Package 'WAreg' reference manual

Title:	While-Alive Regression for Composite Endpoints with CRT-Robust Inference
Description:	Implements while-alive regression for composite endpoints with recurrent and terminal events. Supports flexible time bases (B-spline, natural spline, M-spline, piecewise polynomial, interval-local, etc.), cluster-robust inference for cluster randomized trials, prediction, plotting, and K-fold cross-validation.
Authors:	Xi Fang [aut, cre], Hajime Uno [aut], Fan Li [aut]
Maintainer:	Xi Fang <[email protected]>
License:	GPL-3
Version:	0.1.0
Built:	2026-05-12 09:12:37 UTC
Source:	https://github.com/fancy575/wareg

Clustered Recurrent-Time Dataset: crt_dt

Description

A simulated dataset of clustered recurrent events with terminal/censoring outcomes and covariates, suitable for examples and tests.

Usage

data(crt_dt)
data(crt_dt)

Format

A data frame with the following columns:

id: Integer subject ID (within the whole sample).
cluster: Integer cluster ID.
time: Numeric event/censoring time.
status: Integer event type indicator: 0 = censored, 1 = recurrent type 1, 2 = recurrent type 2, 3 = death (terminal).
trt: Cluster-level treatment indicator carried to subjects (e.g., 0/1).
Z1: Numeric covariate.
Z2: Numeric covariate.

Details

Rows represent observed events (including censoring and death) for each subject. Multiple rows per id indicate multiple recurrent events; terminal/censoring rows mark the end of observation for that subject.

Source

Generated by the package's simulation utilities.

Examples

data(crt_dt)
head(crt_dt)
data(crt_dt)
head(crt_dt)

Individual Recurrent-Time Dataset: irt_dt

Description

A simulated dataset of recurrent events with terminal/censoring outcomes and covariates, organized in long format.

Usage

data(irt_dt)
data(irt_dt)

Format

A data frame with the following columns:

id: Integer subject ID (within the whole sample).
cluster: Integer cluster ID.
time: Numeric event/censoring time.
status: Integer event type indicator: 0 = censored, 1 = recurrent type 1, 2 = recurrent type 2, 3 = death (terminal).
trt: Cluster-level treatment indicator carried to subjects (e.g., 0/1).
Z1: Numeric covariate.
Z2: Numeric covariate.

Details

Long-format events: each row is an event (or censoring/death) for a subject.

Source

Generated by the package's simulation utilities.

Examples

data(irt_dt)
head(irt_dt)
data(irt_dt)
head(irt_dt)

Plot while-alive trajectory or a covariate's time-varying effect

Description

Plot while-alive trajectory or a covariate's time-varying effect

Usage

## S3 method for class 'WA'
plot(
  x,
  newdata,
  t_seq,
  id = 1,
  mode = c("wa", "cov"),
  covariate = NULL,
  ylab_wa = "While-alive loss rate",
  ylab_cov = NULL,
  xlab = "Time",
  level = 0.95,
  smooth = FALSE,
  span = 0.3,
  ...
)
## S3 method for class 'WA'
plot(
  x,
  newdata,
  t_seq,
  id = 1,
  mode = c("wa", "cov"),
  covariate = NULL,
  ylab_wa = "While-alive loss rate",
  ylab_cov = NULL,
  xlab = "Time",
  level = 0.95,
  smooth = FALSE,
  span = 0.3,
  ...
)

Arguments

x

A "WA" object.

newdata

Data used to rebuild the RHS design (same columns as in the model).

t_seq

Times to plot over (numeric vector).

id

Row index of newdata to use for the while-alive trajectory (mode = "wa").

mode

"wa" to plot the while-alive loss rate, or "cov" to plot a specific covariate's time-varying effect.

covariate

Character; covariate name (must appear on RHS) when mode="cov".

ylab_wa

Y-axis label for while-alive plot.

ylab_cov

Y-axis label for covariate-effect plot; default "Effect of <covariate> on \u03B7(t)".

xlab

X-axis label.

level

Confidence level for ribbons (default 0.95).

smooth

Logical; if TRUE, apply LOESS smoothing to the displayed curve/CI.

span

LOESS span used when smooth=TRUE.

...

Unused.

Value

A ggplot2 object.

