| Title: | Yang and Prentice Model with Piecewise Exponential Baseline Distribution |
|---|---|
| Description: | Semiparametric modeling of lifetime data with crossing survival curves via Yang and Prentice model with piecewise exponential baseline distribution. Details about the model can be found in Demarqui and Mayrink (2021) <doi:10.1214/20-BJPS471>. Model fitting carried out via likelihood-based and Bayesian approaches. The package also provides point and interval estimation for the crossing survival times. |
| Authors: | Fabio Demarqui [aut, cre, cph] |
| Maintainer: | Fabio Demarqui <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 1.1.0 |
| Built: | 2025-02-23 04:50:01 UTC |
| Source: | https://github.com/fndemarqui/yppe |
Semiparametric modeling of lifetime data with crossing survival curves via Yang and Prentice model with piecewise exponential baseline distribution. Details about the model can be found in (Demarqui and Mayrink 2021) <doi.org/10.1214/20-BJPS471>. Model fitting carried out via likelihood-based and Bayesian approaches. The package also provides point and interval estimation for the crossing survival times.
Demarqui FN, Mayrink VD (2021). “Yang and Prentice model with piecewise exponential baseline distribution for modeling lifetime data with crossing survival curves.” Brazilian Journal of Probability and Statistics, 35(1), 172 – 186. doi:10.1214/20-BJPS471.
Yang S, Prentice RL (2005). “Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data.” Biometrika, 92(1), 1-17.
Stan Development Team (2019). RStan: the R interface to Stan. R package version 2.19.2. https://mc-stan.org
Akaike information criterion
## S3 method for class 'yppe' AIC(object, ..., k = 2)## S3 method for class 'yppe' AIC(object, ..., k = 2)
object |
an object of the class yppe. |
... |
further arguments passed to or from other methods. |
k |
numeric, the penalty per parameter to be used; the default k = 2 is the classical AIC. |
the Akaike information criterion
Compute analysis of variance (or deviance) tables for one or more fitted model objects.
## S3 method for class 'yppe' anova(...)## S3 method for class 'yppe' anova(...)
... |
further arguments passed to or from other methods. |
the ANOVA table.
This function returns the estimated regression coefficients when the maximum likelihood estimation approach is used in the model fitting.
## S3 method for class 'yppe' coef(object, ...)## S3 method for class 'yppe' coef(object, ...)
object |
an object of the class yppe. |
... |
further arguments passed to or from other methods. |
the estimated regression coefficients.
## Not run: fit <- yppe(Surv(time, status)~arm, data=ipass, init = 0) coef(fit) ## End(Not run)## Not run: fit <- yppe(Surv(time, status)~arm, data=ipass, init = 0) coef(fit) ## End(Not run)
Confidence intervals for the regression coefficients
## S3 method for class 'yppe' confint(object, parm = NULL, level = 0.95, ...)## S3 method for class 'yppe' confint(object, parm = NULL, level = 0.95, ...)
object |
an object of the class yppe. |
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 or from other methods. |
100(1-alpha) confidence intervals for the regression coefficients.
Generic S3 method crossTime
crossTime(object, ...)crossTime(object, ...)
object |
a fitted model object |
... |
further arguments passed to or from other methods. |
the crossing survival time
Computes the crossing survival times
## S3 method for class 'yppe' crossTime(object, newdata1, newdata2, conf.level = 0.95, nboot = 1000, ...)## S3 method for class 'yppe' crossTime(object, newdata1, newdata2, conf.level = 0.95, nboot = 1000, ...)
