Package 'ICcalib'

Title: Cox Model with Interval-Censored Starting Time of a Covariate
Description: Calibration and risk-set calibration methods for fitting Cox proportional hazard model when a binary covariate is measured intermittently. Methods include functions to fit calibration models from interval-censored data and modified partial likelihood for the proportional hazard model, Nevo et al. (2018+) <arXiv:1801.01529>.
Authors: Daniel Nevo
Maintainer: Daniel Nevo <[email protected]>
License: GPL (>= 2)
Version: 1.0.8
Built: 2025-01-31 04:39:08 UTC
Source: https://github.com/daniel258/iccalib

Help Index

Calculating the probabilities of positive binary exposure status at a given time point using a proportional hazards calibration model

Description

For a given time point, calculate the probability of positive exposure value for multiple observations (participants). The function uses the results of a proportional hazards calibration model fit, and given covariates and collected data on the history of the binary exposure for each participant.

Usage

CalcCoxCalibP(w, w.res, point, fit.cox, hz.times, Q)

Arguments

w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. Each measurement corresponds to the time points in w
point

The time point at which the probabilities are estimated
fit.cox

The result of icenReg::ic_sp on the interval-censored data
hz.times

Times used for calculating the baseline hazard function from PH calibration model
Q

Matrix of covariates for the PH calibration model

Value

A vector of estimated probabilities of positive exposure status at time point.

Examples

sim.data <- ICcalib:::SimCoxIntervalCensCox(n.sample = 200, lambda = 0.1, 
                                            alpha = 0.25, beta0 = 0, 
                                            gamma.q = c(log(0.75), log(2.5)), 
                                            gamma.z = log(1.5), mu = 0.2, 
                                            n.points = 2)
# The baseline hazard for the calibration model is calculated in observation times
cox.hz.times <- sort(unique(sim.data$obs.tm)) 
# Fit proprtional hazards calibration model
fit.cox <- FitCalibCox(w = sim.data$w, w.res = sim.data$w.res, Q = sim.data$Q, 
                       hz.times = cox.hz.times, n.int = 5, order = 2)
# Calculate the conditional probabilities of binary covariate=1 at time one
probs <- CalcCoxCalibP(w = sim.data$w, w.res = sim.data$w.res, point = 1,
                       Q = sim.data$Q, fit.cox = fit.cox, hz.times = cox.hz.times)
summary(probs)

Calculating the probabilities of positive binary exposure status at a given time point using proportional hazards grouped risk-set calibration models

Description

For a given time point, calculate the probability of positive exposure value for multiple observations (participants). The function uses the results of proportional hazards grouped risk-set calibration model fit, and given covariates and collected data on the history of the binary exposure for each participant.

Usage

CalcCoxCalibRSIntsP(w, w.res, point, fit.cox.rs.ints, hz.times, Q, pts.for.ints)

Arguments

w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. Each measurement corresponds to the time points in w
point

The time point at which the probabilities are estimated
fit.cox.rs.ints

The result of FitCalibCoxRSInts on the interval-censored data
hz.times

Times used for calculating the baseline hazard function from PH calibration model
Q

Matrix of covariates for the PH calibration model
pts.for.ints

Points defining the intervals for grouping risk-sets (first one has to be zero). Should be sorted from zero up

Value

A vector of estimated probabilities of positive exposure status at time point.

Examples

set.seed(17)
sim.data <- ICcalib:::SimCoxIntervalCensCox(n.sample = 100, lambda = 0.1, 
                                            alpha = 0.25, beta0 = 0, 
                                            gamma.q = c(log(0.75), log(2.5)), 
                                            gamma.z = log(1.5), mu = 0.2, 
                                            n.points = 2)
# The baseline hazard for the calibration model is calculated in observation times
cox.hz.times <- sort(unique(sim.data$obs.tm)) 
# Fit proprtional hazards calibration model
fit.cox.rs.ints <- FitCalibCoxRSInts(w = sim.data$w, w.res = sim.data$w.res, 
                                     Q = sim.data$Q, hz.times = cox.hz.times, 
                                     n.int = 5, order = 2, pts.for.ints = seq(0,4,1), 
                                     tm = sim.data$obs.tm, event = sim.data$delta)
# Calculate the conditional probabilities of binary covariate=1 at time one
probs <- CalcCoxCalibRSIntsP(w = sim.data$w, w.res = sim.data$w.res, point = 1,
                             fit.cox.rs.ints = fit.cox.rs.ints,
                             pts.for.ints = seq(0,4,1), Q = sim.data$Q, 
                             hz.times = cox.hz.times)
summary(probs)

