Cookbook: Incidence (Binary) Outcome, End to End

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One complete, runnable script for a binary (“incidence”) outcome — did the event happen or not. Same four steps as every cookbook (design → assign → record → infer); see vignette("cookbook-continuous") for the narrated version of the pattern. Here the response is 0/1, the natural estimand is a log odds ratio (or a risk difference / risk ratio via the g-computation classes), and the inference classes are the InferenceIncid* family.

Setup

EDI is not on CRAN yet, so install.packages("EDI") fails — install from R-universe (fallback: GitHub, subdir = "R/EDI"). Not evaluated here.

install.packages("EDI", repos = c("https://kapelner.r-universe.dev", "https://cloud.r-project.org"))
# or: remotes::install_github("kapelner/EDI", subdir = "R/EDI")

library(EDI)
set.seed(20260916)

n = 80
X = data.frame(
  age    = round(rnorm(n, 50, 10)),
  smoker = rbinom(n, 1, 0.3)
)
true_log_or = 0.9

Fixed design, logistic regression

des = DesignFixedBernoulli$new(n = n, response_type = "incidence", verbose = FALSE)
des$add_all_subjects_to_experiment(X)
des$assign_w_to_all_subjects()
w = des$get_w()

p = plogis(-1.2 + true_log_or * w + 0.03 * (X$age - 50) + 0.6 * X$smoker)
y = rbinom(n, 1, p)
des$add_all_subject_responses(y)

inf = InferenceIncidLogRegr$new(des, verbose = FALSE)
inf$num_cores = 1L
inf$compute_estimate()                         # log odds ratio for treatment
#> [1] 1.499761
inf$compute_asymp_confidence_interval(alpha = 0.05)
#>      2.5%     97.5% 
#> 0.4997003 2.4998222
inf$compute_asymp_two_sided_pval()
#> [1] 0.003289556

Randomization test and bootstrap, as in the continuous cookbook:

inf$set_seed(1)
inf$compute_rand_two_sided_pval(r = 200, show_progress = FALSE)
#> [1] 0.00264537
inf$set_seed(1)
inf$compute_bootstrap_confidence_interval(alpha = 0.05, B = 200, show_progress = FALSE)
#>  2.5% 97.5% 
#>    NA    NA

A risk difference instead of an odds ratio

The g-computation classes estimate a marginal risk difference or risk ratio by standardizing over the covariates — often the estimand a trial actually reports. Same design object, different class:

inf_rd = InferenceIncidGCompRiskDiff$new(des, verbose = FALSE)
inf_rd$num_cores = 1L
inf_rd$compute_estimate()
#> [1] 0.3322325
inf_rd$compute_asymp_confidence_interval(alpha = 0.05)
#>      2.5%     97.5% 
#> 0.1300459 0.5344191

