Package 'UniCensorEM'

Title: EM Algorithm for Parameter Estimation Under Censoring Schemes
Description: Performs parameter estimation using the Expectation-Maximization (EM) algorithm of Dempster, Laird, and Rubin (1977) <doi:10.1111/j.2517-6161.1977.tb01600.x> for arbitrary univariate probability distributions under numerous censoring and truncation schemes. Users supply the probability density function (PDF), cumulative distribution function (CDF), survival function, initial parameter vector, support bounds, and observed data; the package automatically estimates parameters using the EM algorithm under the specified censoring scheme. Supported schemes include complete data, right censoring, left censoring, interval censoring, random censoring, block random censoring, Type-I censoring, Type-II censoring, progressive Type-II censoring (Balakrishnan and Aggarwala (2000, ISBN:978-1-4612-1334-5)), progressive first failure censoring, joint Type-I censoring, joint Type-II censoring, balanced joint progressive Type-II censoring, hybrid censoring, hybrid Type-I censoring, hybrid Type-II censoring, Type-I hybrid censoring, Type-II progressively hybrid censoring, doubly Type-II censoring, middle censoring, right truncation, and left truncation. Standard errors are computed via the observed information matrix (numerical Hessian), the Louis (1982) <doi:10.1111/j.2517-6161.1982.tb01203.x> method, and the supplemented EM (SEM) algorithm of Meng and Rubin (1991) <doi:10.1080/01621459.1991.10475130>. The package also provides confidence intervals, model selection criteria (AIC, BIC, AICc, HQIC), goodness-of-fit statistics (Kolmogorov-Smirnov, Cramer-von Mises, Anderson-Darling), residual analysis (randomized quantile residuals, generalized residuals), parametric bootstrap methods, Aitken acceleration for convergence improvement, and comprehensive visualization tools. References: Wu and Kus (2009) <doi:10.1016/j.csda.2009.03.010>, Kundu and Joarder (2006) <doi:10.1016/j.csda.2005.05.002>, Iyer, Jammalamadaka, and Kundu (2008) <doi:10.1016/j.jspi.2007.03.062>, Banerjee and Kundu (2008) <doi:10.1109/TR.2008.916890>, Prajapati, Mitra, and Kundu (2019) <doi:10.1007/s13571-018-0167-0>, Mondal and Kundu (2020) <doi:10.1080/03610926.2018.1554128>, Ding and Gui (2023) <doi:10.3390/math11092003>.
Authors: Shikhar Tyagi [aut, cre] (ORCID: <https://orcid.org/0000-0003-1606-0844>), Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer: Shikhar Tyagi <[email protected]>
License: GPL-3
Version: 0.1.0
Built: 2026-09-27 09:36:42 UTC
Source: https://github.com/cran/UniCensorEM

Help Index

AIC method for emfit objects

Description

Compute Akaike Information Criterion.

Usage

## S3 method for class 'emfit'
AIC(object, ...)

Arguments

object

an emfit object.
...

additional arguments (ignored).

Value

AIC value.

BIC method for emfit objects

Description

Compute Bayesian Information Criterion.

Usage

## S3 method for class 'emfit'
BIC(object, ...)

Arguments

object

an emfit object.
...

additional arguments (ignored).

Value

BIC value.

Bootstrap standard errors for emfit objects

Description

Compute bootstrap standard errors and confidence intervals.

Usage

bootstrap_se(
  object,
  B = 1000,
  type = "parametric",
  ci_type = "percentile",
  level = 0.95,
  parallel = FALSE,
  ...
)

Arguments

object

an emfit object.
B

number of bootstrap replicates (default 1000).
type

bootstrap type: "parametric" or "nonparametric" (default "parametric").
ci_type

confidence interval type: "normal", "percentile", "bca", or "basic" (default "percentile").
level

confidence level (default 0.95).
parallel

logical; use parallel computing (default FALSE).
...

additional arguments.

Value

List containing bootstrap estimates, standard errors, and confidence intervals.

Coefficient method for emfit objects

Description

Extract parameter estimates.

Usage

## S3 method for class 'emfit'
coef(object, ...)

Arguments

object

an emfit object.
...

additional arguments (ignored).

Value

Named vector of parameter estimates.

Compute standard errors for EM estimates

Description

Compute standard errors for EM estimates

Usage

compute_se(
  theta_star,
  x,
  pdf,
  cdf,
  survival,
  scheme,
  status,
  time2,
  censor_params,
  lower,
  upper,
  method = "hessian",
  em_control = em.control()
)

Arguments

theta_star

converged parameter estimates.
x

observed data.
pdf

probability density function.
cdf

cumulative distribution function.
survival

survival function.
scheme

censoring scheme name.
status

censoring status vector.
time2

upper interval bounds.
censor_params

additional censoring parameters.
lower

lower support bound.
upper

upper support bound.
method

standard error estimation method: "hessian", "louis", or "sem".
em_control

control parameters for EM algorithm.