Calculating the probabilities of positive binary exposure status at a given time point using a nonparametric calibration model

Description

For a given time point, calculate the probability of positive exposure value for multiple observations (participants). The function uses the results of a nonparametric calibration model fit, and given collected data on the history of the binary exposure for each participant.

Usage

CalcNpmleCalibP(w, w.res, point, fit.npmle)

Arguments

w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. Each measurement corresponds to the time points in w
point

The time point at which the probabilities are estimated.
fit.npmle

The result of icenReg::ic_np on the interval-censored data

Value

A vector of estimated probabilities of positive exposure status at time point.

Examples

sim.data <- ICcalib:::SimCoxIntervalCensSingle(n.sample = 200, lambda = 0.1, 
                                               alpha = 0.25, beta0 = log(0.5), 
                                               mu = 0.2, n.points = 2, 
                                               weib.shape = 1, weib.scale = 2)
# Fit nonparametric calibration model
fit.npmle <- FitCalibNpmle(w = sim.data$w, w.res = sim.data$w.res)
# Calculate the conditional probabilities of binary covariate=1 at time one
probs <- CalcNpmleCalibP(w = sim.data$w, w.res = sim.data$w.res, 
                         point = 1, fit.npmle = fit.npmle)
summary(probs)

Calculating the probabilities of positive binary exposure status at a given time point using a nonparametric risk-set calibration models

Description

For a given time point, calculate the probability of positive exposure value for multiple observations (participants). The function first fits the nonparametric risk-set calibration models at each main event time point and then calculates the probabilities of positive binary exposure status.

Usage

CalcNpmleRSP(w, w.res, point, obs.tm)

Arguments

w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. Each measurement corresponds to the time points in w
point

The time point at which the probabilities are estimated
obs.tm

Vector of observed main event time or censoring time

Details

This function calculates the NPMLE at each main event time point and then provides the estimated probabilities for positive exposure status at time point.

Value

A vector of estimated probabilities of positive exposure status at time point.

See Also

ic_np

Examples

# Simulate data set
sim.data <- ICcalib:::SimCoxIntervalCensSingle(n.sample = 200, lambda = 0.1, 
                                               alpha = 0.25, beta0 = log(0.5), 
                                               mu = 0.2, n.points = 2, 
                                               weib.shape = 1, weib.scale = 2)
# Calculate the conditional probabilities of binary covariate=1 at time one
# Unlike CalcNpmle, CalcNpmleRSP includes the calibration model fitting
probs <- CalcNpmleRSP(w = sim.data$w, w.res = sim.data$w.res, point = 1, 
                      obs.tm = sim.data$obs.tm)
summary(probs)

Variance estimation for the main proportional hazards model

Description

Estimation of the covariance matrix for the parameters of the main proportional hazards model. This includes the variance of the binary exposure estimate and the other covariates, if included in the model. Each function correspond to a different calibration (or risk-set calibration model).

For nonparametric calibration, bootstrap calculations of the variance and confidence interval for the for the log hazard-ratio of the binary exposure.

