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Estimate attributable fraction in the exposed (AFE) and population attributable fraction (PAF)

Source: R/paf.R
paf.Rd

Computes the attributable fraction in the exposed (AFE) and the population attributable fraction (PAF) with 95% Confidence Intervals (95% CIs) for a binary exposure (coded 0/1) and either:

  • a binary outcome (prevalence / risk) when y_t is NULL, or

  • a time-to-event outcome (incidence) using a Cox proportional hazards model when y_t is provided.

For the binary-outcome case, risks are estimated as group-wise means and the relative risk (RR) is risk_exposed / risk_unexposed. Wald 95% confidence intervals are calculated on the log(RR) scale using a delta-method standard error, then transformed to RR, AFE, and PAF.

For the time-to-event case, a Cox model is fitted and the hazard ratio (HR) for exposure is used as the effect measure. Wald 95% confidence intervals are taken from the Cox model, then transformed to AFE and PAF. Crude incidence rates (per 1,000 person-years) are also returned by exposure group (assumes time is in years).

Usage

paf(d, x, y, y_t = NULL, z = "", verbose = FALSE)

Arguments

d

A data frame containing exposure, outcome, and (optionally) follow-up time and covariates.

x

Character string. Column name of the exposure variable (expected 0/1).

y

Character string. Column name of the outcome variable (0/1; event indicator for survival).

y_t

Character string. Optional column name of follow-up time for time-to-event analyses. Ideally this is in years, as crude incidence rates (per 1,000 person-years) are also returned. If not provided then treats y as a binary outcome and estimates RR-based AFE/PAF. default=NULL (character)

z

A string. The covariate formula (e.g., "+age+sex") for variables found in d. Only used for time-to-event. If not provided then the survival model runs without adjustment. default="" (character)

verbose

Logical. Be verbose, default=FALSE

Value

A data frame containing AFE and PAF (as proportions and percentages) with 95% CIs and p-values, plus supporting statistics (RR/HR, group risks or rates, counts, and exposure prevalence).

Details

Coding assumptions:

  1. x should be coded 0/1 (unexposed/exposed).

  2. For the binary-outcome case, y should be 0/1.

  3. For the time-to-event case, y is the event indicator (0/1) and y_t is follow-up time (in years if you want rates per 1,000 person-years).

Model note (time-to-event): the Cox model is not adjusted by default. User can provide covariae string.

Author

Luke Pilling

Examples


# Binary exposure
example_data$hypertension <- dplyr::if_else(example_data$sbp>=140, 1, 0)

# Binary outcome (prevalence / risk)
result_1 <- paf(
  d = example_data,
  x = "hypertension",
  y = "event"
)
cat(sprintf("PAF: %.2f%% (95%% CI: %.2f%% to %.2f%%)\n",
            result_1$paf_percent,
            result_1$paf_ci_lower_percent,
            result_1$paf_ci_upper_percent))
#> PAF: 13.75% (95% CI: 10.84% to 16.71%)

# Time-to-event outcome (incidence)
result_2 <- paf(
  d = example_data,
  x = "hypertension",
  y = "event",
  y_t = "time",
  z = "age+sex"
)
cat(sprintf("PAF: %.2f%% (95%% CI: %.2f%% to %.2f%%)\n",
            result_2$paf_percent,
            result_2$paf_ci_lower_percent,
            result_2$paf_ci_upper_percent))
#> PAF: 17.43% (95% CI: 13.56% to 21.36%)