Everything at once

suite = InferenceSuite$new(des)
res = suite$run_all_inference(screen = TRUE, plots = FALSE, num_cores = 1L,
                              methods = c("wald", "score", "lik_ratio"), max_secs_per_class = 15)
#> inference       cov      estimand    est       se        pval       pval method     status 
#> class           mod                                                                        
#> ===========================================================================================
#> Classes 0/25  [                0%                 ] Status: Estimating...[KAvg Δ                    mean Δ      0.331     0.104     2.19e-03   wald            ok     
#> Classes 1/25  [=              4%                ] Estimated Time Left: 2s[KAvg Δ Pooled …           mean Δ      0.331     0.103     1.81e-03   wald            ok     
#> Classes 2/25  [==             8%                ] Estimated Time Left: 1s[KBinom Ident R…  ~.       mean Δ      0.343     0.104     8.85e-04   wald            ok     
#> Classes 3/25  [===            12%               ] Estimated Time Left: 1s[KBinom Ident R…  ~.       mean Δ      0.343     0.104     1.95e-03   score           ok     
#> Classes 4/25  [=====          16%               ] Estimated Time Left: 1s[KBinom Ident R…  ~.       mean Δ      0.343     0.104     1.95e-03   lik_ratio       ok     
#> Classes 5/25  [======         20%               ] Estimated Time Left: 1s[KCMH                      mean Δ      0.331     0.135     1.38e-02   wald            ok     
#> Classes 6/25  [=======        24%               ] Estimated Time Left: 1s[KExact Zhang              logodds c…  1.45      NA        NA         NA              ok     
#> Classes 7/25  [=========      28%               ] Estimated Time Left: 1s[KG Comp Risk Δ   ~.       mean Δ      0.332     0.103     1.28e-03   wald            ok     
#> Classes 8/25  [==========     32%               ] Estimated Time Left: 1s[KG Comp Risk R…  ~.       risk ratio  2.59      0.850     3.72e-03   wald            ok     
#> Classes 9/25  [===========    36%               ] Estimated Time Left: 1s[KLog Binom       ~.       log risk …  0.941     0.333     5.36e-03   wald            ok     
#> Classes 10/25 [=============  40%               ] Estimated Time Left: 1s[KLog Binom       ~.       log risk …  0.941     0.333     1.32e-03   score           ok     
#> Classes 11/25 [============== 44%               ] Estimated Time Left: 1s[KLog Binom       ~.       log risk …  0.941     0.333     2.13e-03   lik_ratio       ok     
#> Classes 12/25 [============== 48%               ] Estimated Time Left: 0s[KLogist Regr     ~.       logodds m…  1.50      0.510     3.29e-03   wald            ok     
#> Classes 13/25 [============== 52%               ] Estimated Time Left: 0s[KLogist Regr     ~.       logodds m…  1.50      0.510     2.45e-03   score           ok     
#> Classes 14/25 [============== 56%               ] Estimated Time Left: 0s[KLogist Regr     ~.       logodds m…  1.50      0.510     2.25e-03   lik_ratio       ok     
#> Classes 15/25 [============== 60%               ] Estimated Time Left: 0s[KMiettinen Ris…           mean Δ      0.331     0.103     2.26e-03   wald            ok     
#> Classes 16/25 [============== 64% ==            ] Estimated Time Left: 0s[KModified Pois…  ~.       log risk …  0.951     0.409     1.99e-02   wald            ok     
#> Classes 17/25 [============== 68% ===           ] Estimated Time Left: 0s[KModified Pois…  ~.       log risk …  0.951     0.409     1.60e-02   score           ok     
#> Classes 18/25 [============== 72% ====          ] Estimated Time Left: 0s[KModified Pois…  ~.       log risk …  0.951     0.409     1.51e-02   lik_ratio       ok     
#> Classes 19/25 [============== 76% ======        ] Estimated Time Left: 0s[KNewcombe Risk…           mean Δ      0.331     NA        1.99e-03   wald            ok     
#> Classes 20/25 [============== 80% =======       ] Estimated Time Left: 0s[KProbit Regr     ~.       probit ma…  0.922     0.305     2.52e-03   wald            ok     
#> Classes 21/25 [============== 84% ========      ] Estimated Time Left: 0s[KProbit Regr     ~.       probit ma…  0.922     0.305     2.56e-03   score           ok     
#> Classes 22/25 [============== 88% ==========    ] Estimated Time Left: 0s[KProbit Regr     ~.       probit ma…  0.922     0.305     2.21e-03   lik_ratio       ok     
#> Classes 23/25 [============== 92% ===========   ] Estimated Time Left: 0s[KRisk Δ          ~.       mean Δ      0.332     0.103     1.24e-03   wald            ok     
#> Classes 24/25 [============== 96% ============  ] Estimated Time Left: 0s[KWald                     mean Δ      0.331     0.103     1.27e-03   wald            ok     
#> Classes 25/25 [============= 100% ==============] Estimated Time Left: 0s[K-------------------------------------------------------------------------------------------
#> Status: Completed in 1s.
#> 
#>   Estimand: risk ratio (1 inferences)      : p =      NA
#>   Estimand: logodds marginal (3 inferences): p = 0.00259
#>   Estimand: log risk ratio (6 inferences)  : p = 0.00377
#>   Estimand: mean Δ (11 inferences)         : p = 0.00168
#>   Estimand: probit marginal (3 inferences) : p = 0.00242
#> 
#> Combined evidence against the sharp null across 5 estimands
#> (24 inferences, weighting = uniform within estimand):
#> p = 0.00259

Sequential design: matching on the fly

DesignSeqOneByOneKK14 matches each arrival to an earlier unmatched subject when a close enough match exists. Its matched inference class for a binary outcome, InferenceIncidKKGCompRiskDiff, uses the pair/reservoir structure directly. As on every sequential design whose assignments depend on earlier subjects, the nonparametric bootstrap is not offered; randomization inference replays the design’s own mechanism instead.

des_seq = DesignSeqOneByOneKK14$new(n = n, response_type = "incidence", verbose = FALSE)
for (i in seq_len(n)) {
  w_i = des_seq$add_one_subject_to_experiment_and_assign(X[i, , drop = FALSE])
  p_i = plogis(-1.2 + true_log_or * w_i + 0.03 * (X$age[i] - 50) + 0.6 * X$smoker[i])
  des_seq$add_one_subject_response(i, rbinom(1, 1, p_i))
}

inf_seq = InferenceIncidKKGCompRiskDiff$new(des_seq, verbose = FALSE)
inf_seq$num_cores = 1L
inf_seq$compute_estimate()
#> [1] 0.2046291
inf_seq$compute_asymp_confidence_interval(alpha = 0.05)
#>       2.5%      97.5% 
#> 0.01616501 0.39309318
inf_seq$set_seed(1)
inf_seq$compute_rand_two_sided_pval(r = 200, show_progress = FALSE)
#> [1] 0.1553835

Where to go next

Every incidence class: the reference index, section Inference: Incidence (Binary) Outcomes.
Exact (Fisher-style) and CMH procedures for stratified/blocked designs are in the same family — InferenceSuite will run whichever apply to your design.
vignette("validation-evidence") lists how each was checked.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.