Usage

CalcVarParam(theta, tm, event, Z, Q, ps, ps.deriv, w, w.res, fit.cox)

CalcVarParamRSInts(theta, tm, event, Z, Q, ps, ps.deriv, w, w.res,
  fit.cox.rs.ints, pts.for.ints, n.etas.per.fit)

CalcVarThetaWeib(beta, etas, tm, event, ps, ps.deriv.shape, ps.deriv.scale, w,
  w.res)

CalcVarThetaWeibRS(beta, etas.matrix, tm, event, ps.rs, ps.deriv.shape.rs,
  ps.deriv.scale.rs, w, w.res)

CalcVarNpmle(tm, event, w, w.res, BS = 100, CI = T)

CalcVarNpmleRS(tm, event, w, w.res, BS = 100, CI = T)

Arguments

theta

Coefficient vector from main PH model. First coefficient corresponds to X, the rest to Z
tm

Vector of observed main event time or censoring time
event

Vector of censoring indicators. 1 for event 0 for censored
Z

Additional variables for the main model other than the binary covariate
Q

For PH calibration models: additional covariates
ps

A matrix. Rows are observations, columns are time pointas of the events. The entry at the i-th row and j-column is the conditional probability of positive exposure status for observation i at the j-th event time.
ps.deriv

A matrix. Rows are observations, columns are time points of the events. The derivative of ps with respect to the calibration model parameters
w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. The measurement corresponding to the time points in w.
fit.cox

For PH calibration models: The result of icenReg::ic_sp on the interval-censored data
fit.cox.rs.ints

For grouped risk-set PH calibraion: The result of FitCalibCoxRSInts on the interval-censored data
pts.for.ints

For grouped-risk set PH calibraion: Points defining the intervals for grouping risk-sets (first one has to be zero). Should be sorted from zero up
n.etas.per.fit

For grouped-risk set PH calibraion: A vector. Total number of parameters for each PH calibration fit.
beta

Coefficient of the binary covariate. The analogue of theta for non-PH calibration models
etas

For Weibull calibration: Shape and scale parameters of the Weibull calibration model.
ps.deriv.shape

The derivative of ps with respect to the shape parameter of the Weibull calibration model.
ps.deriv.scale

The derivative of ps with respect to the scale parameter of the Weibull calibration model.
etas.matrix

For Weibull risk-set calibration: Two-columns matrix. Each row contains shape and scale parameters from a Weibull risk-set calibration model
ps.rs

A matrix. Rows are observations, columns are time points of the events. The entry at the i-th row and j-column is the conditional probability of positive exposure status for observation i at the j-th event time.
ps.deriv.shape.rs

For Weibull risk-set calibration:The derivative of ps with respect to the shape parameters of the Weibull risk-set calibration models.
ps.deriv.scale.rs

For Weibull risk-set calibration:The derivative of ps with respect to the scale parameters of the Weibull risk-set calibration models.
BS

For nonparametric calibration: Number of bootstrap iterations, Default: 100
CI

For nonparametric calibration: Should the function return confidence intervals?, Default: T

Value

The covariance matrix. The first row and column are for the binary exposure.

For nonparametric calibration: Variance estimate and possibly confidence interval for the log hazard-ratio of the binary exposure under a nonparametric calibration model.

Examples

# Simulate data set
sim.data <- ICcalib:::SimCoxIntervalCensSingle(n.sample = 200, lambda = 0.1, alpha = 0.25, 
                                               beta0 = log(0.5), mu = 0.2, n.points = 2, 
                                               weib.shape = 1, weib.scale = 2)
case.times <- sim.data$obs.tm[sim.data$delta==1]
# Fit a Weibull calibration model for the covariate starting time distribution
calib.weib.params <- FitCalibWeibull(w = sim.data$w, w.res = sim.data$w.res)
px <- t(sapply(case.times, CalcWeibullCalibP, w = sim.data$w, 
               w.res =  sim.data$w.res, weib.params = calib.weib.params))
# Calculate derivative matrices
px.deriv.shape <- t(sapply(case.times, ICcalib:::CalcWeibullCalibPderivShape, 
w = sim.data$w, w.res =  sim.data$w.res, weib.params = calib.weib.params))
px.deriv.scale <- t(sapply(case.times, ICcalib:::CalcWeibullCalibPderivScale, 
w = sim.data$w, w.res = sim.data$ w.res, weib.params = calib.weib.params))
# Point estimate 
est.weib.calib <- optimize(f = ICcalib:::CoxLogLikX,  tm = sim.data$obs.tm, 
                           event = sim.data$delta, ps = px, interval = c(-50,50), 
                           maximum = TRUE)$maximum
# Variance estimate (no addtional covariates)
var.beta.wb <- CalcVarThetaWeib(beta = est.weib.calib, etas = calib.weib.params, 
                                tm = sim.data$obs.tm, event = sim.data$delta, 
                                ps = px, ps.deriv.shape = px.deriv.shape, 
                                ps.deriv.scale =  px.deriv.scale, w = sim.data$w, 
                                w.res = sim.data$w.res)
 print(est.weib.calib)
 print(var.beta.wb)

