Package 'spsurv'

The 'spsurv' package.

Description

A set of flexible routines to allow semiparametric survival regression modeling based on Bernstein polynomial, including Bernstein based proportinal hazards model (BPPH), Bernstein polynomial based proportional odds model (BPPO) and Bernstein based accelerated failure time model (BPAFT) for right-censored data.

Details

spbp fits semi-parametric models for time-to-event survival data. Non-informative right-censoring assumption is available. Any user-defined Bernstein polynomial can be user-defined using an arbitrary degree, i.e. highest basis polynomials order.

The framework takes advantage of fully likelihood methods since the polynomial parameters are used to estimate the baseline functions. Even so, this is said to be semi-parametric since this approach does not rely on any distribution. Unlike the Cox model, the BP based models provide smooth hazard and survival curve estimates.

_PACKAGE

Value

none

Author(s)

[email protected]

References

Panaro R.V. (2020). spsurv: An R package for semi-parametric survival analysis. arXiv preprint arXiv:2003.10548.

Demarqui, F. N., & Mayrink, V. D. (2019). A fully likelihood-based approach to model survival data with crossing survival curves. arXiv preprint arXiv:1910.02406.

Demarqui, F. N., Mayrink, V. D., & Ghosh, S. K. (2019). An Unified Semiparametric Approach to Model Lifetime Data with Crossing Survival Curves. arXiv preprint arXiv:1910.04475.

Osman, M., & Ghosh, S. K. (2012). Nonparametric regression models for right-censored data using Bernstein polynomials. Computational Statistics & Data Analysis, 56(3), 559-573.

Lorentz, G. G. (1953). Bernstein polynomials. American Mathematical Society.

---

Bernstein basis polynomials calculations

Description

Bernstein basis polynomials calculations

Usage

bp.basis(time, degree, tau = max(time))

Arguments

time	a vector of times.
degree	Bernstein polynomial degree
tau	must be greater than times maximum value observed.

Value

A list containing matrices g and G corresponding BP basis and corresponding tau value used to compute them.

---

Bernstein Polynomial Based Accelerated Failure Time Model

Description

Fits the BPAFT model to time-to-event data.

Usage

bpaft(formula, degree, data, approach = c("mle", "bayes"), ...)

Arguments

formula	a Surv object with time to event observations, right censoring status and explanatory terms.
degree	Bernstein polynomial degree.
data	a data.frame object.
approach	Bayesian or maximum likelihood estimation methods, default is approach = "mle".
...	further arguments passed to or from other methods

Value

An object of class 'spbp'.

See Also

spbp, bpph and bppo for other BP based models.

Examples

library("spsurv")
data("veteran", package = "survival")

fit <- bpaft(Surv(time, status) ~ karno + celltype,
  data = veteran
)

summary(fit)

---

Bernstein Polynomial Based Proportional Hazards Model

Description

Fits the BPPH model to time-to-event data.

Usage

bpph(formula, degree, data, approach = c("mle", "bayes"), ...)

Arguments

formula	a Surv object with time to event observations, right censoring status and explanatory terms.
degree	Bernstein polynomial degree.
data	a data.frame object.
approach	Bayesian or maximum likelihood estimation methods, default is approach = "mle".
...	further arguments passed to or from other methods

Value

An object of class 'spbp'.

See Also

spbp, bppo and bpaft for other BP based models.

Examples

library("spsurv")
data("veteran", package = "survival")

fit <- bpph(Surv(time, status) ~ karno + factor(celltype),
  data = veteran
)

summary(fit)

---

Bernstein Polynomial Based Proportional Odds Model

Description

Fits the BPPO model to time-to-event data.

Usage

bppo(formula, degree, data, approach = c("mle", "bayes"), ...)

Arguments

formula	a Surv object with time-to-event observations, right censoring status and explanatory terms.
degree	Bernstein polynomial degree.
data	a data.frame object.
approach	Bayesian or maximum likelihood estimation methods, default is approach = "mle".
...	further arguments passed to or from other methods

Value

An object of class 'spbp'.

See Also

spbp, bpph and bpaft for other BP based models.

Examples

library("spsurv")
data("veteran", package = "survival")

fit <- bppo(Surv(time, status) ~ karno + celltype,
  data = veteran
)

summary(fit)

---

Estimated regression coefficients

Description

Estimated regression coefficients

Usage

## S3 method for class 'spbp'
coef(object, summary = c("mean", "median", "mode"), ...)

Arguments

object	an object of the class spbp
summary	posterior summary if method ="bayes" in x
...	further arguments passed to or from other methods

Value

the estimated regression coefficients

---

Confidence intervals for the regression coefficients

Description

Confidence intervals for the regression coefficients

Usage

## S3 method for class 'spbp'
confint(object, parm = names(coef(object)), level = 0.95, ...)

Arguments

object	a fitted model object.
parm	a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.
level	the confidence level required.
...	further arguments passed to parent method

Value

100(1-alpha) confidence intervals for the regression coefficients

---

Generic S3 method credint

Description

Generic S3 method credint

Usage

credint(x, ...)

