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Power or required sample size for a 2x2 table with PPI++ surrogates

power_ppi_2x2.Rd

Computes power or solves for the required labeled sample size for testing an odds ratio (OR) or relative risk (RR) from a 2x2 contingency table when a binary PPI++ surrogate is available.

Follows the pwr convention: exactly one of n or power must be NULL.

Odds ratio (default): Uses logistic regression with design matrix \([1, X]\) where \(X \in \{0,1\}\) is the group indicator. The effect is \(\beta_1 = \log(\text{OR})\). Analytical variance blocks are computed from the cell probabilities and surrogate performance, then passed to power_ppi_regression().

Relative risk: Uses the delta method on per-group PPI++ mean estimates. The test statistic is a Wald test for \(\log(\hat p_1 / \hat p_0)\).

Usage

power_ppi_2x2(
  p_exp,
  p_ctrl,
  N,
  n = NULL,
  power = NULL,
  alpha = 0.05,
  prev_exp = 0.5,
  sens,
  spec,
  effect_measure = c("OR", "RR"),
  lambda_mode = "oracle",
  lambda_user = NULL,
  warn_smallN = TRUE,
  ...
)

Arguments

p_exp

Numeric scalar. Probability of outcome in the exposed group, \(P(Y = 1 \mid X = 1)\).

p_ctrl

Numeric scalar. Probability of outcome in the control group, \(P(Y = 1 \mid X = 0)\).

N

Positive integer. Total number of unlabeled observations.

n

Total number of labeled observations. Set to NULL to solve for the required n.

power

Target power. Set to NULL to compute power from n.

alpha

Significance level (default 0.05).

prev_exp

Numeric scalar. Prevalence of exposure, \(P(X = 1)\). Default 0.5 (balanced groups).

sens

Sensitivity of the binary surrogate classifier.

spec

Specificity of the binary surrogate classifier.

effect_measure

Character. "OR" (odds ratio, default) or "RR" (relative risk).

lambda_mode

"oracle" (default), "vanilla", or "user".

lambda_user

Scalar lambda when lambda_mode = "user".

warn_smallN

Logical. Warn when N is small.

...

Additional arguments (currently unused).

Value

When computing power: scalar in [0, 1]. When computing sample size: integer n required.

Examples

# OR test: exposed group has higher risk
power_ppi_2x2(
  p_exp = 0.40, p_ctrl = 0.20,
  N = 500, n = 80, alpha = 0.05,
  sens = 0.85, spec = 0.85,
  effect_measure = "OR"
)
#> [1] 0.6631492

# Solve for required n
power_ppi_2x2(
  p_exp = 0.40, p_ctrl = 0.20,
  N = 500, power = 0.80, alpha = 0.05,
  sens = 0.85, spec = 0.85,
  effect_measure = "OR"
)
#> [1] 115

# RR test
power_ppi_2x2(
  p_exp = 0.40, p_ctrl = 0.20,
  N = 500, n = 80, alpha = 0.05,
  sens = 0.85, spec = 0.85,
  effect_measure = "RR"
)
#> [1] 0.6410825