Weighted Survival Analysis Tools

Description

Provides functions for weighted and stratified survival analysis, including Cox proportional hazards models, weighted log-rank tests, Kaplan-Meier curves, and RMST calculations with various weighting schemes.

Main Functions

• df_counting: Main function for weighted survival analysis

• KM_diff: Kaplan-Meier difference calculations

• cox_rhogamma: Weighted Cox model with flexible weights

• plot_weight_schemes: Visualize weighting schemes

• cumulative_rmst_bands: RMST analysis with confidence bands

Weighting Schemes

The package supports multiple weighting schemes for log-rank tests:

• Fleming-Harrington (fh): Emphasizes early or late differences

• Magirr-Burman (MB): Modest downweighting after cutoff time

• Schemper: Adjusts for censoring distribution

• Xu-O'Quigley (XO): Adjusts for risk set size

• Custom time-based weights

Typical Workflow

1. Prepare data with treatment (0/1), time-to-event, and event indicator

2. Run df_counting() for comprehensive analysis

3. Use plot_weighted_km() to visualize survival curves

4. Calculate survival differences with KM_diff()

5. Perform weighted Cox regression with cox_rhogamma()

6. Compute RMST with cumulative_rmst_bands()

Key Features

• Flexible weighting schemes for hypothesis testing

• Resampling-based inference for improved small-sample properties

• Simultaneous confidence bands for survival curves

• Stratified analysis support

• Weighted observations

• Comprehensive diagnostic checks

Author(s)

Maintainer: Larry Leon larry.leon.05@post.harvard.edu

References

Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis. Wiley.

Magirr, D. and Burman, C. F. (2019). Modestly weighted logrank tests. Statistics in Medicine, 38(20), 3782-3790.

See Also

Useful links:

• https://github.com/larry-leon/weightedsurv

• Report bugs at https://github.com/larry-leon/weightedsurv/issues

Examples

library(survival)
str(veteran)
veteran$treat <- as.numeric(veteran$trt) - 1

# Basic analysis
result <- df_counting(
  df = veteran,
  tte.name = "time",
  event.name = "status",
  treat.name = "treat"
)

# Plot results
plot_weighted_km(result)

# Weighted log-rank emphasizing late differences
result_fh <- df_counting(
  df = veteran,
  tte.name = "time",
  event.name = "status",
  treat.name = "treat",
  scheme = "fh",
  scheme_params = list(rho = 0, gamma = 1)
)

Kaplan-Meier Difference Between Groups

Description

Calculates the difference in Kaplan-Meier curves between two groups, with confidence intervals and optional resampling-based simultaneous confidence bands.

Usage

KM_diff(
  df,
  tte.name = "tte",
  event.name = "event",
  treat.name = "treat",
  weight.name = NULL,
  at_points = sort(df[[tte.name]]),
  alpha = 0.05,
  seedstart = 8316951,
  draws = 0,
  risk.points = NULL,
  draws.band = 0,
  tau.seq = 0.25,
  qtau = 0.025,
  show_resamples = TRUE,
  modify_tau = FALSE
)

Arguments

Details

This function computes the difference in Kaplan-Meier survival curves, delta(t) = S_1(t) - S_0(t),

along with variance estimates and confidence intervals.

When draws.band > 0, simultaneous confidence bands are constructed using the supremum distribution of the standardized difference process. These bands maintain the specified coverage probability across all time points simultaneously.

The variance is estimated using Greenwood's formula for unweighted data, or resampling-based methods when draws > 0.

Value

A list containing:

at_points

Time points used in calculations

surv0, surv1

Survival estimates for control and treatment groups

sig2_surv0, sig2_surv1

Variance estimates for survival curves

dhat

Survival difference (S1 - S0) at each time point

sig2_dhat

Variance of survival difference

lower, upper

Pointwise confidence limits (1 - alpha/2)

sb_lower, sb_upper

Simultaneous band limits (if draws.band > 0)

c_alpha_band

Critical value for simultaneous band (if draws.band > 0)

dhat_star

Matrix of resampled differences (if draws.band > 0)

Zdhat_star

Standardized resampled differences (if draws.band > 0)

Confidence Intervals vs Bands

• Pointwise CIs (lower, upper): Cover the true difference at each time point with probability 1-alpha

• Simultaneous bands (sb_lower, sb_upper): Cover the entire difference curve with probability 1-alpha

Note

Treatment must be coded as 0=control, 1=experimental. Event must be binary (0/1).