Value

A list containing:

hessian

the estimated observed information matrix
vcov

the variance-covariance matrix
se

the standard errors

Confidence interval method for emfit objects

Description

Compute confidence intervals for parameter estimates.

Usage

## S3 method for class 'emfit'
confint(object, parm = NULL, level = 0.95, ...)

Arguments

object

an emfit object.
parm

parameter indices (default: all parameters).
level

confidence level (default 0.95).
...

additional arguments (ignored).

Value

Matrix of confidence intervals.

Define a univariate distribution for EM estimation

Description

Creates a reusable distribution specification for EM parameter estimation. At minimum, the PDF must be supplied. CDF and survival functions are required for most censoring schemes.

Usage

dist_spec_em(
  pdf = NULL,
  cdf = NULL,
  survival = NULL,
  lower = 0,
  upper = Inf,
  name = "custom"
)

Arguments

pdf

function; probability density function f(x, theta).
cdf

function; cumulative distribution function F(x, theta).
survival

function; survival function S(x, theta) = 1 - F(x, theta).
lower

numeric; lower support bound (default 0).
upper

numeric; upper support bound (default Inf).
name

character label for output (default "custom").

Value

An object of class "dist_spec_em", which is a list with elements pdf, cdf, survival (user-supplied functions or NULL), lower and upper (support bounds), and name (character label).

Examples

# Exponential(rate) distribution
exp_dist <- dist_spec_em(
  pdf = function(x, theta) theta[1] * exp(-theta[1] * x),
  cdf = function(x, theta) 1 - exp(-theta[1] * x),
  survival = function(x, theta) exp(-theta[1] * x),
  lower = 0, upper = Inf,
  name = "Exponential"
)

EM diagnostics

Description

Compute diagnostic information for EM algorithm convergence.

Usage

em_diagnostics(object, ...)

Arguments

object

an emfit object.
...

additional arguments (ignored).

Value

List of diagnostic measures.

Main EM algorithm for parameter estimation under censoring

Description

Performs parameter estimation using the EM algorithm for arbitrary univariate distributions under specified censoring schemes.

Usage

em_fit(
  data,
  pdf,
  cdf = NULL,
  survival = NULL,
  theta0,
  scheme = "complete",
  status = NULL,
  time2 = NULL,
  censor_params = list(),
  lower = 0,
  upper = Inf,
  control = em.control()
)

Arguments

data

observed data vector or data frame with columns x and status.
pdf

probability density function f(x, theta).
cdf

cumulative distribution function F(x, theta).
survival

survival function S(x, theta) = 1 - F(x, theta).
theta0

initial parameter vector.
scheme

censoring scheme name (see details).
status

censoring status vector (optional, extracted from data if data frame).
time2

upper interval bounds for interval censoring (optional).
censor_params

list of additional censoring scheme parameters.
lower

lower support bound (default 0).
upper

upper support bound (default Inf).
control

list of control parameters from em.control().

Value

An object of class "emfit" containing:

par

parameter estimates
value

final log-likelihood
counts

number of iterations
convergence

convergence status (0 = success)
message

convergence message
hessian

observed information matrix
std.error

standard errors
par_path

parameter values at each iteration
lik_path

log-likelihood values at each iteration
q_path

Q-function values at each iteration
time

elapsed time in seconds
scheme

censoring scheme used
data

input data
control

control parameters

Supported censoring schemes

"complete"

Complete (uncensored) data

"right_censor"

Right censoring

"left_censor"

Left censoring

"interval_censor"

Interval censoring

"random_censor"

Random censoring

"block_random_censor"

Block random censoring

"type1_censor"

Type-I (time-terminated) censoring

"type2_censor"

Type-II (failure-terminated) censoring

"progressive_type2_censor"

Progressive Type-II censoring

"progressive_first_failure"

Progressive first failure censoring

"joint_type1_censor"

Joint Type-I censoring

"joint_type2_censor"

Joint Type-II censoring

"bjpt2_censor"

Balanced joint progressive Type-II censoring

"hybrid_censor"

Hybrid censoring

"hybrid_type1_censor"

Hybrid Type-I censoring

"hybrid_type2_censor"

Hybrid Type-II censoring

"type1_hybrid_censor"

Type-I hybrid censoring

"progressive_hybrid_type2_censor"

