Construct Case II Interval Censoring Data

Description

This function constructs case II interval-censored data using the provided event times and censoring (survey) times. Each individual's event time is either left-censored, right-censored, or interval-censored based on two survey times: the left and right bounds of the interval.

Usage

case_II_X(event_times, survey_times)

Arguments

Value

A matrix with two columns, where each row represents an individual's interval-censored data. The first column is the left endpoint, and the second column is the right endpoint. If the event time is before the left survey time, the interval is (0, left survey time]. If the event time is after the right survey time, the interval is (right survey time, Inf). If the event time falls between the left and right survey times, the interval is (left survey time, right survey time].

Construct Case I Interval Censoring Data (Current Status Data)

Description

This function constructs case I interval-censored data (current status data) using the provided event times and censoring (survey) times. Each individual's event time is either left-censored or right-censored at their survey time, depending on whether the event has occurred by the survey time.

Usage

current_status_X(event_times, survey_times)

Arguments

Value

A matrix with two columns, where each row represents an individual's interval-censored data. The first column is the left endpoint, and the second column is the right endpoint. If the event time is before the survey time, the interval is (0, survey_time]. If the event time is after the survey time, the interval is (survey_time, Inf).

Prepare Data for Interval-Censored Model

Description

This function processes interval-censored data and prepares various components needed for model fitting, including unique time points, censoring intervals, and weights.

Usage

data_prep(X)

Arguments

Value

A list containing:

tau

Unique time points.

m

The number of unique time points (excluding infinity if present).

L_Rc

Indices of observations where the event is in the intersection of L group and the complement of R group. The L group consists of samples with left intervals time <= min(all right intervals time). The R group consists of samples with infinity right interval time.

Lc_R

Indices of observations where the event is in the intersection of the complement of L group and R group.

Lc_Rc

Indices of observations where the event is in the intersection of the complement of L group and the complement of R group.

ri

Indices corresponding to the right bounds of the intervals in tau.

li

Indices corresponding to the left bounds of the intervals in tau.

tau_no_Inf

Unique time points excluding infinity.

weight

Weights for each unique interval.

X

Processed matrix of interval-censored data with unique rows.

Compute Directional Derivatives for Active Set Algorithm

Description

This function computes the directional derivatives for the active set algorithm used in the estimation of the distribution function under log-concavity with interval-censored data. The calculation takes advantage of the specific structure of the basis matrix, making it efficient to compute in O(n) time complexity.

Usage

find_dir_deriv(diff_tau, first_order)

Arguments

Value

A numeric vector of length length(diff_tau) + 1 representing the directional derivatives for the active set algorithm.

Compute qsi Matrix

Description

This function computes the qsi matrix for specified indices and time points.

Usage

find_qsi(is, tau_no_Inf)

Arguments

Value

qsi matrix.

Generic Function to compute F at X

Description

Computes the value of the function F(x) for a given object of class iclogcondist. This is a generic function to compute F(x) for object class iclogcondist. For usage details, please refer to function get_F_at_x.iclogcondist

Usage

get_F_at_x(object, ...)

Arguments

Value

A numeric vector of values, either F(x) or log(F(x)).

Examples

# Example usage:
data(lgnm)

# Evaluate for LCMLE object
fit_LCMLE <- ic_LCMLE(lgnm)
get_F_at_x(fit_LCMLE)

# Evaluate for UMLE object
fit_UMLE <- ic_UMLE(lgnm)
x = seq(0.001, 6, length.out = 1000)
get_F_at_x(fit_UMLE, x = x)

Evaluate F(x) for Objects of Class 'iclogcondist'

Description

Computes the value of the function F(x) for a given object of class iclogcondist.

Usage

## S3 method for class 'iclogcondist'
get_F_at_x(object, x = NA, log = FALSE, ...)

Arguments

Value

A numeric vector of values, either F(x) or log(F(x)).

Examples

# Example usage:
data(lgnm)

# Evaluate for LCMLE object
fit_LCMLE <- ic_LCMLE(lgnm)
get_F_at_x(fit_LCMLE)

# Evaluate for UMLE object
fit_UMLE <- ic_UMLE(lgnm)
x = seq(0.001, 6, length.out = 1000)
get_F_at_x(fit_UMLE, x = x)

Compute the log-concave MLE for Interval-censored Data using an Active Set Algorithm

Description

This function computes the log-concave MLE of the cumulative distribution function for interval-censored data under log-concavity on the underlying distribution function based on an active set algorithm. The active set algorithm adjusts the knots set based on certain directional derivatives.