See Also

df_counting for full survival analysis plotKM.band_subgroups for visualization cumulative_rmst_bands for RMST analysis

Other survival_analysis: cox_rhogamma(), df_counting(), wt.rg.S()

Examples

library(survival)
str(veteran)
veteran$treat <- as.numeric(veteran$trt) - 1

# Basic KM difference
result <- KM_diff(
  df = veteran,
  tte.name = "time",
  event.name = "status",
  treat.name = "treat"
)

# Plot the difference
plot(result$at_points, result$dhat, type = "s",
     xlab = "Time", ylab = "Survival Difference")

# With simultaneous confidence bands
result_band <- KM_diff(
  df = veteran,
  tte.name = "time",
  event.name = "status",
  treat.name = "treat",
  draws.band = 1000,
  modify_tau = TRUE
)

Kaplan-Meier Survival Estimates and Variance

Description

Computes Kaplan-Meier survival estimates and their variances given risk and event counts.

Usage

KM_estimates(ybar, nbar, sig2w_multiplier = NULL)

Arguments

Value

List with survival estimates and variances.

Plot Weighted Kaplan-Meier Curves for Two Samples (Counting Process Format)

Description

Plots Kaplan-Meier survival curves for two groups using precomputed risk/event counts and survival estimates. Optionally displays confidence intervals, risk tables, median survival annotations, and statistical test results.

Usage

KM_plot_2sample_weighted_counting(
  dfcount,
  show.cox = TRUE,
  cox.cex = 0.725,
  show.logrank = FALSE,
  logrank.cex = 0.725,
  cox.eps = 0.001,
  lr.eps = 0.001,
  show_arm_legend = TRUE,
  arms = c("treat", "control"),
  put.legend.arms = "left",
  stop.onerror = TRUE,
  check.KM = TRUE,
  put.legend.cox = "topright",
  put.legend.lr = "topleft",
  lr.digits = 2,
  cox.digits = 2,
  tpoints.add = c(0),
  by.risk = NULL,
  Xlab = "time",
  Ylab = "proportion surviving",
  col.0 = "black",
  col.1 = "blue",
  show.med = TRUE,
  med.digits = 2,
  med.font = 4,
  conf.int = FALSE,
  conf_level = 0.95,
  choose_ylim = FALSE,
  arm.cex = 0.7,
  quant = 0.5,
  med.cex = 0.725,
  ymed.offset = 0.1,
  xmed.fraction = 0.8,
  risk.cex = 0.725,
  ltys = c(1, 1),
  lwds = c(1, 1),
  censor.mark.all = TRUE,
  censor.cex = 0.5,
  show.ticks = TRUE,
  risk.set = TRUE,
  ymin = 0,
  ymax = 1,
  ymin.del = 0.035,
  ymin2 = NULL,
  risk_offset = 0.125,
  risk_delta = 0.05,
  y.risk0 = NULL,
  show.Y.axis = TRUE,
  cex_Yaxis = 1,
  y.risk1 = NULL,
  add.segment = FALSE,
  risk.add = NULL,
  xmin = 0,
  xmax = NULL,
  x.truncate = NULL,
  time.zero = 0,
  prob.points = NULL
)

Arguments

Value

Invisibly returns NULL. Used for plotting side effects.

Weighted event count for Cox model

Description

Calculates the weighted event count for the Cox model with rho-gamma weights.

Usage

N_rhogamma(x, error, delta, weight = 1)

Arguments

Value

Numeric value of weighted event count.

Add legends to KM plot

Description

Adds legends for Cox model, log-rank test, and arms to a Kaplan-Meier plot.

Usage

add_legends(
  dfcount,
  show.cox,
  cox.cex,
  put.legend.cox,
  show.logrank,
  logrank.cex,
  put.legend.lr,
  show_arm_legend,
  arms,
  col.1,
  col.0,
  ltys,
  lwds,
  arm.cex,
  put.legend.arms
)

Arguments

Value

Invisibly returns NULL. Used for plotting side effects.

Add median annotation to KM plot

Description

Adds median survival annotation to a Kaplan-Meier plot.

Usage

add_median_annotation(
  medians_df,
  med.digits,
  med.cex,
  med.font,
  xmed.fraction,
  ymed.offset
)

Arguments

Value

Invisibly returns NULL. Used for plotting side effects.

Add risk table annotation to KM plot

Description

Adds risk set counts for two groups to a Kaplan-Meier plot.