Arguments

x	a fitted model object
...	further arguments passed to parent method

Value

the estimated regression coefficients

---

Confidence intervals for the regression coefficients

Description

Confidence intervals for the regression coefficients

Usage

## S3 method for class 'spbp'
credint(x, prob = 0.95, type = c("HPD", "Equal-Tailed"), ...)

Arguments

x	an object of the class x.
prob	the probability level required.
type	interval type.
...	further arguments passed to or from other methods.

Value

100(1-alpha) confidence intervals for the regression coefficients

---

Model.matrix method for fitted spbp models

Description

Model.matrix of a fitted spbp model.

Usage

## S3 method for class 'spbp'
model.matrix(object, ...)

Arguments

object	an object of class 'spbp', see spbp.
...	arguments passed to parent method.

Value

The model matrix.

See Also

spbp, model.matrix

Examples

library("spsurv")
data("veteran", package = "survival")

fit <- bpph(Surv(time, status) ~ karno + factor(celltype),
  data = veteran
)

model.matrix(fit)

---

BP based models plot.

Description

Plot for a fitted spbp model.

Usage

## S3 method for class 'spbp'
plot(
  x,
  main,
  graph = c("baseline", "basis"),
  cumulative = F,
  frame = F,
  lwd = 3,
  ...
)

Arguments

x	an object of class 'spbp' result of a spbp fit.
main	graph title
graph	type of polynomial graph, default is "basis"
cumulative	TRUE for odds and cumulative hazard
frame	graphical parameter; default is FALSE
lwd	graphical parameter; default is 3
...	further arguments passed to or from other methods

See Also

spbp.

Examples

library("spsurv")
data("veteran", package = "survival")

fit <- bpph(Surv(time, status) ~ karno + factor(celltype),
  data = veteran
)
plot(fit)

---

Bernstein Polynomial Based Regression Object Print

Description

Bernstein Polynomial Based Regression Object Print

Usage

## S3 method for class 'spbp'
print(
  x,
  bp.param = FALSE,
  digits = max(getOption("digits") - 4, 3),
  signif.stars = getOption("show.signif.stars"),
  ...
)

Arguments

x	an object of class spbp.
bp.param	print BP parameters.
digits	number of digits to display.
signif.stars	see getOption.
...	further arguments passed to or from other methods.

Value

none

---

Bernstein Polynomial Based Regression Object Summary BPAFT Bayes

Description

Bernstein Polynomial Based Regression Object Summary BPAFT Bayes

Usage

## S3 method for class 'summary.bpaft.bayes'
print(...)

Arguments

...	further arguments passed to or from other methods

Value

none

---

Bernstein Polynomial Based Regression Object Summary BPAFT MLE

Description

Bernstein Polynomial Based Regression Object Summary BPAFT MLE

Usage

## S3 method for class 'summary.bpaft.mle'
print(...)

Arguments

...	further arguments passed to or from other methods

Value

none

---

Bernstein Polynomial Based Regression Object Summary BPPH Bayes

Description

Bernstein Polynomial Based Regression Object Summary BPPH Bayes

Usage

## S3 method for class 'summary.bpph.bayes'
print(...)

Arguments

...	further arguments passed to or from other methods

Value

none

---

Bernstein Polynomial Based Regression Object Summary BPPH MLE

Description

Bernstein Polynomial Based Regression Object Summary BPPH MLE

Usage

## S3 method for class 'summary.bpph.mle'
print(...)

Arguments

...	further arguments passed to or from other methods

Value

none

---

Bernstein Polynomial Based Regression Object Summary BPPO Bayes

Description

Bernstein Polynomial Based Regression Object Summary BPPO Bayes

Usage

## S3 method for class 'summary.bppo.bayes'
print(...)

Arguments

...	further arguments passed to or from other methods

Value

none

---

Bernstein Polynomial Based Regression Object BPPO MLE

Description

Bernstein Polynomial Based Regression Object BPPO MLE

Usage

## S3 method for class 'summary.bppo.mle'
print(...)

Arguments

...	further arguments passed to or from other methods

Value

none

---

Bernstein Polynomial Based Regression Object Summary Bayes

Description

Bernstein Polynomial Based Regression Object Summary Bayes

Usage

## S3 method for class 'summary.spbp.bayes'
print(x, digits = max(getOption("digits") - 4, 3), ...)

Arguments

x	a summary.spbp.bayes object
digits	number of digits to display.
...	further arguments passed to or from other methods

Value

none

---

Bernstein Polynomial Based Regression Object Summary MLE

Description

Bernstein Polynomial Based Regression Object Summary MLE

Usage

## S3 method for class 'summary.spbp.mle'
print(
  x,
  digits = max(getOption("digits") - 4, 3),
  signif.stars = getOption("show.signif.stars"),
  ...
)

Arguments

x	a summary.spbp.mle object
digits	number of digits to display.
signif.stars	see getOption
...	further arguments passed to or from other methods

Value

none

---

Power basis polynomials calculations

Description

Power basis polynomials calculations

Usage

pw.basis(degree)

Arguments

degree

Bernstein polynomial degree

Value

A list containing matrices g and G corresponding BP basis and corresponding tau value used to compute them.

