Fx_survival {OptimalDesign}

Matrix of candidate regressors for a survival model

Description

Creates the matrix of all candidate regressors for a linearization of a proportional hazards survival model.

Usage

Fx_survival(formula, theta0, censor.time, survival.model="phI", lower=NULL,
            upper=NULL, n.levels=NULL, echo=TRUE)

Arguments

formula

the formula of the linear part of the model. The rules for creating the formula are standard for R but: 1) the formula must not contain the dependent variable (it is one-sided); 2) the d factors (variables) must be labeled x1,x2,x3,...

theta0

the d-dimensional vector of values of the unknown parameter in which to linearize the model.

censor.time

the censoring time, a positive constant.

survival.model

the type of the survival model, can be either proportional hazards with Type I censoring ("phI") or with random censoring ("phrand"). Both models assume a constant baseline hazard.

lower

the d-dimensional vector of the smallest values of factors. If lower=NULL, the program sets lower <- rep(-1, d).

upper

the d-dimensional vector of the largest values of factors. If upper=NULL, the program sets upper <- rep(1, d).

n.levels

the d-dimensional vector of the numbers of levels of each factor. If n.levels=NULL, the program sets n.levels <- rep(2, d).

echo

Print the call of the function?

Details

For mathematical details, see the referenced paper.

Value

The n times m matrix of all candidate regressors of a proportional hazards model linearized in theta0.

Author(s)

Radoslav Harman, Lenka Filova

References

Konstantinou M, Biedermann S, Kimber A (2014). Optimal designs for two-parameter nonlinear models with application to survival models. Statistica Sinica, 24(1), 415-428.

See Also

Fx_cube, Fx_simplex, Fx_blocks, Fx_glm, Fx_dose

Examples

# The proportional hazards model with random censoring
# for three binary explanatory variables x1,x2,x3 without intercept
# censoring time 30 and parameter values theta0=c(1,1,1)
Fx <- Fx_survival(~x1 + x2 + x3 - 1, c(1, 1, 1), 30, "phrand",
      lower = c(0, 0, 0), upper = c(1, 1, 1), n.levels = c(2, 2, 2))

# The locally D-optimal approximate design
w <- od_REX(Fx, crit="D")$w.best
od_print(Fx, w, Fx)

## Not run: 
# The proportional hazards model with random censoring
# for explanatory variables x1,x2,x3 in the range [0,1] discretized into 11 points
# censoring time 30 and parameter values theta0=c(1,1,1)
Fx <- Fx_survival(~x1 + x2 + x3 - 1, c(1, 1, 1), 30, "phrand",
      lower = c(0, 0, 0), upper = c(1, 1, 1), n.levels = c(11, 11, 11))

# The locally A-optimal exact design of size 50 without replications
w <- od_KL(Fx, 50, crit="A", bin=TRUE, t.max=5)$w.best
od_plot(Fx, w, Fx)

## End(Not run)