Usage

add_risk_table(
  risk.points,
  rpoints0,
  rpoints1,
  col.0,
  col.1,
  risk.cex,
  ymin,
  risk_offset,
  risk_delta,
  y.risk0,
  y.risk1
)

Arguments

Value

Invisibly returns NULL. Used for plotting side effects.

Calculate risk set and event counts at time points

Description

Calculates risk set and event counts for a group at specified time points, with variance estimation.

Usage

calculate_risk_event_counts(U, D, W, at_points, draws = 0, seedstart = 816951)

Arguments

Value

List with ybar (risk set counts), nbar (event counts), sig2w_multiplier (variance term).

Check KM curve for validity

Description

Checks that a Kaplan-Meier curve is valid (values in [0,1], non-increasing).

Usage

check_km_curve(S.KM, group_name = "Group", stop_on_error = TRUE)

Arguments

Value

None. Stops or warns if invalid.

Check and Compare Statistical Test Results

Description

Calculates and compares three equivalent test statistics from weighted survival analysis: the squared standardized weighted log-rank statistic, the log-rank chi-squared statistic, and the squared Cox model z-score. These should be approximately equal under correct implementation.

Usage

check_results(dfcount, verbose = TRUE)

Arguments

Details

This function serves as a diagnostic tool to verify computational consistency. The three statistics should be numerically equivalent (within rounding error):

(lr / \sqrt{sig2\_lr})^2 \approx logrank\_chisq \approx z.score^2

Discrepancies between these values may indicate:

• Numerical instability in variance estimation

• Incorrect weighting scheme application

• Data processing errors

Value

A data frame with one row and three columns, returned invisibly:

zlr_sq

Squared standardized weighted log-rank: (lr / \sqrt{sig2\_lr})^2

logrank_chisq

Chi-squared statistic from log-rank test

zCox_sq

Squared z-score from Cox model: z.score^2

Note

This function is primarily used for package development and validation. End users typically don't need to call it directly.

See Also

df_counting for generating the input object

Examples

# After running df_counting
library(survival)
data(veteran)
veteran$treat <- as.numeric(veteran$trt) - 1

result <- df_counting(
  df = veteran,
  tte.name = "time",
  event.name = "status",
  treat.name = "treat"
)

# Check consistency of test statistics
check_results(result)

# Store results without printing
stats_comparison <- check_results(result, verbose = FALSE)
print(stats_comparison)


# Simple example with constructed data
dfcount_example <- list(
  lr = 2.5,
  sig2_lr = 1.0,
  z.score = 2.5,
  logrank_results = list(chisq = 6.25)
)
check_results(dfcount_example)

Confidence interval for Cox model estimate

Description

Calculates the confidence interval for a Cox model log hazard ratio estimate.

Usage

ci_cox(bhat, sig_bhat, alpha = 0.05, verbose = FALSE)

Arguments

Value

Data frame with log hazard ratio, standard error, hazard ratio, lower and upper confidence limits.

Weighted counting process

Description

Computes the weighted count of events up to a specified time.

Usage

count_weighted(x, y, w = rep(1, length(y)))

Arguments

Value

Weighted count of events up to time x.

Weighted Cox Model with Rho-Gamma Weights

Description

Fits a weighted Cox proportional hazards model using flexible time-dependent weights (e.g., Fleming-Harrington, Magirr-Burman). Supports resampling-based inference for variance estimation and bias correction.

Usage

cox_rhogamma(
  dfcount,
  scheme = "fh",
  scheme_params = list(rho = 0, gamma = 0.5),
  draws = 0,
  alpha = 0.05,
  verbose = FALSE,
  lr.digits = 4
)

Arguments

Details

This function solves the weighted Cox partial likelihood score equation: U(beta) = sum_i w_i K_i (dN_0/Y_0 - dN_1/Y_1) = 0

where K_i are time-dependent weights and Y_j, dN_j are risk sets and event counts for group j.

When draws > 0, the function performs resampling to:

• Estimate finite-sample variance (more accurate than asymptotic)

• Compute bias correction for \hat{\beta}

• Provide improved confidence intervals for small samples

The score test at \beta=0 corresponds to the weighted log-rank test.

