deterministic_bias_analysis

Deterministic Bias Analysis for an Unmeasured Confounder

Description

Adjusts an observed arm risk difference for a single hypothetical dichotomous, time-fixed unmeasured confounder, given its prevalence in each arm and its effect on the outcome. This ports the deterministic unmeasured-confounding sensitivity analysis of García-Albéniz et al. (supplementary analysis): how far would the screening effect move if a confounder of a specified strength, more common in one arm than the other, were left uncontrolled?

Usage

deterministic_bias_analysis(
  rd,
  prev_continue,
  prev_stopbase,
  confounder_effect
)

Arguments

rd Observed arm risk difference (CONTINUE minus STOPBASE).

prev_continue Confounder prevalence in the CONTINUE arm (0-1).

prev_stopbase Confounder prevalence in the STOPBASE arm (0-1).

confounder_effect Additive effect of the confounder on outcome risk (risk when present minus risk when absent), on the same scale as rd.

Details

For a dichotomous confounder with prevalence prev_continue in the CONTINUE arm and prev_stopbase in the STOPBASE arm, and an additive effect confounder_effect on the outcome risk (the risk when the confounder is present minus the risk when it is absent), the bias it induces in the arm risk difference (CONTINUE minus STOPBASE) is (prev_continue - prev_stopbase) * confounder_effect. The bias-adjusted risk difference is rd minus that bias.

The arguments are recycled to a common length, so passing vectors sweeps a grid of assumptions in one call (e.g., several confounder prevalences against a fixed effect). Express rd and confounder_effect on the same scale (a risk difference, e.g., cases per person or per 1000); the result is on that scale.

Value

A data frame with one row per assumption set, containing rd, prev_continue, prev_stopbase, confounder_effect, bias ((prev_continue - prev_stopbase) * confounder_effect), and adjusted_rd (rd - bias).

References

García-Albéniz X, Uno H, Bhatt DL, McArdle PH, Joffe MM, Hernán MA. Continuation of Annual Screening Mammography and Breast Cancer Mortality in Women Older Than 70 Years: A Prospective Observational Study. Ann Intern Med. 2020;172(6):381-389. doi:10.7326/M18-1199

Examples

Code

library("ettbc")

# A confounder 4 points more common in STOPBASE, raising outcome risk by 0.01
deterministic_bias_analysis(
  rd = -0.012,
  prev_continue = c(0.01, 0.05, 0.10),
  prev_stopbase = 0.05,
  confounder_effect = 0.01
)

      rd prev_continue prev_stopbase confounder_effect   bias adjusted_rd
1 -0.012          0.01          0.05              0.01 -4e-04     -0.0116
2 -0.012          0.05          0.05              0.01  0e+00     -0.0120
3 -0.012          0.10          0.05              0.01  5e-04     -0.0125