Calculating the probabilities of positive binary exposure status at a given time point using a Weibull calibration model

Description

For a given time point, calculate the probability of positive exposure value for multiple observations (participants). The function uses the results of a Weibull calibration model fit, and given collected data on the history of the binary exposure for each participant.

Usage

CalcWeibullCalibP(w, w.res, point, weib.params)

Arguments

w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. Each measurement corresponds to the time points in w
point

The time point at which the probabilities are estimated.
weib.params

A bivariate vector. Shape and scale parameters of the Weibull calibration model.

Value

A vector of estimated probabilities of positive exposure status at time point.

See Also

Weibull

Examples

# Simulate data set
sim.data <- ICcalib:::SimCoxIntervalCensSingle(n.sample = 200, lambda = 0.1, 
                                               alpha = 0.25, beta0 = log(0.5), 
                                               mu = 0.2, n.points = 2, 
                                               weib.shape = 1, weib.scale = 2)
# Fit a Weibull calibration model for the covariate starting time distribution
calib.weib.params <- FitCalibWeibull(w = sim.data$w, w.res = sim.data$w.res)
# Calculate the conditional probabilities of binary covariate=1 at time one
probs <- CalcWeibullCalibP(w = sim.data$w, w.res = sim.data$w.res, point = 1,
                           weib.params = calib.weib.params)
summary(probs)

Calculating the probabilities of positive binary exposure status at a given time point using risk-set Weibull calibration models

Description

For a given time point, calculate the probability of positive exposure value for multiple observations (participants). The function uses the results of a Weibull calibration model fit, and given collected data on the history of the binary exposure for each participant.

Usage

CalcWeibullRSP(w, w.res, point, weib.params)

Arguments

w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. Each measurement corresponds to the time points in w
point

The time point at which the probabilities are estimated.
weib.params

A bivariate vector. Shape and scale parameters of the Weibull calibration model.

Details

At its present form this function is identical to CalcWeibullCalibP. This is because the current version of the ICcalib package (Version 1.0.005), the user loop over the main event times. Then, at each event time point, the user should include the appropriate Weibull parameters as estimated by FitCalibWeibullRS.

Value

A vector of estimated probabilities of positive exposure status at time point.

See Also

Weibull

Examples

# Simulate data set
sim.data <- ICcalib:::SimCoxIntervalCensSingle(n.sample = 200, lambda = 0.1, 
                                               alpha = 0.25, beta0 = log(0.5), 
                                               mu = 0.2, n.points = 2, 
                                               weib.shape = 1, weib.scale = 2)
case.times <- sim.data$obs.tm[sim.data$delta==1]
# Fit Weibull risk-set calibration models
calib.weib.params <- FitCalibWeibullRS(w = sim.data$w, w.res = sim.data$w.res, 
                                       tm = sim.data$obs.tm, 
                                       event = sim.data$delta)
# Calculate the conditional probabilities of binary covariate=1 at time one
probs <- CalcWeibullRSP(w = sim.data$w, w.res = sim.data$w.res, point = 1,
                        weib.params = calib.weib.params)
summary(probs)
## Not run: 
if(interactive()){
 #EXAMPLE1
 }

## End(Not run)

Fitting Proportional Hazards Calibration Models with Covariates

Description

Fits a proportional hazards calibration model for time-to-exposure from interval-censored data with covariates. The exposure is a binary covariate measured in intermittent times. The covariates (Q) are associated with the time-to-exposure.