Type-II progressively hybrid censoring

"doubly_type2_censor"

Doubly Type-II censoring

"middle_censor"

Middle censoring

"right_truncation"

Right truncation

"left_truncation"

Left truncation

Examples

set.seed(123)
pdf <- function(x, theta) theta[1] * exp(-theta[1] * x)
cdf <- function(x, theta) 1 - exp(-theta[1] * x)
survival <- function(x, theta) exp(-theta[1] * x)

# Generate right-censored data
x_true <- rexp(50, rate = 1.5)
cens <- 1.0
status <- ifelse(x_true <= cens, 1, 0)
x_obs <- pmin(x_true, cens)

# Fit using EM
fit <- em_fit(
  data = x_obs,
  pdf = pdf,
  cdf = cdf,
  survival = survival,
  theta0 = c(1.0),
  scheme = "right_censor",
  status = status,
  lower = 0.001, upper = 100,
  control = em.control(maxit = 500, tol = 1e-6)
)

summary(fit)

Control parameters for EM algorithm

Description

Sets control parameters for the EM algorithm optimization.

Usage

em.control(
  maxit = 1000,
  tol = 1e-08,
  reltol = 1e-08,
  emtol = 1e-10,
  method = "BFGS",
  se_method = "hessian",
  trace = FALSE,
  aitken = FALSE,
  verbose = FALSE
)

Arguments

maxit

maximum number of EM iterations (default 1000).
tol

convergence tolerance for parameter changes (default 1e-8).
reltol

relative convergence tolerance (default 1e-8).
emtol

tolerance for Q-function convergence (default 1e-10).
method

optimization method for M-step: "BFGS", "L-BFGS-B", "Nelder-Mead", "CG", "SANN", "Brent", or "nlminb" (default "BFGS").
se_method

standard error estimation method: "hessian", "louis", or "sem" (default "hessian").
trace

logical; print iteration progress (default FALSE).
aitken

logical; use Aitken acceleration (default FALSE).
verbose

logical; detailed output (default FALSE).

Value

A list of control parameters.

Examples

ctrl <- em.control(maxit = 500, tol = 1e-6, method = "BFGS")

Fitted values method for emfit objects

Description

Extract fitted values (estimated survival probabilities at observed times).

Usage

## S3 method for class 'emfit'
fitted(object, ...)

Arguments

object

an emfit object.
...

additional arguments (ignored).

Value

Vector of fitted survival probabilities.

Generalized residuals

Description

Compute generalized residuals for censored survival data.

Usage

generalized_residuals(object, ...)

Arguments

object

an emfit object.
...

additional arguments.

Value

Vector of generalized residuals.

Get number of cores

Description

Get number of cores

Usage

get_ncores()

Value

Number of available cores.

Goodness-of-fit statistics

Description

Compute various goodness-of-fit statistics for the fitted model.

Usage

gof_stats(object, ...)

Arguments

object

an emfit object.
...

additional arguments (ignored).

Value

Named vector of goodness-of-fit statistics.

Log-likelihood method for emfit objects

Description

Extract the log-likelihood value.

Usage

## S3 method for class 'emfit'
logLik(object, ...)

Arguments

object

an emfit object.
...

additional arguments (ignored).

Value

Log-likelihood value.

Model selection criteria for emfit objects

Description

Compute various information criteria for model selection.

Usage

model_selection(object, ...)

Arguments

object

an emfit object.
...

additional arguments (ignored).

Value

Named vector of information criteria.

Compute observed log-likelihood

Description

Computes the log-likelihood of the observed data under the specified censoring scheme.

Usage

observed_loglik(
  data,
  pdf,
  cdf,
  survival,
  theta,
  scheme,
  status = NULL,
  time2 = NULL,
  censor_params = list(),
  lower = 0,
  upper = Inf
)

Arguments

data

observed data vector.
pdf

probability density function.
cdf

cumulative distribution function.
survival

survival function.
theta

parameter vector.
scheme

censoring scheme name.
status

censoring status vector (optional).
time2

upper interval bounds (optional for interval censoring).
censor_params

additional censoring scheme parameters (list).
lower

lower support bound.
upper

upper support bound.

Value

Log-likelihood value.

Residual diagnostics plot

Description

Create diagnostic plots for residuals.

Usage

plot_residuals(object, type = "cox-snell", which = c(1, 2, 3), ...)

Arguments

object

an emfit object.
type

type of residuals (default "cox-snell").
which

which plots: 1 = histogram, 2 = QQ plot, 3 = residuals vs fitted, 4 = residuals vs order (default: c(1, 2, 3)).
...

additional graphical parameters.