Value

A list containing:

fit

List with fitted model components:

• bhat: Estimated log hazard ratio

• sig_bhat_asy: Asymptotic standard error

• u.zero: Score statistic at beta=0 (log-rank)

• z.score: Standardized score statistic

• sig2_score: Variance of score statistic

• wt_rg: Vector of time-dependent weights

• bhat_debiased: Bias-corrected estimate (if draws > 0)

• sig_bhat_star: Resampling-based standard error (if draws > 0)

hr_ci_asy

Data frame with asymptotic HR and CI

hr_ci_star

Data frame with resampling-based HR and CI (if draws > 0)

cox_text_asy

Formatted string with HR and asymptotic CI

cox_text_star

Formatted string with HR and resampling CI (if draws > 0)

z.score_debiased

Bias-corrected score statistic (if draws > 0)

zlogrank_text

Formatted log-rank test result

Note

The treatment variable in dfcount must be coded as 0=control, 1=experimental.

References

Magirr, D. and Burman, C. F. (2019). Modestly weighted logrank tests. Statistics in Medicine, 38(20), 3782-3790.

See Also

df_counting for preprocessing wt.rg.S for weighting schemes cox_score_rhogamma for score function

Other survival_analysis: KM_diff(), df_counting(), wt.rg.S()

Other weighted_tests: df_counting(), wt.rg.S()

Examples

# First get counting process data
library(survival)
str(veteran)
veteran$treat <- as.numeric(veteran$trt) - 1

dfcount <- df_counting(
  df = veteran,
  tte.name = "time",
  event.name = "status",
  treat.name = "treat"
)

# Fit weighted Cox model with FH(0,0.5) weights
fit <- cox_rhogamma(
  dfcount = dfcount,
  scheme = "fh",
  scheme_params = list(rho = 0, gamma = 0.5),
  draws = 1000,
  verbose = TRUE
)

print(fit$cox_text_star)  # Resampling-based CI
print(fit$zlogrank_text)  # Weighted log-rank test

# Compare asymptotic and resampling CIs
print(fit$hr_ci_asy)
print(fit$hr_ci_star)

Resampling for Weighted Cox Model (rho, gamma)

Description

Performs resampling to estimate uncertainty for the weighted Cox model (rho, gamma).

Usage

cox_rhogamma_resample(
  fit_rhogamma,
  i_bhat,
  K_wt_rg,
  i_zero,
  K_zero,
  G1.draws = NULL,
  G0.draws = NULL,
  draws = 100,
  seedstart = 8316951
)

Arguments

Value

List with resampling results (score, beta, standard error, etc.).

Cox score with rho-gamma weights

Description

Calculates the Cox score statistic for weighted log-rank tests.

Usage

cox_score_rhogamma(
  beta,
  time,
  delta,
  z,
  w_hat = rep(1, length(time)),
  wt_rg = rep(1, length(time)),
  score_only = TRUE
)

Arguments

Value

Numeric value of the score or a list with additional results.

Create Baseline Characteristics Table by Treatment Arm

Description

This function generates publication-ready baseline characteristic tables commonly used in clinical trials and observational studies. It calculates summary statistics, p-values, and standardized mean differences for continuous, categorical, and binary variables.

Usage

create_baseline_table(
  data,
  treat_var = "treat",
  vars_continuous = NULL,
  vars_categorical = NULL,
  vars_binary = NULL,
  var_labels = NULL,
  digits = 1,
  show_pvalue = TRUE,
  show_smd = TRUE,
  show_missing = TRUE
)

Arguments

Value

A gt table object (if gt package is available) or data frame

Examples

# Create sample data
set.seed(123)
n <- 500
sample_data <- data.frame(
  treat = rbinom(n, 1, 0.5),
  age = rnorm(n, mean = 55, sd = 10),
  stage = sample(c("I", "II", "III", "IV"), n, replace = TRUE),
  sex = rbinom(n, 1, 0.45),
  smoking = rbinom(n, 1, 0.3)
)

# Create table
table <- create_baseline_table(
  data = sample_data,
  treat_var = "treat",
  vars_continuous = "age",
  vars_categorical = "stage",
  vars_binary = c("sex", "smoking"),
  var_labels = c(
    age = "Age (years)",
    stage = "Disease Stage",
    sex = "Female",
    smoking = "Current Smoker"
  )
)

Cumulative RMST bands for survival curves

Description

Calculates cumulative Restricted Mean Survival Time (RMST) and confidence bands for survival curves using resampling. Optionally plots the cumulative RMST curve, pointwise confidence intervals, and simultaneous confidence bands.