Examples

## Not run: 
plot.WA(fit, newdata = crt_dt,
        t_seq = seq(0, max(fit$tau_grid), length.out = 200),
        id = 1, mode = "wa", smooth = TRUE)

plot.WA(fit, newdata = crt_dt,
        t_seq = seq(0, max(fit$tau_grid), length.out = 200),
        id = 1, mode = "cov", covariate = "numchron",
        ylab_cov = "Effect of numchron on linear predictor",
        smooth = TRUE)

## End(Not run)
## Not run: 
plot.WA(fit, newdata = crt_dt,
        t_seq = seq(0, max(fit$tau_grid), length.out = 200),
        id = 1, mode = "wa", smooth = TRUE)

plot.WA(fit, newdata = crt_dt,
        t_seq = seq(0, max(fit$tau_grid), length.out = 200),
        id = 1, mode = "cov", covariate = "numchron",
        ylab_cov = "Effect of numchron on linear predictor",
        smooth = TRUE)

## End(Not run)

Predict while-alive loss rates

Description

Predict while-alive loss rates

Usage

## S3 method for class 'WA'
predict(object, newdata, t_seq, level = 0.95, ...)
## S3 method for class 'WA'
predict(object, newdata, t_seq, level = 0.95, ...)

Arguments

object

A "WA" object.

newdata

Data frame with columns matching the RHS of the fitted model. Predictions are computed for the rows of newdata.

t_seq

Numeric vector of times at which to evaluate predictions.

level

Confidence level for pointwise intervals (default 0.95).

...

Unused.

Value

A data frame with columns id (row index in newdata), t, mu (predicted while-alive rate), and CI columns lb, ub.

Examples

## Not run: 
newdata_ex <- crt_dt |>
  dplyr::select(intv, demo_sex_male, numchron) |>
  dplyr::distinct() |>
  dplyr::slice(1:2)
pred <- predict.WA(fit, newdata = newdata_ex, t_seq = seq(0, 3.5, by = 0.05))
head(pred)

## End(Not run)
## Not run: 
newdata_ex <- crt_dt |>
  dplyr::select(intv, demo_sex_male, numchron) |>
  dplyr::distinct() |>
  dplyr::slice(1:2)
pred <- predict.WA(fit, newdata = newdata_ex, t_seq = seq(0, 3.5, by = 0.05))
head(pred)

## End(Not run)

Summarize a WA object

Description

Summarize a WA object

Usage

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

Arguments

object

A "WA" object from WA_fit.

...

Unused.

Value

An object of class "summary.WA" containing configuration and a coefficient table with estimates, standard errors, and z-scores.

Examples

## Not run: 
fit <- WA_fit(Surv(time, status) ~ intv + demo_sex_male + numchron,
              crt_dt, id="screenid", cluster="practiceid",
              knots=seq(0,3.5,length.out=6), tau_grid=seq(0,3.5,length.out=6),
              basis="bz", degree=1, link="log",
              w_recur=c(1), w_term=2, ipcw="cox",
              ipcw_formula=~ demo_sex_male + numchron)
summary(fit)

## End(Not run)
## Not run: 
fit <- WA_fit(Surv(time, status) ~ intv + demo_sex_male + numchron,
              crt_dt, id="screenid", cluster="practiceid",
              knots=seq(0,3.5,length.out=6), tau_grid=seq(0,3.5,length.out=6),
              basis="bz", degree=1, link="log",
              w_recur=c(1), w_term=2, ipcw="cox",
              ipcw_formula=~ demo_sex_male + numchron)
summary(fit)

## End(Not run)

K-fold cross-validation for WA configuration selection

Description

Runs K-fold CV over a grid of basis types, degrees, interior-knot counts, and link functions. For each configuration, fits the model on K-1 folds and accumulates the prediction error (PE) on the held-out fold using WA_PE() (IPCW computed on the training subjects).

