Attributable Risk

# Forward attributable fraction
af <- attrdl(exposure, cb, outcome, model, type = "af", cen = cen_value)

# Forward attributable number
an <- attrdl(exposure, cb, outcome, model, type = "an", cen = cen_value)

Key Arguments

• cen: Centering value (reference for "no effect"). Must match crosspred() centering.
• type: "af" or "an".
• dir: "forw" (forward) or "back" (backward).
• range: Exposure range to consider (e.g., c(cen_value, max(exposure)) for heat only).

📈 Confidence Intervals via Monte Carlo

set.seed(42)
nsim <- 1000
sim_coefs <- mvrnorm(nsim, coef(model), vcov(model))

af_sim <- sapply(1:nsim, function(i) {
  attrdl(exposure, cb, outcome, model, type = "af",
         cen = cen_value, coef = sim_coefs[i, ], vcov = NULL)
})

af_ci <- quantile(af_sim, c(0.025, 0.975))

• mvrnorm: From MASS package. Simulates from multivariate normal.
• 1000 simulations: Standard minimum. Use more (5000-10000) for publication.
• Report: Point estimate with 95% empirical CI.

🎯 Component Attribution

For temperature studies, split into:

• Heat-attributable: Exposure > optimum (cen value)
• Cold-attributable: Exposure < optimum
• Mild/extreme: Further split by percentile thresholds

# Cold vs. Heat
af_cold <- attrdl(exposure, cb, outcome, model, type = "af",
                  cen = cen_value, range = c(min(exposure), cen_value))
af_heat <- attrdl(exposure, cb, outcome, model, type = "af",
                  cen = cen_value, range = c(cen_value, max(exposure)))

📚 References

• Attributable Risk Code
• Gasparrini & Leone 2014 (BMC Med Res Methodology)