a trade-off between trend filtering penalty and group lasso penalty. Covariate matrix X is not standardized before solving the optimization problem.

Value

An object with S3 class "tfCox".

`ord`	the polynomial order of the trend filtering fit. Specified by user (or default).
`alpha`	as specified by user (or default).
`lambda.seq`	vector of lambda values considered.
`theta.list`	list of estimated theta matrices of dimension n x p. Each component in the list corresponds to the fit from `lambda.seq`.
`num.knots`	vector of number of knots of the estimated theta. Each component corresponds to the fit from `lambda.seq`.
`num.nonsparse`	vector of proportion of non-sparse/non-zero covariates/features. Each component corresponds to the fit from `lambda.seq`.
`dat`	as specified by user.

Author(s)

Jiacheng Wu

References

Jiacheng Wu & Daniela Witten (2019) Flexible and Interpretable Models for Survival Data, Journal of Computational and Graphical Statistics, DOI: 10.1080/10618600.2019.1592758

Examples

###################################################################
#constant trend filtering (fused lasso) with adaptively chosen knots
#generate data from simulation scenario 1 with piecewise constant functions
set.seed(1234)
dat = sim_dat(n=100, zerof=0, scenario=1)

#fit piecewise constant for alpha=1 and a range of lambda
fit = tfCox(dat, ord=0, alpha=1)
summary(fit)
#plot the fit of lambda index 15 and the first predictor
plot(fit, which.lambda=15, which.predictor=1)

#cross-validation to choose the tuning parameter lambda with fixed alpha=1
cv = cv_tfCox(dat, ord=0, alpha=1, n.fold=2)
summary(cv)
cv$best.lambda
#plot the cross-validation curve
plot(cv)

#fit the model with the best tuning parameter chosen by cross-validation
one.fit = tfCox(dat, ord=0, alpha=1, lambda.seq=cv$best.lambda)
#predict theta from the fitted tfCox object
theta_hat = predict(one.fit, newX=dat$X, which.lambda=1)

#plot the fitted theta_hat (line) with the true theta (dot)
for (i in 1:4) {
  ordi = order(dat$X[,i])
  plot(dat$X[ordi,i], dat$true_theta[ordi,i],
    xlab=paste("predictor",i), ylab="theta" )
  lines(dat$X[ordi,i], theta_hat[ordi,i], type="s")
}


#################################################################
#linear trend filtering with adaptively chosen knots
#generate data from simulation scenario 3 with piecewise linear functions
set.seed(1234)
dat = sim_dat(n=100, zerof=0, scenario=3)

#fit piecewise constant for alpha=1 and a range of lambda
fit = tfCox(dat, ord=1, alpha=1)
summary(fit)
#plot the fit of lambda index 15 and the first predictor
plot(fit, which.lambda=15, which.predictor=1)

#cross-validation to choose the tuning parameter lambda with fixed alpha=1
cv = cv_tfCox(dat, ord=1, alpha=1, n.fold=2)
summary(cv)
#plot the cross-validation curve
plot(cv)

#fit the model with the best tuning parameter chosen by cross-validation
one.fit = tfCox(dat, ord=1, alpha=1, lambda.seq=cv$best.lambda)
#predict theta from the fitted tfCox object
theta_hat = predict(one.fit, newX=dat$X, which.lambda=1)

#plot the fitted theta_hat (line) with the true theta (dot)
for (i in 1:4) {
  ordi = order(dat$X[,i])
  plot(dat$X[ordi,i], dat$true_theta[ordi,i],
       xlab=paste("predictor",i), ylab="theta" )
  lines(dat$X[ordi,i], theta_hat[ordi,i], type="l")
}

[Package tfCox version 0.1.0 Index]