Usage

WA_cv(
  formula,
  data,
  id,
  cluster = NULL,
  basis_set = c("il", "pl", "bz"),
  degree_vec = 1:2,
  n_int_vec = c(0, 2, 4),
  knot_scheme = c("equidist", "quantile"),
  link_set = c("log"),
  time_range = NULL,
  tau_grid = NULL,
  w_recur,
  w_term,
  ipcw = c("cox", "km"),
  ipcw_formula = ~1,
  K = 5,
  seed = 1L,
  verbose = TRUE
)
WA_cv(
  formula,
  data,
  id,
  cluster = NULL,
  basis_set = c("il", "pl", "bz"),
  degree_vec = 1:2,
  n_int_vec = c(0, 2, 4),
  knot_scheme = c("equidist", "quantile"),
  link_set = c("log"),
  time_range = NULL,
  tau_grid = NULL,
  w_recur,
  w_term,
  ipcw = c("cox", "km"),
  ipcw_formula = ~1,
  K = 5,
  seed = 1L,
  verbose = TRUE
)

Arguments

formula

data, id, cluster See WA_fit.

basis_set

Character vector of candidate bases.

degree_vec

Integer vector of candidate degrees.

n_int_vec

Integer vector of interior-knot counts; 0 means boundaries only.

knot_scheme

"equidist" or "quantile" to construct interior knots.

link_set

Character vector of candidate links (subset of c("log","identity")).

time_range

Optional numeric length-2 vector c(tmin, tmax). If NULL, inferred from data.

tau_grid

Optional numeric vector; if NULL, a default dense grid over time_range is created.

w_recur

w_term Event-type weights (see WA_fit).

ipcw

IPCW method ("cox" or "km") for PE computation.

ipcw_formula

One-sided RHS formula for IPCW Cox model (if ipcw="cox").

K

Number of folds.

seed

RNG seed for fold assignment.

verbose

Logical; show a text progress bar and per-fold messages.

Value

A data frame with columns: basis, degree, n_int, link, and aggregated PE. Lower PE is better.

Examples

## Not run: 
tmin <- 0
tmax <- max(crt_dt$time, na.rm = TRUE)
cv_tab <- WA_cv(
  Surv(time, status) ~ intv + demo_sex_male + numchron,
  data = crt_dt, id = "screenid", cluster = "practiceid",
  basis_set = "bz", degree_vec = c(1,2,3,4),
  n_int_vec = c(0,2,3,4,5),
  knot_scheme = "equidist",
  link_set = "log",
  time_range = c(tmin, tmax),
  tau_grid = seq(0, 3.5, length.out = 6),
  w_recur = c(1), w_term = 2,
  ipcw = "cox", ipcw_formula = ~ demo_sex_male + numchron,
  K = 5, seed = 2025
)
head(cv_tab[order(cv_tab$PE), ], 10)

## End(Not run)
## Not run: 
tmin <- 0
tmax <- max(crt_dt$time, na.rm = TRUE)
cv_tab <- WA_cv(
  Surv(time, status) ~ intv + demo_sex_male + numchron,
  data = crt_dt, id = "screenid", cluster = "practiceid",
  basis_set = "bz", degree_vec = c(1,2,3,4),
  n_int_vec = c(0,2,3,4,5),
  knot_scheme = "equidist",
  link_set = "log",
  time_range = c(tmin, tmax),
  tau_grid = seq(0, 3.5, length.out = 6),
  w_recur = c(1), w_term = 2,
  ipcw = "cox", ipcw_formula = ~ demo_sex_male + numchron,
  K = 5, seed = 2025
)
head(cv_tab[order(cv_tab$PE), ], 10)

## End(Not run)

While-Alive Regression (WA) for Composite Endpoints

Description

Fits the while-alive regression model targeting the while-alive loss rate for composite endpoints with recurrent and terminal events. Time-varying covariate effects are represented via user-chosen time bases (e.g., B-spline, piecewise polynomial, interval-local). Robust inference supports cluster-randomized trials (CRTs) via cluster-robust variance; if cluster = NULL, IID (subject-as-cluster) variance is used.

Usage

WA_fit(
  formula,
  data,
  id,
  cluster = NULL,
  knots,
  tau_grid,
  basis = c("il", "pl", "bz", "ns", "ms", "st", "tl", "tf"),
  degree = 1,
  link = c("log", "identity"),
  w_recur,
  w_term,
  ipcw = c("km", "cox"),
  ipcw_formula = ~1
)
WA_fit(
  formula,
  data,
  id,
  cluster = NULL,
  knots,
  tau_grid,
  basis = c("il", "pl", "bz", "ns", "ms", "st", "tl", "tf"),
  degree = 1,
  link = c("log", "identity"),
  w_recur,
  w_term,
  ipcw = c("km", "cox"),
  ipcw_formula = ~1
)