Usage

FitCalibCox(w, w.res, Q, hz.times, n.int = 5, order = 2)

Arguments

w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. It corresponds to the time points in w
Q

Matrix of covariates for PH calibration model
hz.times

Times used for calculating the baseline hazard function from PH calibration model
n.int

The number of interior knots to be used, see ICsurv::fast.PH.ICsurv.EM, Default: 5
order

the order of the basis functions. See ICsurv::fast.PH.ICsurv.EM, Default: 2

Value

An object created by ICsurv::fast.PH.ICsurv.EM, with additional variables knots and order.

See Also

fast.PH.ICsurv.EM

Examples

sim.data <- ICcalib:::SimCoxIntervalCensCox(n.sample = 200, lambda = 0.1, 
                                            alpha = 0.25, beta0 = 0, 
                                            gamma.q = c(log(0.75), log(2.5)), 
                                            gamma.z = log(1.5), mu = 0.2, 
                                            n.points = 2)
# The baseline hazard for the calibration model is calculated in observation times
cox.hz.times <- sort(unique(sim.data$obs.tm)) 
# Fit proprtional hazards calibration model
FitCalibCox(w = sim.data$w, w.res = sim.data$w.res, Q = sim.data$Q, 
            hz.times = cox.hz.times, n.int = 5, order = 2)

Fitting Proportional Hazards Risk-Set Calibration Models with Covariates

Description

FitCalibCoxRS fits proportional hazards risk-set calibration models for time-to-exposure from interval-censored data with covariates. The exposure is a binary covariate measured in intermittent times. The covariates (Q) are associated with the time-to-exposure. This function fits a calibration model at each main event time point, using only members of the risk set at that time point. model is fitted (for all the data) and used for that time point.

FitCalibCoxRSInts fits proportional hazards grouped risk-set calibration models for time-to-exposure from interval-censored data with covariates. The exposure is a binary covariate measured in intermittent times. The covariates (Q) are associated with the time-to-exposure. Unlike FitCalibCoxRS, this function fits a calibration model at each of the given points for pts.for.ints.

Usage

FitCalibCoxRS(w, w.res, Q, hz.times, tm, n.int = 5, order = 2, event)

FitCalibCoxRSInts(w, w.res, Q, hz.times, n.int = 5, order = 2, tm, event,
  pts.for.ints)

Arguments

w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. It corresponds to the time points in w
Q

Matrix of covariates for PH calibration model
hz.times

Times used for calculating the baseline hazard function of a PH calibration model
tm

Vector of observed main event time or censoring time
n.int

The number of interior knots to be used, see ICsurv::fast.PH.ICsurv.EM, Default: 5
order

the order of the basis functions. See ICsurv::fast.PH.ICsurv.EM, Default: 2
event

Vector of censoring indicators. 1 for event 0 for censored
pts.for.ints

Points defining the intervals for grouping risk-sets (first one has to be zero). Should be sorted from zero up. pts.for.ints is used only for FitCalibCoxRSInts.

Details

In case of an error in the model-fitting at a certain time point, a proportional hazards calibration model (for all the data) is fitted and used for that time point.

Value

A list of Cox PH model fits, each supplemented with the knots and order used for the I-splines.

See Also

fast.PH.ICsurv.EM, FitCalibCox

fast.PH.ICsurv.EM, FitCalibCox

Examples

set.seed(2) 
sim.data <- ICcalib:::SimCoxIntervalCensCox(n.sample = 50, lambda = 0.1, 
                                            alpha = 0.25, beta0 = log(0.2),
                                            gamma.q = c(log(0.75), log(2.5)), 
                                            gamma.z = log(1.5), mu = 0.2, 
                                            n.points = 2)
# The baseline hazard for the calibration model is calculated in observation times
cox.hz.times <- sort(unique(sim.data$obs.tm)) 
# Fit proprtional hazards grouped risk-sets calibration models
calib.ph.rs.fit <- FitCalibCoxRSInts(w = sim.data$w, w.res = sim.data$w.res, Q = sim.data$Q, 
                                     hz.times = cox.hz.times, tm = sim.data$obs.tm, 
                                     event = sim.data$delta, pts.for.ints = seq(0, 3, 1.5),
                                     n.int = 5, order = 2)
# Below is a more time consuming option (no grouping of risk-sets)
# FitCalibCoxRS(w = sim.data$w, w.res = sim.data$w.res, Q = sim.data$Q, 
#                hz.times = cox.hz.times, obs.tm = sim.data$obs.tm, 
#               event = sim.data$delta, n.int = 5, order = 1)