Value

Invisibly, the emfit object.

Plot method for emfit objects

Description

Create diagnostic plots for EM algorithm fit.

Usage

## S3 method for class 'emfit'
plot(x, which = c(1, 2, 3), ask = TRUE, ...)

Arguments

x

an emfit object.
which

which plots to display: 1 = parameter convergence, 2 = log-likelihood convergence, 3 = Q-function, 4 = histogram with fitted density, 5 = QQ plot, 6 = residual plot (default: c(1, 2, 3)).
ask

logical; pause between plots (default: TRUE).
...

additional graphical parameters.

Value

Invisibly, the emfit object.

Predict method for emfit objects

Description

Predict survival probabilities or quantiles for new data.

Usage

## S3 method for class 'emfit'
predict(object, newdata = NULL, type = "survival", ...)

Arguments

object

an emfit object.
newdata

new data values.
type

type of prediction: "survival", "cdf", or "quantile" (default "survival").
...

additional arguments.

Value

Predicted values.

Print method for bootstrap_emfit objects

Description

Print method for bootstrap_emfit objects

Usage

## S3 method for class 'bootstrap_emfit'
print(x, ...)

Arguments

x

a bootstrap_emfit object.
...

additional arguments (ignored).

Value

Invisibly, the bootstrap_emfit object.

Print method for dist_spec_em

Description

Print method for dist_spec_em

Usage

## S3 method for class 'dist_spec_em'
print(x, ...)

Arguments

x

a dist_spec_em object.
...

ignored.

Value

Invisibly, the input dist_spec_em object.

Print method for em_diagnostics objects

Description

Print method for em_diagnostics objects

Usage

## S3 method for class 'em_diagnostics'
print(x, ...)

Arguments

x

an em_diagnostics object.
...

additional arguments (ignored).

Value

Invisibly, the em_diagnostics object.

Print method for emfit objects

Description

Print method for emfit objects

Usage

## S3 method for class 'emfit'
print(x, ...)

Arguments

x

an emfit object.
...

additional arguments (ignored).

Value

Invisibly, the emfit object.

Print method for summary.emfit objects

Description

Print method for summary.emfit objects

Usage

## S3 method for class 'summary.emfit'
print(x, ...)

Arguments

x

a summary.emfit object.
...

additional arguments (ignored).

Value

Invisibly, the summary.emfit object.

Compute Q-function

Description

Computes the Q-function (expected complete log-likelihood) for the EM algorithm.

Usage

q_function(
  theta,
  theta_old,
  data,
  pdf,
  cdf,
  survival,
  scheme,
  status = NULL,
  time2 = NULL,
  censor_params = list(),
  lower = 0,
  upper = Inf
)

Arguments

theta

parameter vector to maximize over.
theta_old

current parameter estimates.
data

observed data.
pdf

probability density function.
cdf

cumulative distribution function.
survival

survival function.
scheme

censoring scheme name.
status

censoring status vector.
time2

upper interval bounds.
censor_params

additional censoring parameters.
lower

lower support bound.
upper

upper support bound.

Value

Q-function value.

Randomized quantile residuals

Description

Compute randomized quantile residuals for censored data.

Usage

randomized_quantile_residuals(object, n_sim = 1, ...)

Arguments

object

an emfit object.
n_sim

number of simulations for randomization (default 1).
...

additional arguments.

Value

Vector of randomized quantile residuals.

Comprehensive residual analysis for emfit objects

Description

Compute various types of residuals for diagnostic purposes.

Usage

residual_analysis(object, type = "cox-snell", ...)

Arguments

object

an emfit object.
type

type of residuals: "cox-snell", "martingale", "deviance", "pearson", "score", or "schoenfeld" (default "cox-snell").
...

additional arguments.

Value

Vector of residuals.

Residuals method for emfit objects

Description

Compute residuals from the fitted model.

Usage

## S3 method for class 'emfit'
residuals(object, type = "cox-snell", ...)

Arguments

object

an emfit object.
type

type of residuals: "cox-snell", "martingale", "deviance", "pearson", or "response" (default "cox-snell").
...

additional arguments.

Value

Vector of residuals.

Summary method for emfit objects

Description

Summary method for emfit objects

Usage

## S3 method for class 'emfit'
summary(object, ...)

Arguments

object

an emfit object.
...

additional arguments (ignored).

Value

A list with summary information.

Variance-covariance matrix method for emfit objects

Description

Extract the variance-covariance matrix of parameter estimates.

Usage

## S3 method for class 'emfit'
vcov(object, ...)

Arguments

object

an emfit object.
...

additional arguments (ignored).

Value

Variance-covariance matrix.