Design quantities and trigger probabilities at a trial size

At trial size n, for the standard sets of an ahr_population() with hazard ratio b outside H* and h inside: each set's limit and its model-based and robust SEs (using \(E[1/n_S]\), \(n_S \sim Bin(n, \pi_S)\)), expected events, the exact and SE-ratio correlations between nested sets' estimates, and, from the trivariate normal approximation (estimates \(\sim N(\beta^*, SE_{robust}^2)\), exact correlations, the Wald limit of the ITT with the model SE):

p_itt_ub_lt1: P(ITT upper 95\
p_region_itt_gt1: P(region ITT estimate > 1);
p_region_Gstar_lt1: P(region(G*) estimate < 1);
p_trigger: P(ITT ub < 1 and region ITT > 1);
p_trigger_and_Gstar_lt1: P(trigger and region(G*) < 1), the oracle joint.

Probabilities use mvtnorm::pmvnorm(algorithm = Miwa(steps = 1024)).

Usage

ahr_design(
  pop,
  b,
  h,
  n,
  sets = c("all", "region", "region_Gstar"),
  b_R = b,
  h_R = h
)

Arguments

pop: An ahr_population().
b, h: Hazard ratios outside and inside H*. All sets use the population's cached grid (built for \(0.2 \le b, h \le 30\); outside that range the grid's first panel is coarser than the library's).
n: Trial size (both arms).
sets: Standard set names to report (see ahr_limit()); the trigger sets "all", "region" and "region_Gstar" are always computed.
b_R, h_R: Hazard ratios inside the region, outside and inside H* (the four-cell model of ahr_limit()); default b_R = b, h_R = h, the two-cell model.

Value

A list: sets (a data.frame per set: set, share, beta, marghr (at the analysis time), se_model, se_robust, se_d4 (\(\sqrt{4/events}\)), info_ratio, events (expected, of n), ahr, cde), corr (a data.frame per nested pair: big, small, exact, se_ratio, pi), prob (the named probabilities above), and b, h, n, b_R, h_R.

Limits

Weibull AFT DGMs from inject_mrct_structure() only; entry uniform on \((a_i, a_i + R)\) for each entry group; administrative censoring only (the random censoring model of the DGM, e.g. cens_adjust, is not in the layer); correlations exact for nested sets. Each distinct delay is one quadrature group with its own breaks, so a delay vector with many distinct values is slow. Derivations: the technical report (docs/manuscript/techreport/analytic-layer.qmd, Chapter 6, of the mrct-consistency repository) and the theory notes (docs/theory/AHR_mrct_dgm.qmd, docs/theory/AHR_complete.qmd).

Examples

if (FALSE) { # \dontrun{
pop <- ahr_population(dgm, 40, 11)
ahr_design(pop, b = 0.55, h = 2, n = 1000)$prob
} # }