Usage

cumulative_rmst_bands(
  df,
  fit,
  tte.name,
  event.name,
  treat.name,
  weight.name = NULL,
  draws_sb = 1000,
  xlab = "months",
  ylim_pad = 0.5,
  rmst_max_legend = "left",
  rmst_max_cex = 0.7,
  plot = TRUE
)

Arguments

Value

A list with elements:

Weighted and Stratified Survival Analysis

Description

Performs comprehensive weighted and/or stratified survival analysis, including Cox proportional hazards model, logrank/Fleming-Harrington tests, and calculation of risk/event sets, Kaplan-Meier curves, quantiles, and variance estimates.

Usage

df_counting(
  df,
  tte.name = "tte",
  event.name = "event",
  treat.name = "treat",
  weight.name = NULL,
  strata.name = NULL,
  arms = c("treat", "control"),
  time.zero = 0,
  tpoints.add = c(0),
  by.risk = 6,
  time.zero.label = 0,
  risk.add = NULL,
  get.cox = TRUE,
  cox.digits = 2,
  lr.digits = 2,
  cox.eps = 0.001,
  lr.eps = 0.001,
  verbose = FALSE,
  qprob = 0.5,
  scheme = "fh",
  scheme_params = list(rho = 0, gamma = 0),
  conf_level = 0.95,
  check.KM = TRUE,
  check.seKM = FALSE,
  draws = 0,
  seedstart = 8316951,
  stop.onerror = FALSE,
  censoring_allmarks = TRUE
)

Arguments

Details

This function implements a comprehensive survival analysis framework supporting:

• Weighted observations via weight.name

• Stratified analysis via strata.name

• Multiple weighting schemes for log-rank tests

• Resampling-based variance estimation

• Automatic validation against survival package results

The function performs time-fixing using survival::aeqSurv to handle tied event times. For stratified analyses, stratum-specific estimates are computed and combined appropriately.

Value

A list with the following components:

cox_results

List with Cox model results including hazard ratio, confidence interval, p-value, and formatted text

logrank_results

List with log-rank test chi-square statistic, p-value, and formatted text

z.score

Standardized weighted log-rank test statistic

at_points

Vector of all time points used in calculations

surv0, surv1

Kaplan-Meier survival estimates for control and treatment groups

sig2_surv0, sig2_surv1

Variance estimates for survival curves

survP

Pooled survival estimates

survG

Censoring distribution estimates

quantile_results

Data frame with median survival and confidence intervals by group

lr, sig2_lr

Weighted log-rank statistic and its variance

riskpoints0, riskpoints1

Risk set counts at specified time points

z.score_stratified

Stratified z-score (if stratified analysis)

Weighting Schemes

fh

Fleming-Harrington: w(t) = S(t)^rho * (1-S(t))^gamma

MB

Magirr-Burman: w(t) = 1/max(S(t), S(t*))

schemper

Schemper: w(t) = S(t)/G(t) where G is the censoring distribution

XO

Xu-O'Quigley: w(t) = S(t)/Y(t) where Y is risk set size

References

Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis. Wiley.

Magirr, D. and Burman, C. F. (2019). Modestly weighted logrank tests. Statistics in Medicine, 38(20), 3782-3790.

See Also

coxph, survdiff, survfit cox_rhogamma for weighted Cox models KM_diff for Kaplan-Meier differences

Other survival_analysis: KM_diff(), cox_rhogamma(), wt.rg.S()

Other weighted_tests: cox_rhogamma(), wt.rg.S()

Examples

# Basic survival analysis
library(survival)
str(veteran)
veteran$treat <- as.numeric(veteran$trt) - 1

result <- df_counting(
  df = veteran,
  tte.name = "time",
  event.name = "status",
  treat.name = "treat",
  arms = c("Treatment", "Control")
)

# Print results
print(result$cox_results$cox_text)
print(result$zlogrank_text)

# Fleming-Harrington (0,1) weights (emphasizing late differences)
result_fh <- df_counting(
  df = veteran,
  tte.name = "time",
  event.name = "status",
  treat.name = "treat",
  scheme = "fh",
  scheme_params = list(rho = 0, gamma = 1)
)

# Stratified analysis
result_strat <- df_counting(
  df = veteran,
  tte.name = "time",
  event.name = "status",
  treat.name = "treat",
  strata.name = "celltype"
)

Extract and calculate weights for multiple schemes

Description

Extracts and calculates weights for multiple schemes and returns a combined data frame.

Usage

extract_and_calc_weights(atpoints, S.pool, weights_spec_list)

Arguments

Value

Data frame with weights for each scheme.

Extract time, event, and weight data for a group

Description

Extracts time, event, and weight vectors for a specified group.