---

BP based models residuals.

Description

Residuals for a fitted spbp model.

Usage

## S3 method for class 'spbp'
residuals(object, type = c("martingale", "deviance", "coobject-snell"), ...)

Arguments

object	an object of class 'spbp' result of a spbp fit.
type	type of residuals, default is "cox-snell"
...	arguments passed to parent method.

See Also

spbp, spbp.

Examples

library("spsurv")
data("veteran", package = "survival")

fit <- bpph(Surv(time, status) ~ karno + factor(celltype),
  data = veteran
)

residuals(fit)

---

spbp: The BP Based Survival Analysis Function

Description

Semiparametric Survival Analysis Using Bernstein Polynomial

Usage

spbp(formula, ...)

Arguments

formula	a Surv object with time to event, status and explanatory terms.
...	Arguments passed to 'rstan::sampling' (e.g. iter, chains) or 'rstan::optimizing'.

Details

Fits Bernstein Polynomial based Proportional regression to survival data.

Value

An object of class 'spbp'.

See Also

spbp.default

spbp.default, bpph, bppo, bpaft, https://mc-stan.org/users/documentation/

Examples

library("spsurv")
data("veteran", package = "survival")

fit_mle <- spbp(Surv(time, status) ~ karno + factor(celltype),
  data = veteran, model = "po"
)
summary(fit_mle)

fit_bayes <- spbp(Surv(time, status) ~ karno + factor(celltype),
  data = veteran, model = "po", approach = "bayes",
  cores = 1, iter = 300, chains = 1,
  priors = list(
    beta = c("normal(0,5)"),
    gamma = "halfnormal(0,5)"
  )
)

summary(fit_bayes)

---

spbp: The BP Based Semiparametric Survival Analysis Function

Description

spbp: The BP Based Semiparametric Survival Analysis Function

Usage

## Default S3 method:
spbp(
  formula,
  degree,
  data,
  approach = c("mle", "bayes"),
  model = c("ph", "po", "aft"),
  priors = list(beta = c("normal(0,4)"), gamma = c("lognormal(0,4)"), frailty =
    c("gamma(0.01,0.01)")),
  cores = min(parallel::detectCores() - 1, 4),
  scale = TRUE,
  verbose = FALSE,
  chains = 4,
  ...
)

Arguments

formula	a Surv object with time to event, status and explanatory terms
degree	Bernstein Polynomial degree
data	a data.frame object
approach	Bayesian or Maximum Likelihood estimation methods, default is approach = "bayes"
model	Proportional Hazards or Proportional Odds BP based regression, default is model = "ph"
priors	prior settings for the Bayesian approach; 'normal' or 'cauchy' for beta; 'lognormal' or 'loglogistic' for gamma (BP coefficients)
cores	number of core threads to use
scale	logical; indicates whether to center and scale the data
verbose	verbose passed to stan
chains	number of chains passed to stan
...	further arguments passed to or from other methods

Value

An object of class spbp

---

Bernstein Polynomial Based Regression Object Summary

Description

Bernstein Polynomial Based Regression Object Summary

Usage

## S3 method for class 'spbp'
summary(object, interval = 0.95, ...)

Arguments

object	an object of class spbp
interval	interval coverage (confidence or credibility)
...	further arguments passed to or from other methods

Value

An object of class analogous to for e.g. 'summary.bppo.bayes'.

---

BP-based model survival curves

Description

Compute survival curves for a fitted spbp model.

Usage

## S3 method for class 'spbp'
survfit(
  formula,
  newdata,
  times,
  se.fit = TRUE,
  interval = 0.95,
  type = c("log", "log-log", "plain"),
  ...
)

Arguments

formula	An object of class "spbp" returned by spbp.
newdata	Optional data frame used to obtain survival curves for specific covariate values.
times	Optional numeric vector of time points at which to return estimates.
se.fit	Logical; if TRUE, compute standard errors.
interval	Confidence level for intervals (e.g. 0.95).
type	Character; confidence interval transformation. One of "log", "log-log", or "plain".
...	Further arguments (currently ignored or reserved for future use).

Value

An object of class "survfit".

See Also

spbp, survfit.

Examples

library(spsurv)
data(veteran, package = "survival")
fit <- bpph(Surv(time, status) ~ karno + factor(celltype), data = veteran)
survfit(fit)

---

Covariance of the regression coefficients

Description

Uses block-wise inversion of the negative Hessian, with a clear split between the regression coefficients (beta) and the Bernstein polynomial coefficients (gamma).

Usage

## S3 method for class 'spbp'
vcov(object, bp.param = FALSE, ...)

Arguments

object	an object of the class spbp
bp.param	return Bernstein Polynomial variance.
...	arguments passed to parent method.

Value

the variance-covariance matrix associated with the regression coefficients.

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