Power calculation to detect overall treatment effect and interaction effect

Calculate power for overall treatment effect (not utilizing any covariates) and the power of the interaction test (under the true model, which is Y=f_prog+(b0+b1*f_pred)*trt). The calculation is performed conditional on a given data set of covariates (prognostic effects specified via prog_vals; predictive effects specified via pred_vals) and a treatment indicator. It is assumed that the treatment indicator is independent of the columns in X). The power of the overall test and the interaction test will depend on the actual observed covariates. To make calculations independent of the actual observed covariates (to focus on the super-population) it is suggested to simulate a large number of covariates (e.g. 100 times larger sample size than one would be interested in), based on this one can determine the covariance matrix of the estimates. To obtain a covariance matrix estimate for the sample size one is interested in one can then scale up the covariance matrix estimate (e.g. by 100-fold in the example above).

calc_power(
  b,
  scal,
  prog_vals,
  trt,
  pred_vals,
  alpha,
  type,
  theta,
  sign_better,
  sigma_error,
  lambda0,
  cens_time,
  t_mile
)

Arguments

b

Vector of length 2: Coefficient for treatment indicator and predictive term in the true model

scal

Scaling parameter for the covariance matrix

prog_vals

Vector of main effects (one value per patient)

trt

Vector of treatment indicators

pred_vals

Vector of predictive effects (one value per patient)

alpha

Vector of length 2, specifying the desired type 1 error for the overall and the interaction test. The overall test is performed as a one-sided test (see also argument sign_better). The interaction test is performed as a two-sided test.

type

type of data "continuous", "binary", "count" and "survival" are allowed here, but calculations are only implemented for "continuous" and "binary".

theta

overdispersion parameter for type "count"

sign_better

1 if larger response is better, -1 is smaller response is better (used in power calculation for the overall test only)

sigma_error

Residual variance assumed for type = "continuous"

lambda0

Intercept of exponential regression (on non-log scale)

cens_time

function that generates random censoring times

t_mile

time-point for comparing the survival probabilities for test of overall treatment effect

Value

Vector of two power values

Examples

###### generate a matrix of covariates
scal <- 100
X <- generate_X_dist(n = 500 * scal, p = 30, rho = 0.5)
trt <- generate_trt(n = 500 * scal, p_trt = 0.5)
prog <- "0.5*((X1=='Y')+X11)"
pred <- "X11>0.5"
pred_vals <- with(X, eval(parse(text = pred)))
prog_vals <- with(X, eval(parse(text = prog)))
alpha <- c(0.025, 0.1)
calc_power(
  b = c(0, 0), scal, prog_vals, trt, pred_vals, alpha,
  type = "continuous", sigma_error = 1, sign_better = 1
)
#> [1] 0.025 0.100
calc_power(
  b = c(0.2, 0.3), scal, prog_vals, trt, pred_vals, alpha,
  type = "continuous", sigma_error = 1, sign_better = 1
)
#> [1] 0.7969131 0.6069333
calc_power(
  b = c(0, 0), scal, prog_vals, trt, pred_vals, alpha,
  type = "binary", sign_better = 1
)
#> [1] 0.025 0.100
calc_power(
  b = c(0.5, 0.8), scal, prog_vals, trt, pred_vals, alpha,
  type = "binary", sign_better = 1
)
#> [1] 0.9161490 0.5881828