object |
an object of class yppe |
newdata1 |
a data frame containing the first set of explanatory variables |
newdata2 |
a data frame containing the second set of explanatory variables |
conf.level |
level of the confidence/credible intervals |
nboot |
number of bootstrap samples (default nboot=1000); ignored if approach="bayes". |
... |
further arguments passed to or from other methods. |
the crossing survival time
# ML approach: library(YPPE) mle <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle", init = 0) summary(mle) newdata1 <- data.frame(arm=0) newdata2 <- data.frame(arm=1) tcross <- crossTime(mle, newdata1, newdata2, nboot = 10) tcross ekm <- survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(mle, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2)) abline(v=tcross, col="blue") # Bayesian approach: bayes <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes", chains=1, iter=10) summary(bayes) newdata1 <- data.frame(arm=0) newdata2 <- data.frame(arm=1) tcross <- crossTime(bayes, newdata1, newdata2) tcross ekm <- survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(bayes, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2)) abline(v=tcross, col="blue")# ML approach: library(YPPE) mle <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle", init = 0) summary(mle) newdata1 <- data.frame(arm=0) newdata2 <- data.frame(arm=1) tcross <- crossTime(mle, newdata1, newdata2, nboot = 10) tcross ekm <- survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(mle, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2)) abline(v=tcross, col="blue") # Bayesian approach: bayes <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes", chains=1, iter=10) summary(bayes) newdata1 <- data.frame(arm=0) newdata2 <- data.frame(arm=1) tcross <- crossTime(bayes, newdata1, newdata2) tcross ekm <- survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(bayes, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2)) abline(v=tcross, col="blue")
Data set from a clinical trial conducted by the Gastrointestinal Tumor Study Group (GTSG) in 1982. The data set refers to the survival times of patients with locally nonresectable gastric cancer. Patients were either treated with chemotherapy combined with radiation or chemotherapy alone.
A data frame with 90 rows and 3 variables:
time: survival times (in days)
status: failure indicator (1 - failure; 0 - otherwise)
trt: treatments (1 - chemotherapy + radiation; 0 - chemotherapy alone)
Fabio N. Demarqui [email protected]
Gastrointestinal Tumor Study Group. (1982) A Comparison of Combination Chemotherapy and Combined Modality Therapy for Locally Advanced Gastric Carcinoma. Cancer 49:1771-7.
Reconstructed IPASS clinical trial data reported in Argyropoulos and Unruh (2015). Although reconstructed, this data set preserves all features exhibited in references with full access to the observations from this clinical trial. The data base is related to the period of March 2006 to April 2008. The main purpose of the study is to compare the drug gefitinib against carboplatin/paclitaxel doublet chemotherapy as first line treatment, in terms of progression free survival (in months), to be applied to selected non-small-cell lung cancer (NSCLC) patients.
A data frame with 1217 rows and 3 variables:
time: progression free survival (in months)
status: failure indicator (1 - failure; 0 - otherwise)
arm: (1 - gefitinib; 0 - carboplatin/paclitaxel doublet chemotherapy)
Fabio N. Demarqui [email protected]
Argyropoulos, C. and Unruh, M. L. (2015). Analysis of time to event outcomes in randomized controlled trials by generalized additive models. PLOS One 10, 1-33.
Extract Log-Likelihood
## S3 method for class 'yppe' logLik(object, ...)## S3 method for class 'yppe' logLik(object, ...)
object |
an object of the class yppe. |
... |
further arguments passed to or from other methods. |
the log-likelihood associated with the fitted model.
Reconstruct the model matrix (or matrices if the alternative formulation of the YP model is used) for a yppe model.
## S3 method for class 'yppe' model.matrix(object, ...)## S3 method for class 'yppe' model.matrix(object, ...)
object |
an object of the class yppe. |
... |
further arguments passed to or from other methods. |
The model matrix (or matrices) for the fit.
## Not run: fit <- yppe(Surv(time, status)~arm, data=ipass) model.matrix(fit) ## End(Not run)## Not run: fit <- yppe(Surv(time, status)~arm, data=ipass) model.matrix(fit) ## End(Not run)
Hazard and cumulative hazard functions of the PE distribution
hpexp(x, rho, rates) Hpexp(x, rho, rates)hpexp(x, rho, rates) Hpexp(x, rho, rates)
x |
vector of time points. |
rho |
vector of time grid knots. |
rates |
vector of failure rates. |
hpexp gives the hazard function and Hpexp gives the cumulative hazard function of the PE distribution.