Usage

ic_LCMLE(
  X,
  initial = "LCM",
  print = FALSE,
  max_iter = 500,
  tol_conv = 1e-07,
  tol_conv_like = 1e-10,
  tol_K = 1e-05
)

Arguments

Value

A list with the following components:

Examples

# Example usage:
data(lgnm)
result <- ic_LCMLE(X = lgnm, initial = "LCM", print = TRUE, max_iter = 500)
print(result$est)

Compute Least Concave Majorant (LCM) of the log of the Unconstrained MLE for Interval-Censored Data

Description

This function computes the Least Concave Majorant (LCM) of the log of the unconstrained MLE for interval-censored data.

Usage

ic_LCM_UMLE(X)

Arguments

Value

A list containing:

Examples

data(lgnm)
result <- ic_LCM_UMLE(X = lgnm)

Compute Unconstrained Maximum Likelihood Estimate for Interval-Censored Data

Description

This function computes the unconstrained maximum likelihood estimate (UMLE) for interval-censored data. It utilizes the non-parametric MLE from the ic_np function in the icenReg package as a starting point and prepares key components such as cumulative probabilities, log-transformed values, and knot information.

Usage

ic_UMLE(X)

Arguments

Details

The ic_np function from the icenReg package is used to compute the non-parametric MLE for interval-censored data. This provides initial estimates of probabilities (p_hat) and jump points (knot) in the cumulative distribution function. These are then processed to compute the cumulative probabilities (F_hat) and log-transformed values (phi_hat) at unique time points.

Value

A list containing:

References

Anderson-Bergman, C. (2016) An efficient implementation of the EMICM algorithm for the interval censored NPMLE Journal of Computational and Graphical Statistics.

Examples

data(lgnm)
result <- ic_UMLE(X = lgnm)

Visualize the Estimated Cumulative Distribution Functions

Description

This function visualizes a user-specified distribution true_dist (if available) and the estimated cumulative distribution functions (CDF) F(t) and log F(t) for a given range. The function overlays the estimated functions from a list of fitted models on the same plot, allowing comparison with the user-specified distribution (if provided). In a simulation study, the user-specified distribution can correspond to the true underlying distribution.

Usage

iclogcondist_visualization(X, range = NA, fit_list = list(), true_dist = NA)

Arguments

Value

A list containing two ggplot objects: logF_plot for log F(t) and F_plot for F(t).

Examples

# Example usage
data(lgnm)
fit_LCMLE <- ic_LCMLE(lgnm)
fit_UMLE <- ic_UMLE(lgnm)
iclogcondist_visualization(
  X = lgnm,
  range = c(0, 10),
  fit_list = list(
    "UMLE" = fit_UMLE,
    "LCMLE" = fit_LCMLE
  )
)

Iterative Convex Minorant (ICM) Subset Algorithm

Description

This function implements the ICM algorithm for solving the sub-problem in the active set algorithm. This is a support of the active set algorithm, computing the optimal values phi_tilde with reduced number of knots in the sub-problem. It uses backtracking to ensure convergence (Jongbloed, 1998).

Usage

icm_subset_cpp(
  phi_tilde_initial,
  is,
  tau_no_Inf,
  L_Rc,
  Lc_R,
  Lc_Rc,
  ri,
  li,
  weight,
  tol = 1e-10,
  max_iter = 500
)

Arguments

Value

A list containing:

phi_tilde_hat

The estimated values of the reduced variable phi_tilde at the end of the ICM iterations.

References

Jongbloed, G.: The iterative convex minorant algorithm for nonparametric estimation. J. Comput. Gr. Stat. 7(3), 310–321 (1998)

Initial Values for Estimation under Log-concavity with Interval-Censored Data

Description

This function obtains initial values for the maximum likelihood estimation under log-concavity with interval-censored data based on the unconstrained maximum likelihood estimate (MLE) or its least concave majorant (LCM). Alternatively, the user can provide a numeric vector of initial values.

