tern (version 0.9.8)

estimate_coef: Hazard ratio estimation in interactions

Description

This function estimates the hazard ratios between arms when an interaction variable is given with specific values.

Usage

estimate_coef(
  variable,
  given,
  lvl_var,
  lvl_given,
  coef,
  mmat,
  vcov,
  conf_level = 0.95
)

Value

A list of matrices (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.

Arguments

variable, given

(character(2))
names of the two variables in the interaction. We seek the estimation of the levels of variable given the levels of given.

lvl_var, lvl_given

(character)
corresponding levels given by levels().

coef

(numeric)
vector of estimated coefficients.

mmat

(named numeric) a vector filled with 0s used as a template to obtain the design matrix.

vcov

(matrix)
variance-covariance matrix of underlying model.

conf_level

(proportion)
confidence level of estimate intervals.

Details

Given the cox regression investigating the effect of Arm (A, B, C; reference A) and Sex (F, M; reference Female). The model is abbreviated: y ~ Arm + Sex + Arm x 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)

Given that I want an estimation of the Hazard Ratio for arm C/sex M, the estimation will be given in reference to arm A/Sex M by exp(b2 + b3 + b5)/ exp(b3) = exp(b2 + b5), therefore the interaction coefficient is given by b2 + b5 while the standard error is obtained as $1.96 * sqrt(Var b2 + Var b5 + 2 * covariance (b2,b5))$ for a confidence level of 0.95.

See Also

s_cox_multivariate().

Examples

library(dplyr)
library(survival)

ADSL <- tern_ex_adsl %>%
  filter(SEX %in% c("F", "M"))

adtte <- tern_ex_adtte %>% filter(PARAMCD == "PFS")
adtte$ARMCD <- droplevels(adtte$ARMCD)
adtte$SEX <- droplevels(adtte$SEX)

mod <- coxph(
  formula = Surv(time = AVAL, event = 1 - CNSR) ~ (SEX + ARMCD)^2,
  data = adtte
)

mmat <- stats::model.matrix(mod)[1, ]
mmat[!mmat == 0] <- 0