Probability function, distribution function, quantile function and random generation for the Piecewise Exponential (PE) distribution.
dpexp(x, rho, rates, log = FALSE) ppexp(q, rho, rates, lower.tail = TRUE, log.p = FALSE) qpexp(p, rho, rates, lower.tail = TRUE, log.p = FALSE) rpexp(n, rho, rates)dpexp(x, rho, rates, log = FALSE) ppexp(q, rho, rates, lower.tail = TRUE, log.p = FALSE) qpexp(p, rho, rates, lower.tail = TRUE, log.p = FALSE) rpexp(n, rho, rates)
x |
vector of time points. |
rho |
vector of time grid knots. |
rates |
vector of failure rates. |
log, log.p
|
logical; if TRUE, probabilities p are given as log(p). |
q |
vector of quantiles. |
lower.tail |
logical; if TRUE (default), probabilities are |
p |
vector of probabilities. |
n |
number of random values to return. |
dpexp gives the (log) probability function, ppexp gives the (log) distribution function, qpexp gives the quantile function, and rpexp generates random deviates.
n <- 10 rho <- c(0, 1, 3, 7, Inf) rates <- c(0.5, 4, 0.8, 0.1) x <- sort(rpexp(n, rho=rho, rates=rates)) Fx <- ppexp(x, rho, rates) y <- qpexp(Fx, rho, rates) # checking: x==yn <- 10 rho <- c(0, 1, 3, 7, Inf) rates <- c(0.5, 4, 0.8, 0.1) x <- sort(rpexp(n, rho=rho, rates=rates)) Fx <- ppexp(x, rho, rates) y <- qpexp(Fx, rho, rates) # checking: x==y
phpe: Fit Proportional Hazards Regression Model with Piecewise Exponential baseline distribution.
phpe( formula, data, n_int = NULL, rho = NULL, tau = NULL, hessian = TRUE, approach = c("mle", "bayes"), hyper_parms = list(h1_gamma = 0, h2_gamma = 4, mu_beta = 0, sigma_beta = 4), ... )phpe( formula, data, n_int = NULL, rho = NULL, tau = NULL, hessian = TRUE, approach = c("mle", "bayes"), hyper_parms = list(h1_gamma = 0, h2_gamma = 4, mu_beta = 0, sigma_beta = 4), ... )
formula |
an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. |
data |
an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which phpe is called. |
n_int |
number of intervals of the PE distribution. If NULL, default value (square root of n) is used. |
rho |
the time grid of the PE distribution. If NULL, the function timeGrid is used to compute rho. |
tau |
the maximum time of follow-up. If NULL, tau = max(time), where time is the vector of observed survival times. |
hessian |
logical; If TRUE (default), the hessian matrix is returned when approach="mle". |
approach |
approach to be used to fit the model (mle: maximum likelihood; bayes: Bayesian approach). |
hyper_parms |
a list containing the hyper-parameters of the prior distributions (when approach = "bayes"). If not specified, default values are used. |
... |
Arguments passed to either 'rstan::optimizing' or 'rstan::sampling' . |
phpe returns an object of class "phpe" containing the fitted model.
# ML approach: library(YPPE) mle <- phpe(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle") summary(mle) # Bayesian approach: bayes <- phpe(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes)# ML approach: library(YPPE) mle <- phpe(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle") summary(mle) # Bayesian approach: bayes <- phpe(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes)
pope: Fit Proportional Odds Regression Model with Piecewise Exponential baseline distribution.
pope( formula, data, n_int = NULL, rho = NULL, tau = NULL, hessian = TRUE, approach = c("mle", "bayes"), hyper_parms = list(h1_gamma = 0, h2_gamma = 4, mu_beta = 0, sigma_beta = 4), ... )pope( formula, data, n_int = NULL, rho = NULL, tau = NULL, hessian = TRUE, approach = c("mle", "bayes"), hyper_parms = list(h1_gamma = 0, h2_gamma = 4, mu_beta = 0, sigma_beta = 4), ... )
formula |
an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. |
data |
an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which pope is called. |
n_int |
number of intervals of the PE distribution. If NULL, default value (square root of n) is used. |
rho |
the time grid of the PE distribution. If NULL, the function timeGrid is used to compute rho. |
tau |
the maximum time of follow-up. If NULL, tau = max(time), where time is the vector of observed survival times. |
hessian |
logical; If TRUE (default), the hessian matrix is returned when approach="mle". |
approach |
approach to be used to fit the model (mle: maximum likelihood; bayes: Bayesian approach). |
hyper_parms |
a list containing the hyper-parameters of the prior distributions (when approach = "bayes"). If not specified, default values are used. |
... |
Arguments passed to either 'rstan::optimizing' or 'rstan::sampling' . |
pope returns an object of class "pope" containing the fitted model.