Usage

extract_group_data(time, delta, wgt, z, group = 1)

Arguments

Value

List with U (times), D (events), W (weights).

Root-finding for Cox score function

Description

Finds the root of the Cox model score equation for weighted log-rank statistics.

Usage

find_cox_root(time, delta, z, w_hat, wt_rg)

Arguments

Value

List with root and additional information, or NA if not found.

Format p-value for display

Description

Formats a p-value for display, showing "<eps" for small values.

Usage

format_pval(pval, eps = 0.001, digits = 3)

Arguments

Value

Formatted p-value as character.

Get censoring and event times and their indices

Description

Extracts censoring and event times and their indices for a group at specified time points.

Usage

get_censoring_and_events(time, delta, z, group, censoring_allmarks, at_points)

Arguments

Value

List with cens (censored times), ev (event times), idx_cens, idx_ev, idx_ev_full.

Get df_counting results

Description

Wrapper for df_counting, safely executes and returns results for survival analysis.

Usage

get_dfcounting(...)

Arguments

Value

Result from df_counting or NULL if error.

See Also

df_counting

Event and Risk Matrices for Survival Analysis

Description

Constructs matrices indicating event and risk status for each subject at specified time points.

Usage

get_event_risk_matrices(U, at.points)

Arguments

Value

A list with event and risk matrices.

Get risk set counts at specified risk points

Description

Returns risk set counts at specified risk points.

Usage

get_riskpoints(ybar, risk_points, at_points)

Arguments

Value

Numeric vector of risk set counts at risk points.

Get validated weights for a data frame

Description

Validates and returns weights for a data frame according to specified schemes.

Usage

get_validated_weights(
  df_weights,
  scheme = "fh",
  scheme_params = list(rho = 0, gamma = 0),
  details = FALSE
)

Arguments

Value

Numeric vector or list of validated weights.

Get weights for a weighting scheme

Description

Calculates weights for a specified scheme at given time points.

Usage

get_weights(scheme, scheme_params, S.pool, tpoints)

Arguments

Value

Numeric vector of weights.

Kaplan-Meier quantile and confidence interval

Description

Calculates the quantile and confidence interval for a Kaplan-Meier curve.

Usage

km_quantile(
  time_points,
  survival_probs,
  se_probs = NULL,
  qprob = 0.5,
  type = c("midpoint", "min"),
  conf_level = 0.95
)

Arguments

Value

List with quantile and confidence interval.

Table of KM quantiles for two groups

Description

Returns a data frame of quantiles and confidence intervals for two groups.

Usage

km_quantile_table(
  time_points,
  surv0,
  se0,
  surv1,
  se1,
  arms = c("treat", "control"),
  qprob = 0.5,
  type = c("midpoint", "min"),
  conf_level = 0.95
)

Arguments

Value

Data frame of quantiles and CIs for each group.

Kaplan-Meier quantile calculation

Description

Calculates the quantile time for a Kaplan-Meier curve.

Usage

kmq_calculations(time_points, survival_probs, qprob = 0.5, type = "midpoint")

Arguments

Value

Estimated quantile time.

Plot Kaplan-Meier Survival Difference Curves with Subgroups and Confidence Bands

Description

Plots the difference in Kaplan-Meier survival curves between two groups, optionally including simultaneous confidence bands and subgroup curves. Also displays risk tables for the overall population and specified subgroups.

Usage

plotKM.band_subgroups(
  df,
  tte.name,
  event.name,
  treat.name,
  weight.name = NULL,
  sg_labels = NULL,
  ltype = "s",
  lty = 1,
  draws = 20,
  lwd = 2,
  sg_colors = NULL,
  color = "lightgrey",
  ymax.pad = 0.01,
  ymin.pad = -0.01,
  taus = c(-Inf, Inf),
  yseq_length = 5,
  cex_Yaxis = 0.8,
  risk_cex = 0.8,
  by.risk = 6,
  risk.add = NULL,
  xmax = NULL,
  ymin = NULL,
  ymax = NULL,
  ymin.del = 0.035,
  y.risk1 = NULL,
  y.risk2 = NULL,
  ymin2 = NULL,
  risk_offset = NULL,
  risk.pad = 0.01,
  risk_delta = 0.0275,
  tau_add = NULL,
  time.zero.pad = 0,
  time.zero.label = 0,
  xlabel = NULL,
  ylabel = NULL,
  Maxtau = NULL,
  seedstart = 8316951,
  ylim = NULL,
  draws.band = 20,
  qtau = 0.025,
  show_resamples = FALSE,
  modify_tau = FALSE
)

Arguments

Value

(Invisible) list containing KM_diff results, time points, subgroup curves, risk tables, and confidence intervals.

