Cox Regression Helper: Interactions — cox_regression

Test and estimate the effect of a treatment in interaction with a covariate. The effect is estimated as the HR of the tested treatment for a given level of the covariate, in comparison to the treatment control.

Usage

h_coxreg_inter_effect(x, effect, covar, mod, label, control, ...)

# S3 method for numeric
h_coxreg_inter_effect(x, effect, covar, mod, label, control, at, ...)

# S3 method for factor
h_coxreg_inter_effect(x, effect, covar, mod, label, control, data, ...)

h_coxreg_extract_interaction(effect, covar, mod, data, at, control)

h_coxreg_inter_estimations(
  variable,
  given,
  lvl_var,
  lvl_given,
  mod,
  conf_level = 0.95
)

Arguments

x: (numeric or factor)
the values of the effect to be tested.
effect: (string)
the name of the effect to be tested and estimated.
covar: (string)
the name of the covariate in the model.
mod: (coxph)
a fitted Cox regression model (see survival::coxph()).
label: (string)
the label to be return as term_label (see return).
control: (list)
a list of controls as returned by control_coxreg().
...: see methods.
at: (list)
a list with items named after the covariate, every item is a vector of levels at which the interaction should be estimated.
data: (data.frame)
the data frame on which the model was fit.
variable, given: (string)
the name of variables in interaction. We seek the estimation of the levels of variable given the levels of given.
lvl_var, lvl_given: (character)
corresponding levels has given by levels().
conf_level: (proportion)
confidence level of the interval.

Value

A list of matrix (one per level of variable) with rows corresponding to the combinations of variable and given, with columns:

coef_hat: Estimation of the coefficient.
coef_se: Standard error of the estimation.
hr: Hazard ratio.
lcl, ucl: Lower/upper confidence limit of the hazard ratio.

Details

Given the cox regression investigating the effect of Arm (A, B, C; reference A) and Sex (F, M; reference Female) and the model being abbreviated: y ~ Arm + Sex + Arm:Sex. The cox regression estimates the coefficients along with a variance-covariance matrix for:

b1 (arm b), b2 (arm c)
b3 (sex m)
b4 (arm b: sex m), b5 (arm c: sex m)

The estimation of the Hazard Ratio for arm C/sex M is given in reference to arm A/Sex M by exp(b2 + b3 + b5)/ exp(b3) = exp(b2 + b5). The interaction coefficient is deduced by b2 + b5 while the standard error is obtained as $sqrt(Var b2 + Var b5 + 2 * covariance (b2,b5))$.

Functions

h_coxreg_inter_effect(numeric): Estimate the interaction with a numerical covariate
h_coxreg_inter_effect(factor): Estimate the interaction with a factor covariate.
h_coxreg_extract_interaction(): a higher level function that returns the test of the interaction test and the estimated values. If no interaction, h_coxreg_univar_extract() is applied.
h_coxreg_inter_estimations(): hazard ratio estimation in interactions.

Examples

library(survival)

set.seed(1, kind = "Mersenne-Twister")

# Testing dataset [survival::bladder].
dta_bladder <- with(
  data = bladder[bladder$enum < 5, ],
  data.frame(
    time = stop,
    status = event,
    armcd = as.factor(rx),
    covar1 = as.factor(enum),
    covar2 = factor(
      sample(as.factor(enum)),
      levels = 1:4,
      labels = c("F", "F", "M", "M")
    )
  )
)
labels <- c("armcd" = "ARM", "covar1" = "A Covariate Label", "covar2" = "Sex (F/M)")
formatters::var_labels(dta_bladder)[names(labels)] <- labels
dta_bladder$age <- sample(20:60, size = nrow(dta_bladder), replace = TRUE)

plot(
  survfit(Surv(time, status) ~ armcd + covar1, data = dta_bladder),
  lty = 2:4,
  xlab = "Months",
  col = c("blue1", "blue2", "blue3", "blue4", "red1", "red2", "red3", "red4")
)


mod <- coxph(Surv(time, status) ~ armcd * covar1, data = dta_bladder)
h_coxreg_extract_interaction(
  mod = mod, effect = "armcd", covar = "covar1", data = dta_bladder,
  control = control_coxreg()
)
#>                    effect   term        term_label level   n        hr
#> 1              Covariate: covar1 A Covariate Label       340        NA
#> armcd2/covar11 Covariate: covar1                 1     1  NA 0.6341111
#> armcd2/covar12 Covariate: covar1                 2     2  NA 0.5845305
#> armcd2/covar13 Covariate: covar1                 3     3  NA 0.5507703
#> armcd2/covar14 Covariate: covar1                 4     4  NA 0.6910643
#>                      lcl      ucl      pval pval_inter
#> 1                     NA       NA 0.1302825   0.988245
#> armcd2/covar11 0.3514676 1.144051        NA         NA
#> armcd2/covar12 0.2716689 1.257692        NA         NA
#> armcd2/covar13 0.2244668 1.351415        NA         NA
#> armcd2/covar14 0.2315248 2.062715        NA         NA
mod <- coxph(Surv(time, status) ~ armcd * covar1, data = dta_bladder)
result <- h_coxreg_inter_estimations(
  variable = "armcd", given = "covar1",
  lvl_var = levels(dta_bladder$armcd),
  lvl_given = levels(dta_bladder$covar1),
  mod = mod, conf_level = .95
)
result
#> $armcd2
#>                      coef  se(coef)        hr       lcl      ucl
#> armcd2/covar11 -0.4555312 0.3010803 0.6341111 0.3514676 1.144051
#> armcd2/covar12 -0.5369464 0.3909383 0.5845305 0.2716689 1.257692
#> armcd2/covar13 -0.5964375 0.4579624 0.5507703 0.2244668 1.351415
#> armcd2/covar14 -0.3695225 0.5579418 0.6910643 0.2315248 2.062715
#> 
#> attr(,"details")
#> [1] "Estimations of armcd hazard ratio given the level of covar1 compared to armcd level 1."