Arguments

formula

A Surv(time, status) ~ RHS formula. time and status must exist in data. The RHS contains baseline covariates (no explicit time-varying covariates here; time-variation is induced via the chosen basis).

data

Long-format data frame with one row per event/checkpoint per subject, containing time, status, id, optional cluster, and RHS covariates.

id

Character scalar; subject ID column name.

cluster

Optional character scalar; cluster column name for CRT-robust inference. If NULL, IID inference treats each subject as its own cluster.

knots

Numeric vector (length $\ge 2$ ) specifying the basis boundaries and optional interior knots that define the time basis shape.

tau_grid

Numeric vector of evaluation times used to stack the estimating equations. Independent of knots.

basis

One of "il","pl","bz","ns","ms","st","tl","tf": interval-local ("il"), piecewise polynomial ("pl"), B-spline ("bz"), natural spline ("ns"), M-spline ("ms", requires splines2), step ("st"), truncated linear ("tl"), or time-fixed ("tf").

degree

Integer degree for bases that use it (e.g., "bz", "pl", "ns", "ms").

link

Link function: "log" (default) or "identity".

w_recur

Numeric vector of weights for each recurrent event type. Its length must match the number of recurrent status codes in data (i.e., excluding 0 for censoring and the max code for terminal).

w_term

Numeric scalar; weight for the terminal event.

ipcw

IPCW method: "km" or "cox".

ipcw_formula

A one-sided formula specifying RHS covariates for the IPCW Cox model when ipcw = "cox" (e.g., ~ x1 + x2). Ignored for ipcw = "km".

Details

The estimating equations solve $E[Z(t)\{L(t) - \mu_\beta(t)X_{\min}(t)\}V/G]=0$ over tau_grid, where $L(t)$ is the weighted composite loss (recurrent+terminal), $\mu_\beta(t)$ the while-alive loss rate under the chosen link, $X_{\min}(t) = \min(T, t)$ , $V$ the at-risk/terminal indicator, and $G$ the censoring survival modeled via ipcw.

Value

An object of class "WA" with elements:

est: named coefficient vector.
vcov: cluster-robust variance matrix.
se: standard errors.
converged: logical.
basis, degree, link, Z_cols, knots, tau_grid, id_var, cluster_var, w_recur, w_term, status_codes, formula.

Examples

## Not run: 
# Example (non-running) using included 'crt_dt' long dataset
fit <- WA_fit(
  Surv(time, status) ~ intv + demo_sex_male + numchron,
  data     = crt_dt,
  id       = "screenid",
  cluster  = "practiceid",
  knots    = seq(0, 3.5, length.out = 6),
  tau_grid = seq(0, 3.5, length.out = 6),
  basis    = "bz", degree = 1, link = "log",
  w_recur  = c(1), w_term = 2,
  ipcw     = "cox", ipcw_formula = ~ demo_sex_male + numchron
)
s <- summary(fit)

## End(Not run)

## Not run: 
# Example (non-running) using included 'crt_dt' long dataset
fit <- WA_fit(
  Surv(time, status) ~ intv + demo_sex_male + numchron,
  data     = crt_dt,
  id       = "screenid",
  cluster  = "practiceid",
  knots    = seq(0, 3.5, length.out = 6),
  tau_grid = seq(0, 3.5, length.out = 6),
  basis    = "bz", degree = 1, link = "log",
  w_recur  = c(1), w_term = 2,
  ipcw     = "cox", ipcw_formula = ~ demo_sex_male + numchron
)
s <- summary(fit)

## End(Not run)

Package 'WAreg'

Help Index

Clustered Recurrent-Time Dataset: crt_dt

Description

Usage

Format

Details

Source

Examples

Individual Recurrent-Time Dataset: irt_dt

Description

Usage

Format

Details

Source

Examples

Plot while-alive trajectory or a covariate's time-varying effect

Description

Usage

Arguments

Value

Examples

Predict while-alive loss rates

Description

Usage

Arguments

Value

Examples

Summarize a WA object

Description

Usage

Arguments

Value

Examples

K-fold cross-validation for WA configuration selection

Description

Usage

Arguments

Value

Examples

While-Alive Regression (WA) for Composite Endpoints

Description

Usage

Arguments

Details

Value

Examples