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Discriminatory accuracy of a binary MAIHDA model

Source: R/discriminatory_accuracy.R
maihda_discriminatory_accuracy.Rd

Bundles the individual-level discriminatory-accuracy summaries for a binomial MAIHDA model: the AUC / C-statistic (how well the model's predicted probabilities separate cases from non-cases) and the Median Odds Ratio. Applied to a strata-only (null) model, the AUC is the discriminatory accuracy of the intersectional strata themselves – Merlo's central quantity; comparing it with an adjusted model shows whether individual covariates beyond stratum membership sharpen classification. The AUC is computed for any binomial link; the Median Odds Ratio is reported only for the logit link and is NA otherwise (e.g. for a probit fit), since the MOR is an odds-ratio-scale quantity.

Aggregated-binomial fits are supported on both engines that fit them – an lme4 cbind(success, failure) response and a brms y | trials(n) response: the AUC is the count-weighted C-statistic over the implied individual-level 0/1 data, and n_case / n_control are the total successes / failures.

Usage

maihda_discriminatory_accuracy(model)

Arguments

model

A maihda_model from fit_maihda fitted with a binomial family – including an aggregated response (an lme4 cbind(success, failure) or a brms y | trials(n)) – or the bernoulli family a binary 0/1 outcome is fit with under engine = "brms".

Value

An object of class maihda_da: a list with auc, mor, n_case, n_control, family, link and engine. mor is NA for a non-logit binomial link, where the AUC is still reported. For an aggregated-binomial fit n_case / n_control are the total successes / failures.

References

Merlo, J. (2018). Multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) within an intersectional framework. Social Science & Medicine, 203, 74-80.

See also

maihda_auc, maihda_mor

Examples

# \donttest{
# Obese (Yes/No) by intersectional strata of Gender x Race
strata <- make_strata(maihda_health_data, vars = c("Gender", "Race"))
d <- maihda_health_data
d$stratum <- strata$data$stratum
m <- fit_maihda(Obese ~ (1 | stratum), data = d, family = "binomial")
#> Binary outcome 'Obese' recoded to 0/1: 'No' = 0 (reference), 'Yes' = 1 (modeled event). Set the factor levels (or supply a 0/1 outcome) to control which level is the event.
maihda_discriminatory_accuracy(m)
#> Discriminatory accuracy (binomial MAIHDA)
#>   AUC (C-statistic): 0.571
#>   Median Odds Ratio: 1.482
#>   Cases / controls:  1077 / 1923
# }