# ML approach: library(YPPE) mle <- pope(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle") summary(mle) # Bayesian approach: bayes <- pope(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes)# ML approach: library(YPPE) mle <- pope(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle") summary(mle) # Bayesian approach: bayes <- pope(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes)
Print the summary.phpe output
## S3 method for class 'summary.phpe' print(x, ...)## S3 method for class 'summary.phpe' print(x, ...)
x |
an object of the class summary.phpe. |
... |
further arguments passed to or from other methods. |
a summary of the fitted model.
Print the summary.pope output
## S3 method for class 'summary.pope' print(x, ...)## S3 method for class 'summary.pope' print(x, ...)
x |
an object of the class summary.pope. |
... |
further arguments passed to or from other methods. |
a summary of the fitted model.
Print the summary.yppe output
## S3 method for class 'summary.yppe' print(x, ...)## S3 method for class 'summary.yppe' print(x, ...)
x |
an object of the class summary.yppe. |
... |
further arguments passed to or from other methods. |
a summary of the fitted model.
Generic S3 method rates
rates(object, ...)rates(object, ...)
object |
a fitted model object. |
... |
further arguments passed to or from other methods. |
Method only available for ML approach.
the estimated failure rates for the PE distribution.
Estimated failure rates for the PE distribution
## S3 method for class 'phpe' rates(object, ...)## S3 method for class 'phpe' rates(object, ...)
object |
a fitted model object. |
... |
further arguments passed to or from other methods. |
Method only available for ML approach.
the estimated failure rates for the PE distribution.
Estimated failure rates for the PE distribution
## S3 method for class 'pope' rates(object, ...)## S3 method for class 'pope' rates(object, ...)
object |
a fitted model object. |
... |
further arguments passed to or from other methods. |
Method only available for ML approach.
the estimated failure rates for the PE distribution.
Estimated failure rates for the PE distribution
## S3 method for class 'yppe' rates(object, ...)## S3 method for class 'yppe' rates(object, ...)
object |
a fitted model object. |
... |
further arguments passed to or from other methods. |
Method only available for ML approach.
the estimated failure rates for the PE distribution.
Function to generate a random sample of survival data.
rsurv( formula, covariates, baseline = "weibull", gamma, psi = NULL, phi = NULL, max_fu )rsurv( formula, covariates, baseline = "weibull", gamma, psi = NULL, phi = NULL, max_fu )
formula |
formula specifying the linear predictors |
covariates |
data frame containing the covariates used to generate the survival times |
baseline |
baseline model (currently only the Weibull distribution is available) |
gamma |
baseline parameters |
psi |
short-term regression coefficients |
phi |
long-term regression coefficients |
max_fu |
maximum follow-up time |
Summary for the yppe model
## S3 method for class 'phpe' summary(object, ...)## S3 method for class 'phpe' summary(object, ...)
object |
an objecto of the class 'yppe'. |
... |
further arguments passed to or from other methods. |
Summary for the yppe model
## S3 method for class 'pope' summary(object, ...)## S3 method for class 'pope' summary(object, ...)
object |
an objecto of the class 'yppe'. |
... |
further arguments passed to or from other methods. |
Summary for the yppe model
## S3 method for class 'yppe' summary(object, ...)## S3 method for class 'yppe' summary(object, ...)
object |
an objecto of the class 'yppe'. |
... |
further arguments passed to or from other methods. |
Computes the predicted survivor function for a phpe model.
## S3 method for class 'phpe' survfit(formula, newdata, ...)## S3 method for class 'phpe' survfit(formula, newdata, ...)
formula |
an object of the class phpe |
newdata |
a data frame containing the set of explanatory variables. |
... |
further arguments passed to or from other methods. |
a list containing the estimated survival probabilities.
# ML approach: library(YPPE) mle <- phpe(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle", init = 0) summary(mle) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(mle, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2)) # Bayesian approach: bayes <- phpe(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(bayes, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2))# ML approach: library(YPPE) mle <- phpe(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle", init = 0) summary(mle) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(mle, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2)) # Bayesian approach: bayes <- phpe(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(bayes, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2))
Computes the predicted survivor function for a pope model.
