Fit Cox Model with Cubic Spline for Treatment Effect Heterogeneity

Estimates treatment effects as a function of a continuous covariate using a Cox proportional hazards model with natural cubic splines. The function models treatment-by-covariate interactions to detect effect modification.

Usage

cox_cs_fit(
  df,
  tte_name = "os_time",
  event_name = "os_event",
  treat_name = "treat",
  strata_name = NULL,
  z_name = "bm",
  alpha = 0.2,
  spline_df = 3,
  z_max = Inf,
  z_by = 1,
  z_window = 0,
  z_quantile = 0.9,
  show_plot = TRUE,
  plot_params = NULL,
  truebeta_name = NULL,
  verbose = TRUE
)

Arguments

df

Data frame containing survival data

tte_name

Character string specifying time-to-event variable name. Default: "os_time"

event_name

Character string specifying event indicator variable name (1=event, 0=censored). Default: "os_event"

treat_name

Character string specifying treatment variable name (1=treated, 0=control). Default: "treat"

strata_name

Character string specifying stratification variable name. If NULL, no stratification is used. Default: NULL

z_name

Character string specifying continuous covariate name for effect modification. Default: "bm"

alpha

Numeric value for confidence level (two-sided). Default: 0.20 (80% confidence intervals)

spline_df

Integer specifying degrees of freedom for natural spline. Default: 3

z_max

Numeric maximum value for z in predictions. Values beyond this are truncated. Default: Inf (no truncation)

z_by

Numeric increment for z values in prediction grid. Default: 1

z_window

Numeric half-width for counting observations near each z value. Default: 0.0 (exact matches only)

z_quantile

Numeric quantile (0-1) for upper limit of z profile. Default: 0.90 (90th percentile)

show_plot

Logical indicating whether to display plot. Default: TRUE

plot_params

List of plotting parameters (see Details). Default: NULL

truebeta_name

Character string specifying variable containing true log(HR) values for validation/simulation. Default: NULL

verbose

Logical indicating whether to print diagnostic information. Default: TRUE

Value

List containing:

z_profile

Vector of z values where treatment effect is estimated

loghr_est

Point estimates of log(HR) at each z value

loghr_lower

Lower confidence bound

loghr_upper

Upper confidence bound

se_loghr

Standard errors of log(HR) estimates

counts_profile

Number of observations near each z value

cox_primary

Log(HR) from standard Cox model (no interaction)

model_fit

The fitted coxph model object

spline_basis

The natural spline basis object

Details

Model Structure

The function fits: $$h(t|Z,A) = h_0(t) \exp(\beta_0 A + f(Z) + g(Z) \cdot A)$$

Where:

• A is treatment (0/1)

• Z is the continuous effect modifier

• f(Z) is modeled with natural splines (main effect)

• g(Z) is modeled with natural splines (interaction)

• The log hazard ratio is: \(\beta(Z) = \beta_0 + g(Z)\)

Plot Parameters

The plot_params argument accepts a list with:

• xlab: x-axis label

• main_title: plot title

• ylimit: y-axis limits c(min, max)

• y_pad_zero: padding below zero line

• y_delta: extra space for count labels

• cex_legend: legend text size

• cex_count: count text size

• show_cox_primary: show standard Cox estimate line

• show_null: show null effect line (log(HR)=0)

• show_target: show target effect line (e.g., log(0.80))

Examples

if (FALSE) { # \dontrun{
# Simulate data
set.seed(123)
df <- data.frame(
  os_time = rexp(500, 0.01),
  os_event = rbinom(500, 1, 0.7),
  treat = rbinom(500, 1, 0.5),
  bm = rnorm(500, 50, 10)
)

# Fit model
result <- cox_cs_fit(df, z_name = "bm", alpha = 0.20)

# Custom plotting
result <- cox_cs_fit(
  df,
  z_name = "bm",
  plot_params = list(
    xlab = "Biomarker Level",
    main_title = "Treatment Effect by Biomarker",
    cex_legend = 1.2
  )
)
} # }