Usage

initial_values(X, initial = "LCM")

Arguments

Value

A list containing:

phi_hat

The initial values of the phi parameter based on the specified method.

phi_hat_MLE

Initial values based on the unconstrained MLE.

phi_hat_LCM

Initial values based on the least concave majorant.

LGNM Data: Case II Interval Censoring Example

Description

This dataset, lgnm, provides an example of case II interval censoring data for illustrating the functions in this package. The event time is simulated from a log-normal distribution with parameters mean = 0 and standard deviation = 1. The left censoring time is drawn from a uniform distribution between 0 and 2, and the right censoring time is drawn from a uniform distribution between the left censoring time and 20. Both the left and right censoring times are rounded to four decimal places.

Format

A data frame with 100 observations on the following 2 variables:

left

The left censoring time.

right

The right censoring time.

Source

Synthetic data generated for illustration purposes.

Examples

data(lgnm)
head(lgnm)

Compute the Negative Log-Likelihood for the Interval-Censored Model

Description

This function computes the negative log-likelihood of an interval-censored model based on the specified parameterization.

Usage

neg_log_like(x, weight, li, ri, L_Rc, Lc_R, Lc_Rc, type = "", tau_no_Inf)

Arguments

Value

The negative log-likelihood value.

Plot Method for iclogcondist_plot Objects

Description

This function generates a plot for objects of class iclogcondist, which are typically generated by ic_UMLE, ic_LCM_UMLE, or ic_LCMLE. The plot can display either the cumulative distribution function F(t) or the log cumulative distribution function logF(t), depending on the setting of the log parameter.

Usage

## S3 method for class 'iclogcondist'
plot(x, log = FALSE, ...)

Arguments

Value

An invisible ggplot object representing the plot. The plot is also displayed in the current graphics device.

Examples

# Example usage with ic_UMLE, ic_LCM_UMLE, and ic_LCMLE
data(lgnm)
X <- lgnm
fit_UMLE <- ic_UMLE(X)
fit_LCM_UMLE <- ic_LCM_UMLE(X)
fit_LCMLE <- ic_LCMLE(X)
plot(fit_UMLE, log = TRUE)   # Plot logF(t) for UMLE
plot(fit_LCM_UMLE, log = FALSE)  # Plot F(t) for LCM_UMLE
plot(fit_LCMLE, log = FALSE) # Plot F(t) for LCMLE

Cumulative Distribution Function of a Truncated Log-Logistic Distribution

Description

This function computes the cumulative distribution function (CDF) of a truncated log-logistic distribution at a given point x.

Usage

ptllogis(x, shape = 1, scale = 1, upper_bound = Inf)

Arguments

Value

A numeric vector of the CDF values of the truncated log-logistic distribution at x.

Examples

# Evaluate the CDF at x = 2 for a truncated log-logistic distribution
ptllogis(2, shape = 2, scale = 1, upper_bound = 5)

Cumulative Distribution Function of a Truncated Log-Normal Distribution

Description

This function computes the cumulative distribution function (CDF) of a truncated log-normal distribution at a given point x.

Usage

ptlnorm(x, meanlog = 0, sdlog = 1, upper_bound = Inf)

Arguments

Value

A numeric vector of the CDF values of the truncated log-normal distribution at x.

Examples

# Evaluate the CDF at x = 2 for a truncated log-normal distribution
ptlnorm(2, meanlog = 0, sdlog = 1, upper_bound = 5)

Cumulative Distribution Function of a Truncated Weibull Distribution

Description

This function computes the cumulative distribution function (CDF) of a truncated Weibull distribution at a given point x.

Usage

ptweibull(x, shape = 1, scale = 1, upper_bound = Inf)

Arguments

Value

A numeric vector of the CDF values of the truncated Weibull distribution at x.

Examples

# Evaluate the CDF at x = 2 for a truncated Weibull distribution
ptweibull(2, shape = 2, scale = 1, upper_bound = 5)

Quantile Function of a Truncated Log-Logistic Distribution

Description

This function computes the quantiles of a truncated log-logistic distribution for a given probability vector.

Usage

qtllogis(q, shape = 1, scale = 1, upper_bound = Inf)

Arguments

Value

A numeric vector of quantiles corresponding to the given probabilities in q.