Plot Kaplan-Meier curves

Description

Plots Kaplan-Meier survival curves for groups in the data.

Usage

plot_km(df, tte.name, event.name, treat.name, weights = NULL, ...)

Arguments

Value

Kaplan-Meier fit object (invisible).

Plot confidence interval polygon for KM curve

Description

Plots a shaded polygon representing the confidence interval for a Kaplan-Meier survival curve.

Usage

plot_km_confint_polygon(x, surv, se, conf_level, col)

Arguments

Value

Invisibly returns NULL. Used for plotting side effects.

Plot KM curves for two groups with optional confidence intervals and censoring marks

Description

Plots Kaplan-Meier survival curves for two groups, with options for confidence intervals and censoring marks.

Usage

plot_km_curves_counting(
  at_points,
  S0.KM,
  idx0,
  idv0,
  S1.KM,
  idx1,
  idv1,
  col.0,
  col.1,
  ltys,
  lwds,
  Xlab,
  Ylab,
  ylim,
  xlim,
  show.ticks = FALSE,
  cens0 = NULL,
  risk.points,
  risk.points.label,
  cens1 = NULL,
  se0.KM = NULL,
  se1.KM = NULL,
  conf.int = FALSE,
  conf_level = 0.95,
  censor.cex = 1,
  time.zero = 0,
  tpoints.add = c(0),
  ...
)

Arguments

Value

Invisibly returns NULL. Used for plotting side effects.

Plot weight schemes for survival analysis

Description

Plots the weights for different schemes over time using ggplot2.

Usage

plot_weight_schemes(
  dfcount,
  tte.name = "time_months",
  event.name = "status",
  treat.name = "treat",
  arms = c("treat", "control"),
  weights_spec_list = list(`MB(12)` = list(scheme = "MB", mb_tstar = 12), `MB(6)` =
    list(scheme = "MB", mb_tstar = 6), `FH(0,1)` = list(scheme = "fh", rho = 0, gamma =
    1), `FH(0.5,0.5)` = list(scheme = "fh", rho = 0.5, gamma = 0.5), custom_time =
    list(scheme = "custom_time", t.tau = 25, w0.tau = 1, w1.tau = 1.5), FHexp2 =
    list(scheme = "fh_exp2")),
  custom_colors = c(`FH(0,1)` = "grey", FHexp2 = "black", `MB(12)` = "#1b9e77", `MB(6)` =
    "#d95f02", `FH(0.5,0.5)` = "#7570b3", custom_time = "green"),
  custom_sizes = c(`FH(0,1)` = 2, FHexp2 = 1, `MB(12)` = 1, `MB(6)` = 1, `FH(0.5,0.5)` =
    1, custom_time = 1),
  transform_fh = FALSE,
  rescheme_fhexp2 = TRUE
)

Arguments

Details

This function visualizes the weights used in various survival analysis schemes (e.g., FH, MB, custom) using ggplot2. Facets and colors are customizable.

Value

A ggplot object showing the weight schemes over time.

Plot weighted Kaplan-Meier curves

Description

Plots weighted Kaplan-Meier curves using a custom function.

Usage

plot_weighted_km(dfcount, ...)

Arguments

Value

None. Plots the curves.

Resampling Survival Curves for Confidence Bands

Description

Performs resampling to generate survival curves for a group, used for constructing confidence bands.

Usage

resampling_survival(U, W, D, at.points, draws.band, surv, G_draws)

Arguments

Value

Matrix of resampled survival curves.

Weighted risk set

Description

Computes the weighted number at risk at a specified time.

Usage

risk_weighted(x, y, w = rep(1, length(y)))

Arguments

Value

Weighted number at risk at time x.

Safe execution wrapper

Description

Executes an R expression safely, returning NULL and printing an error message if an error occurs.

Usage

safe_run(expr)

Arguments

Value

The result of expr, or NULL if an error occurs.

Score calculation for weighted Cox model

Description

Calculates the score and variance for the weighted Cox model.

Usage

score_calculation(ybar1, ybar0, dN1, dN0, wt_rg)

Arguments

Value

List with score, variance, information, and weights.

Validate required columns in a data frame

Description

Checks that all required columns are present in a data frame.

