Log-Binomial Regression Inference for Incidence Responses
Source:R/inference_incidence_log_binomial.R
InferenceIncidLogBinomial.RdFits a binomial regression with the log link for binary
(incidence) responses: \(\log P(Y_i = 1) = \beta_0 + \beta_T W_i +
X_i^\top \gamma\), where \(W_i\) is the treatment indicator and \(X_i\)
are optional recorded covariates, by maximum likelihood
(fast_log_binomial_regression_cpp/
fast_log_binomial_regression_weighted_cpp). \(\hat\beta_T\)
is a log risk ratio: \(\exp(\hat\beta_T)\) is the estimated
treatment risk ratio (relative risk) directly, unlike the log-odds-ratio
from InferenceIncidLogRegr's logit
link. likelihood_tier = "full": Wald, score, gradient, and
likelihood-ratio tests are all available when the model converges, plus
parametric-likelihood-bootstrap calibration of the likelihood-ratio test.
Because the log link does not constrain fitted probabilities to
\([0,1]\) (only to \([0,\infty)\)), fits are hardened by QR
column-dropping and a coefficient-magnitude cap
(max_abs_reasonable_coef) and rejected as nonestimable when the fit
is implausible — the same practical limitation as the identity-link
sibling
InferenceIncidBinomialIdentityRiskDiff, here applying to the upper rather
than both tails of the probability scale. Validity requires the
multiplicative log-linear risk model to be correctly specified over the
covariate range observed.
Computes the randomization distribution of the treatment effect estimate under the sharp null.
Whether compute_rand_two_sided_pval() is actually
usable on this instance right now – FALSE exactly when it
would stop(): an incidence-response instance with no
custom randomization statistic and a design not eligible for
design-randomization-based incidence inference (see
private$should_use_design_randomization_for_incidence()).
TRUE for every other case, including every non-incidence
response type. Public, self-contained (only reads already-set
instance state, no side effects), so InferenceSuite can
check this before attempting the sentinel instead of relying on
the stop() being silently swallowed into a pval = NA
"ok" row – the single source of truth for both this check and
compute_rand_two_sided_pval()'s own guard, so the two can
never drift apart.
Value
When debug = FALSE (default), a numeric vector of length r. When
debug = TRUE, a list with: values, errors (list of character
vectors, one per iteration), warnings (list of character vectors, one per
iteration), num_errors, num_warnings,
prop_iterations_with_errors, prop_iterations_with_warnings, and
prop_illegal_values.
A single logical.
References
McCullagh, P., and Nelder, J. A. (1989). Generalized Linear Models (2nd ed.). Chapman and Hall/CRC, for the binomial GLM family and log-link relative-risk parameterization.
See also
InferenceIncidLogRegr
(logit link, log-odds-ratio estimand),
InferenceIncidBinomialIdentityRiskDiff (identity link, risk-difference
estimand) for alternative link/estimand choices on the same response
type. Comparable Python API:
statsmodels GLM
(family=Binomial(link=log())). See also:
Generalized
linear model (Wikipedia).
Super class
Inference -> InferenceIncidLogBinomial
Methods
+ inherited public methods from Inference
Inference$capabilities()Inference$compute_asymp_confidence_interval()Inference$compute_asymp_two_sided_pval()Inference$compute_estimate()Inference$compute_exact_confidence_interval()Inference$compute_exact_two_sided_pval_for_treatment_effect()Inference$duplicate()Inference$get_analysis_data()Inference$get_covariates()Inference$get_design_object()Inference$get_model_formula()Inference$get_nonestimable_reason()Inference$get_nonestimable_stage()Inference$get_optimization_alg()Inference$get_response()Inference$get_response_type()Inference$get_treatment()Inference$initialize()Inference$is_nonestimable()Inference$set_optimization_alg()Inference$set_seed()Inference$supports()
InferenceIncidLogBinomial$approximate_randomization_distribution_beta_hat_T()
Usage
InferenceIncidLogBinomial$approximate_randomization_distribution_beta_hat_T(
r = 501,
delta = 0,
transform_responses = "none",
show_progress = TRUE,
permutations = NULL,
debug = FALSE,
zero_one_logit_clamp = .Machine$double.eps
)Arguments
rNumber of randomization vectors. Default 501.
deltaThe null difference. Default 0.
transform_responsesType of transformation. Default "none".
show_progressShow progress bar. Default TRUE.
permutationsPre-computed permutations. Default NULL.
debugIf
TRUE, return a list with the distribution values and per-iteration diagnostics including error messages, warning messages, counts of each, and summary proportions for iterations with errors, warnings, and illegal (non-finite) values. Runs serially. DefaultFALSE.zero_one_logit_clampThe clamping amount for exact 0 and 1 values when logging
Examples
# \donttest{
seq_des = DesignSeqOneByOneBernoulli$new(n = 10, response_type = 'incidence')
for (i in 1:10) {
seq_des$add_one_subject_to_experiment_and_assign(data.frame(x1 = rnorm(1)))
}
seq_des$add_all_subject_responses(rbinom(10, 1, 0.5))
inf = InferenceIncidLogBinomial$new(seq_des)
inf$compute_estimate()
#> [1] -0.4743116
# }