Examples

# Calculate the 0.5 quantile of a truncated log-logistic distribution
qtllogis(0.5, shape = 2, scale = 1, upper_bound = 5)

Quantile Function of a Truncated Log-Normal Distribution

Description

This function computes the quantiles of a truncated log-normal distribution for a given probability vector.

Usage

qtlnorm(q, meanlog = 0, sdlog = 1, upper_bound = Inf)

Arguments

Value

A numeric vector of quantiles corresponding to the given probabilities in q.

Examples

# Calculate the 0.5 quantile of a truncated log-normal distribution
qtlnorm(0.5, meanlog = 0, sdlog = 1, upper_bound = 5)

Quantile Function of a Truncated Weibull Distribution

Description

This function computes the quantiles of a truncated Weibull distribution for a given probability vector.

Usage

qtweibull(q, shape = 1, scale = 1, upper_bound = Inf)

Arguments

Value

A numeric vector of quantiles corresponding to the given probabilities in q.

Examples

# Calculate the 0.5 quantile of a truncated Weibull distribution
qtweibull(0.5, shape = 2, scale = 1, upper_bound = 5)

Simulate from a Truncated Log-Logistic Distribution

Description

This function generates random samples from a truncated log-logistic distribution using an acceptance-rejection method.

Usage

rtllogis(n, shape = 1, scale = 1, upper_bound = Inf)

Arguments

Value

A numeric vector of n random samples from the truncated log-logistic distribution.

Examples

# Generate 10 random samples from a truncated log-logistic distribution
rtllogis(10, shape = 2, scale = 1, upper_bound = 5)

Simulate from a Truncated Log-Normal Distribution

Description

This function generates random samples from a truncated log-normal distribution using an acceptance-rejection method.

Usage

rtlnorm(n, meanlog = 0, sdlog = 1, upper_bound = Inf)

Arguments

Value

A numeric vector of n random samples from the truncated log-normal distribution.

Examples

# Generate 10 random samples from a truncated log-normal distribution
rtlnorm(10, meanlog = 0, sdlog = 1, upper_bound = 5)

Simulate from a Truncated Weibull Distribution

Description

This function generates random samples from a truncated Weibull distribution using inverse transform sampling. When shape = 1, it reduces to a truncated exponential distribution.

Usage

rtweibull(n, shape = 1, scale = 1, upper_bound = Inf)

Arguments

Value

A numeric vector of n random samples from the truncated Weibull distribution.

Examples

# Generate 10 random samples from a truncated Weibull distribution
rtweibull(10, shape = 2, scale = 1, upper_bound = 5)

Simulate Interval-Censored Data

Description

This function generates interval-censored data, where the event times are generated from one of the following distributions: Weibull, log-normal and log-logistic. It supports both case 1 and case 2 interval censoring.

Usage

simulate_ic_data(
  n,
  dist,
  para1,
  para2,
  upper_bound = Inf,
  C1_upper = 1,
  case = 2,
  rounding = FALSE,
  round_digit = 4
)

Arguments

Details

• **Censoring Times**:

  • In case = 1 (current status), one censoring time is generated, where it follows U(0, C1_upper).

  • In case = 2 (case 2 interval censoring), two censoring times are generated:

    • C1: sampled from U(0, C1_upper).

    • C2: sampled from U(C1, min(upper_bound, 20)).

• **Distributions**:

  • **Weibull**: Parameterized by shape (para1) and scale (para2).

  • **Log-logistic**: Parameterized by shape (para1) and scale (para2).

  • **Log-normal**: Parameterized by mean (para1) and standard deviation (para2).

Value

A matrix of interval-censored data where each row represents an interval (L, R] containing the unobserved event time.

Examples

# Simulate data with a truncated Weibull distribution and case II interval censoring
simulate_ic_data(n = 100, dist = "weibull", para1 = 2, para2 = 1, upper_bound = 5, case = 2)

Find Unique Rows in a Matrix and Their Weights

Description

This function finds the unique rows of a given matrix and calculates the frequency (weight) of each unique row. It returns both the unique rows and the weights (the number of occurrences of each row).

Usage

unique_X_weight(X)

Arguments

Value

A list containing two components:

unique_X

A matrix of the unique rows from the input matrix.

weight

An integer vector containing the frequency (weight) of each unique row.