Including Interactions and Splines in Piecewise Constant Hazard Regression
This function can be used within a call to
pchreg to automatically include
spline functions in the linear predictor of the model.
a character string indicating whether natural splines (
the degrees of freedom of the spline basis.
the degree of the polynomial (only for
a value between 0 and 1 determining how many principal components of the design matrix must be used in model fitting (see “Details”).
for future arguments.
The piecewise constant hazard model implemented by
pchreg can be used as
a nonparametric maximum likelihood estimator, in which the number of parameters
is allowed to increase with the sample size in order to achieve any desired flexibility.
Modeling the effect of covariates is as important as setting a sufficiently large
splinex = splinex(...), each column of the original design matrix
is automatically replaced by the corresponding spline basis, defined by
This modeling approach has the drawback of generating a potentially large design matrix:
to reduce its dimension, you can choose
v < 1. In this case, only the principal
components explaining at least a proportion
v of the variance
are used to fit the model (see “Examples”).
The function returns its arguments, to be passed to an internal function
that actually computes the design matrix.
A multidimensional spline can be created by including a term like, for example
ns(x1,df)*ns(x2,df). This is not supported by
as it may generate a very large design matrix.
Paolo Frumento <email@example.com>
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require(splines) n <- 1000 x1 <- runif(n,-2,2) x2 <- runif(n,-2,2) t <- rexp(n, exp(-abs(x1 - x2))) # a simple model model1 <- pchreg(Surv(t) ~ x1 + x2) # using splinex: the same as ~ ns(x1, df = 2) + ns(x2, df = 2) model2 <- pchreg(Surv(t) ~ x1 + x2, splinex = splinex("ns", v = 1)) # include interaction: ~ ns(x1, df = 2) + ns(x2, df = 2) + ns(x1*x2, df = 2) model3 <- pchreg(Surv(t) ~ x1 * x2, splinex = splinex("ns", v = 1)) # the same as model 3, only keep the PCs explaining at least 95 percent of the variance model4 <- pchreg(Surv(t) ~ x1 * x2, splinex = splinex("ns", v = 0.95)) # true CDF vs fitted trueF <- pexp(t, exp(-abs(x1 - x2))) par(mfrow = c(2,2)) plot(trueF, 1 - predict(model1)$Surv); abline(0,1, col = "red") # does not fit plot(trueF, 1 - predict(model2)$Surv); abline(0,1, col = "red") # neither plot(trueF, 1 - predict(model3)$Surv); abline(0,1, col = "red") # great! plot(trueF, 1 - predict(model4)$Surv); abline(0,1, col = "red") # almost as good
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