Usage

validate_input(df, required_cols)

Arguments

Value

NULL if all columns present, otherwise error.

Validate weighting scheme parameters

Description

Checks and validates the parameters for a given weighting scheme.

Usage

validate_scheme_params(scheme, scheme_params, S.pool)

Arguments

Value

Logical indicating if parameters are valid, or stops with error.

Weighted log-rank cumulative statistics

Description

Calculates cumulative weighted log-rank statistics for survival data.

Usage

wlr_cumulative(
  df_weights,
  scheme,
  scheme_params = list(rho = 0, gamma = 0),
  return_cumulative = FALSE
)

Arguments

Value

List with score and variance.

Weighted Log-Rank and Difference Estimate at a Specified Time

Description

Computes the weighted log-rank statistic, its variance, the difference in survival at a specified time (tzero), the variance of the difference, their covariance, and correlation, using flexible time-dependent weights. The weighting scheme is selected via the scheme argument and is calculated using wt.rg.S.

Usage

wlr_dhat_estimates(
  dfcounting,
  scheme = "fh",
  scheme_params = list(rho = 0, gamma = 0),
  tzero = NULL
)

Arguments

Details

The weighting scheme is selected via the scheme argument and calculated using wt.rg.S. Supports standard Fleming-Harrington, Schemper, XO (Xu & O'Quigley), MB (Maggir-Burman), custom time-based, and custom code weights.

Value

A list with elements:

Compute Time-Dependent Weights for Survival Analysis

Description

Calculates time-dependent weights for survival analysis according to various schemes (Fleming-Harrington, Schemper, XO, MB, custom).

Usage

wt.rg.S(
  S,
  scheme = c("fh", "schemper", "XO", "MB", "custom_time", "fh_exp1", "fh_exp2"),
  rho = NULL,
  gamma = NULL,
  Scensor = NULL,
  Ybar = NULL,
  tpoints = NULL,
  t.tau = NULL,
  w0.tau = 0,
  w1.tau = 1,
  mb_tstar = NULL,
  details = FALSE
)

Arguments

Details

This function implements several weighting schemes for weighted log-rank tests: See vignette for details This function implements several weighting schemes for weighted log-rank tests:

Fleming-Harrington (fh)

w(t) = S(t-)^rho * (1-S(t-))^gamma. See vignette for common choices.

Schemper

w(t) = S(t-)/G(t-) where G is the censoring distribution.

Xu-O'Quigley (XO)

w(t) = S(t-)/Y(t) where Y is risk set size.

Magirr-Burman (MB)

w(t) = 1/max(S(t-), S(t*)).

Custom time

Step function with weight w_0 before t* and w_1 after t*.

Value

If details=FALSE (default): Numeric vector of weights with length equal to S.

If details=TRUE: List containing:

weights

Numeric vector of calculated weights

S

Input survival probabilities

S_left

Left-continuous survival probabilities

scheme

Scheme name

Note

All weights are calculated using left-continuous survival probabilities S(t-) to ensure consistency with counting process notation.

References

Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis. Wiley.

Magirr, D. and Burman, C. F. (2019). Modestly weighted logrank tests. Statistics in Medicine, 38(20), 3782-3790.

Schemper, M., Wakounig, S., and Heinze, G. (2009). The estimation of average hazard ratios by weighted Cox regression. Statistics in Medicine, 28(19), 2473-2489.

See Also

Other survival_analysis: KM_diff(), cox_rhogamma(), df_counting()

Other weighted_tests: cox_rhogamma(), df_counting()

Examples

# Generate example survival curve
time <- seq(0, 24, by = 0.5)
surv <- exp(-0.05 * time)  # Exponential survival

# Fleming-Harrington (0,1) weights
w_fh01 <- wt.rg.S(surv, scheme = "fh", rho = 0, gamma = 1, tpoints = time)

# Magirr-Burman weights
w_mb <- wt.rg.S(surv, scheme = "MB", mb_tstar = 12, tpoints = time)

# Standard log-rank (equal weights)
w_lr <- wt.rg.S(surv, scheme = "fh", rho = 0, gamma = 0)

# Plotting examples
plot(time, w_fh01, type = "l", main = "FH(0,1) Weights")
plot(time, w_mb, type = "l", main = "MB(12) Weights")

# Compare multiple schemes
plot(time, w_lr, type = "l", ylim = c(0, 2))
lines(time, w_fh01, col = "blue")
legend("topleft", c("Log-rank", "FH(0,1)"), col = 1:2, lty = 1)