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Cox Regression Helper: Interactions

Source: R/cox_regression_inter.R
cox_regression_inter.Rd

[Stable]

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

# Testing dataset [survival::bladder].
library(survival)
library(rtables)

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


library(survival)

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
# Testing dataset [survival::bladder].
library(survival)

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."