Fitting Nonparametric Calibration Models

Description

Fits a Weibull calibration model for time-to-exposure from interval-censored data. The exposure is a binary covariate measured in intermittent times.

Usage

FitCalibNpmle(w, w.res)

Arguments

w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. It corresponds to the time points in w

Value

The result of NPMLE model fitting for interval-censored data, as obtained by icenReg::ic_np

See Also

ic_np

Examples

# Simulate data set
sim.data <- ICcalib:::SimCoxIntervalCensSingle(n.sample = 200, lambda = 0.1, 
                                               alpha = 0.25, beta0 = log(0.5), 
                                               mu = 0.2, n.points = 2, 
                                               weib.shape = 1, weib.scale = 2)
# Calcualte the NPMLE for a nonparametric calibration model for the covariate 
# starting-time distribution
npmle.fit <- ICcalib::FitCalibNpmle(w = sim.data$w, w.res = sim.data$w.res)
# Plot the estimated survival function
plot(npmle.fit)

Fitting Weibull Calibration Models

Description

Fits a Weibull calibration model for time-to-exposure from interval-censored data. The exposure is a binary covariate measured in intermittent times.

Usage

FitCalibWeibull(w, w.res)

Arguments

w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. It corresponds to the time points in w

Value

A bivariate vector: the estimated Weibull shape and scale parameters

See Also

fitdistcens

Examples

# Simulate data set
sim.data <- ICcalib:::SimCoxIntervalCensSingle(n.sample = 200, lambda = 0.1, 
                                               alpha = 0.25, beta0 = log(0.5), 
                                               mu = 0.2, n.points = 2, 
                                               weib.shape = 1, weib.scale = 2)
# Fit a Weibull calibration model for the covariate starting time distribution
ICcalib::FitCalibWeibull(w = sim.data$w, w.res = sim.data$w.res)

Fitting Weibull Risk-Set Calibration Models

Description

Fits Weibull risk-set calibration models for time-to-exposure from interval-censored data. The exposure is a binary covariate measured in intermittent times. This function fits a calibration model at each main event time point, using only members of the risk set at that time point.

Usage

FitCalibWeibullRS(w, w.res, tm, event, lower = 1e-04, upper = 200)

Arguments

w

A matrix of time points when measurements on the binary covariate were obtained.
w.res

A matrix of measurement results of the binary covariate. Each measurement corresponds to the time points in w
tm

Vector of observed main event time or censoring time.
event

Vector of censoring indicators. 1 for event 0 for censored
lower

A value to replace zero in the left point of the interval, Default: 1e-04
upper

A value to replace infinity in the right point of the interval, Default: 200

Details

In case of an error in the model-fitting at a certain time point, a Weibull calibration model is fitted and used for that time point.

Value

A 2-column matrix with the shape and scale parameter for each time-point at which a calibration model was fitted.

See Also

fitdistcens, FitCalibWeibull

Examples

# Simulate data set
sim.data <- ICcalib:::SimCoxIntervalCensSingle(n.sample = 200, lambda = 0.1, 
                                               alpha = 0.25, beta0 = log(0.5), 
                                               mu = 0.2, n.points = 2, 
                                               weib.shape = 1, weib.scale = 2)
# Fit Weibull risk-set calibration models for the conditional covariate 
# starting-time distributions
ICcalib::FitCalibWeibullRS(w = sim.data$w, w.res = sim.data$w.res, 
                           tm = sim.data$obs.tm, event = sim.data$delta)