NAPrior (version 0.2.0)

post_w: Posterior mixture weight calculation

Description

Computes posterior updated mixture weights for a two-component normal–normal model using the standard logit-additive update. The prior mixing weight is either a fixed weight \(w \in (0,1)\) or a dynamic mixing weight as for eNAP prior: \(Z = n_{eff}^{-1/4}|y_{\mathrm{dir}} - y_{\mathrm{ind}}| / s_{\mathrm{link}}\): where, \(n_{eff}= s_{\mathrm{link}}^{-1}\)

\(w_(Z) = 1/exp(a + b \log (Z+1)), \quad a<0, \; b > 0.\)

Usage

post_w(
  w,
  a,
  b,
  s_EC2,
  s_EC1,
  s_C2C1,
  y_EC2,
  y_EC1 = -0.5,
  y_C2C1 = -0.5,
  tau0 = 1000,
  mu0 = 0,
  eps = 1e-12
)

Value

A numeric vector of posterior weights in (0,1) reflecting realized borrowing fraction of the informative component.

Arguments

w

Scalar. If w > 1, use the ADAPTIVE branch (logistic prior on log-Z). If 0 < w < 1, use a fixed prior weight equal to w.

a, b

Parameters used in the elastic function for dynamic mixing weight. Must satisfy a < 0 and b > 0.

s_EC2, s_EC1, s_C2C1

Sampling variances for direct evidence (E vs. C2 trial), and edges of indirect evidence (E vs. C1 trial and C2 vs. C1 trial).

y_EC2, y_EC1, y_C2C1

Estimated log-HR for E vs. C2 tria, E vs. C1 trial, C2 vs. C1 trial, respectively

mu0, tau0

Mean and variance for the vague component.

eps

Numeric scalar used for small-value clipping (default 1e-12).

Details

• Fixed prior mixing weight (Robust NMAP Prior): requires 0 < w < 1.

• Adaptive branch (Adaptive NMAP Prior): triggered by w > 1, requires a<0 and b > 0. This corresponds to a decreasing prior weight as the inconsistency grows.

• All variance/SD arguments may be given as scalars or vectors; scalars are recycled.

Examples

y_EC2  <- -0.5; y_EC1  <- -0.8; y_C2C1 <- -0.3
s_EC2 <- 0.2; s_EC1 <- 0.18; s_C2C1 <- 0.18

# Fixed mixing weight 0.5
post_w(w = 0.5, a = NA, b = NA,s_EC2,s_EC1,s_C2C1,
       y_EC2,y_EC1,y_C2C1)

# Dynamic weight with elastic function of (a=-4.6, b=3):
post_w(w = 2, a = -2.5, b = 10,s_EC2,s_EC1,s_C2C1,
       y_EC2,y_EC1,y_C2C1)