Is a covariate confounded with cohort, and does it track the outcome?

WHY RANK TESTS AND FISHER: the same reasoning as everywhere else here – small n, no free normality assumption. A Fisher exact test asks whether a categorical covariate is balanced across cohorts, which stays exact at the cell counts a 2x3 sex-by-cohort table produces where chi-squared does not; a numeric one gets Kruskal-Wallis.

Usage

stats_confounding(
  freq,
  patients,
  smap,
  group_of,
  covariates = c("age", "sex"),
  value_col = NULL,
  min_n = 3L
)

Arguments

freq

population_frequencies table

patients

patient table (patient_id + the covariates)

smap

sample map (sample_id -> patient_id)

group_of

named vector sample_id -> cohort

covariates

column names in patients to examine

value_col

outcome column in freq; defaults to the abundance measure

min_n

Minimum samples per group before a test is attempted. Default 3L.

Value

data.frame; rows with population = NA carry the covariate-vs-cohort balance test, the rest carry covariate-vs-outcome association

Details

THE OUTCOME ASSOCIATION IS TAKEN WITHIN COHORTS. A confounder is associated with the exposure and with the outcome conditional on the exposure (Rothman, Greenland & Lash 2008, Modern Epidemiology, 3rd ed.). Tested across the pooled cohorts, a real group difference makes any unbalanced covariate track the outcome by itself: with two cohorts of ten, ages 30 and 55 and a group effect on the outcome with none of age, the pooled Spearman test called age a HIGH confounder risk in 199 of 200 simulated cohorts. So the association is a partial Spearman correlation controlling for cohort – the ranks with each cohort's mean rank removed, tested on n - 2 - (k - 1) degrees of freedom, as ppcor does – and, for a categorical covariate, a rank F test of the covariate after the cohort term. Where age and cohort barely overlap this has little power, which is the honest answer: the design cannot separate them, and the balance row already says the covariate is unbalanced.