## S3 method for class 'pope' survfit(formula, newdata, ...)## S3 method for class 'pope' survfit(formula, newdata, ...)
formula |
an object of the class pope |
newdata |
a data frame containing the set of explanatory variables. |
... |
further arguments passed to or from other methods. |
a list containing the estimated survival probabilities.
# ML approach: library(YPPE) mle <- pope(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle", init = 0) summary(mle) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(mle, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2)) # Bayesian approach: bayes <- pope(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(bayes, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2))# ML approach: library(YPPE) mle <- pope(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle", init = 0) summary(mle) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(mle, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2)) # Bayesian approach: bayes <- pope(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(bayes, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2))
Computes the predicted survivor function for a yppe model.
## S3 method for class 'yppe' survfit(formula, newdata, ...)## S3 method for class 'yppe' survfit(formula, newdata, ...)
formula |
an object of the class yppe |
newdata |
a data frame containing the set of explanatory variables. |
... |
further arguments passed to or from other methods. |
a list containing the estimated survival probabilities.
# ML approach: library(YPPE) mle <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle") summary(mle) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(mle, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2)) # Bayesian approach: bayes <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(bayes, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2))# ML approach: library(YPPE) mle <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle") summary(mle) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(mle, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2)) # Bayesian approach: bayes <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes) ekm <- survival::survfit(Surv(time, status)~arm, data=ipass) newdata <- data.frame(arm=0:1) St <- survfit(bayes, newdata) plot(ekm, col=1:2) with(St, lines(time, surv[[1]])) with(St, lines(time, surv[[2]], col=2))
Time grid
timeGrid(time, status, n_int = NULL)timeGrid(time, status, n_int = NULL)
time |
Vector of failure times |
status |
Vector of failure indicators |
n_int |
Optional. Number of intervals. If |
Time grid.
This function extracts and returns the variance-covariance matrix associated with the regression coefficients when the maximum likelihood estimation approach is used in the model fitting.
## S3 method for class 'yppe' vcov(object, ...)## S3 method for class 'yppe' vcov(object, ...)
object |
an object of the class yppe. |
... |
further arguments passed to or from other methods. |
the variance-covariance matrix associated with the regression coefficients.
yppe: Fit the Yang and Prentice Regression Model with Piecewise Exponential baseline distribution.
yppe( formula, data, n_int = NULL, rho = NULL, tau = NULL, hessian = TRUE, approach = c("mle", "bayes"), hyper_parms = list(h1_gamma = 0, h2_gamma = 4, mu_psi = 0, sigma_psi = 4, mu_phi = 0, sigma_phi = 4, mu_beta = 0, sigma_beta = 4), ... )yppe( formula, data, n_int = NULL, rho = NULL, tau = NULL, hessian = TRUE, approach = c("mle", "bayes"), hyper_parms = list(h1_gamma = 0, h2_gamma = 4, mu_psi = 0, sigma_psi = 4, mu_phi = 0, sigma_phi = 4, mu_beta = 0, sigma_beta = 4), ... )
formula |
an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. |
data |
an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which yppe is called. |
n_int |
number of intervals of the PE distribution. If NULL, default value (square root of n) is used. |
rho |
the time grid of the PE distribution. If NULL, the function timeGrid is used to compute rho. |
tau |
the maximum time of follow-up. If NULL, tau = max(time), where time is the vector of observed survival times. |
hessian |
logical; If TRUE (default), the hessian matrix is returned when approach="mle". |
approach |
approach to be used to fit the model (mle: maximum likelihood; bayes: Bayesian approach). |
hyper_parms |
a list containing the hyper-parameters of the prior distributions (when approach = "bayes"). If not specified, default values are used. |
... |
Arguments passed to either 'rstan::optimizing' or 'rstan::sampling' . |
yppe returns an object of class "yppe" containing the fitted model.
# ML approach: library(YPPE) mle <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle") summary(mle) # Bayesian approach: bayes <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes)# ML approach: library(YPPE) mle <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle") summary(mle) # Bayesian approach: bayes <- yppe(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes") summary(bayes)