Risk Difference Inference for Incidence Responses

Fits a linear probability model \(E[Y \mid w, x] = \beta_0 + \beta_T w + \beta_X^\top x\) via ordinary least squares for binary (incidence) responses \(Y \in \{0,1\}\), using the treatment indicator \(w\) and, optionally, all recorded covariates \(x\) as predictors. \(\hat\beta_T\) is reported directly as the risk-difference estimate: because \(Y\) is 0/1, the OLS fit coincides with a saturated/linear model for the conditional risk \(P(Y=1\mid w,x)\), so the coefficient on \(w\) is already on the risk-difference (probability) scale with no back-transformation needed. This is a misspecified working model for a binary response (heteroskedastic, errors not Gaussian: \(\mathrm{Var}(Y \mid w,x) = P(w,x)(1-P(w,x))\) varies by treatment arm and covariates, so a single pooled residual variance is the wrong variance model), so likelihood_tier = "none": standard errors and the Wald CI use the Huber-White (HC0) sandwich variance of \(\hat\beta_T\) – \((X'X)^{-1} X'\,\mathrm{diag}(e_i^2)\,X\, (X'X)^{-1}\), from the OLS residuals \(e_i\) – not the classical homoskedastic OLS variance and not a binomial likelihood, and no likelihood-ratio or parametric-bootstrap methods are exposed.

Super class

Inference -> InferenceIncidRiskDiff

Methods

Public methods

• InferenceIncidRiskDiff$new()

• InferenceIncidRiskDiff$compute_estimate()

• InferenceIncidRiskDiff$compute_asymp_confidence_interval()

• InferenceIncidRiskDiff$compute_asymp_two_sided_pval()

• InferenceIncidRiskDiff$compute_estimate_with_bootstrap_weights()

• InferenceIncidRiskDiff$clone()

+ inherited public methods from Inference

• Inference$capabilities()
• Inference$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$is_nonestimable()
• Inference$set_optimization_alg()
• Inference$set_seed()
• Inference$supports()

---

InferenceIncidRiskDiff$new()

Uses the randomization-CI layer's two-sided p-value contract (InferenceRandCI's version, not InferenceRand's): for incidence responses it dispatches to the Zhang exact randomization test rather than refusing outright, matching this class's pre-migration old-ladder behavior. This deliberately differs from the InferenceAllSimpleAverageDiff-family precedent of pinning InferenceRand's version, which would have regressed the working Zhang dispatch this class had on the old ladder.

Initialize a risk-difference inference object.

Usage

InferenceIncidRiskDiff$new(
  des_obj,
  model_formula = NULL,
  verbose = FALSE,
  smart_cold_start_default = NULL
)

Arguments

des_obj

A completed Design object with an incidence response.

model_formula

Optional formula for covariate adjustment. If NULL (default), the formula from the design object is used and its pre-computed design matrix is reused. If a formula is provided, a new design matrix is constructed from the design's imputed covariates.

verbose

Whether to print progress messages.

smart_cold_start_default

Whether to use smart cold start values.

r

Number of randomization vectors. @param delta Null difference.

transform_responses

Transformation. @param na.rm Remove NAs.

show_progress

Show progress. @param permutations Pre-computed permutations.

type

Optional exact-inference type for incidence dispatch.

args_for_type

Optional arguments for type.

zero_one_logit_clamp

Clamp for exact 0/1 values when logging.

---

InferenceIncidRiskDiff$compute_estimate()

Fits the OLS linear-probability model and returns the risk-difference point estimate \(\hat\beta_T\), the coefficient on treatment. On a hardened design (private$harden), or when estimate_only = FALSE, delegates to fast_ols_with_var_cpp() via the shared model cache so the variance is available for later confidence-interval/p-value calls without refitting.

Usage

InferenceIncidRiskDiff$compute_estimate(estimate_only = FALSE)

Arguments

estimate_only

If TRUE, skip the variance/degrees-of-freedom computation and return only \(\hat\beta_T\) (cheaper for simulation/randomization callers that never request inference).

---

InferenceIncidRiskDiff$compute_asymp_confidence_interval()

Wald confidence interval for the risk difference, \(\hat\beta_T \pm z_{1-\alpha/2}\, \hat s(\hat\beta_T)\), using the Huber-White (HC0) sandwich standard error from the cached model fit (see the class-level documentation) and a normal-quantile multiplier – fast_ols_with_var_cpp() doesn't report residual degrees of freedom, so private$compute_z_or_t_ci_from_s_and_df() always falls back to its \(z\) branch here, never a \(t\) reference, regardless of \(n\). Interval bounds are not clamped to \([-1, 1]\); a linear-probability model can produce out-of-range endpoints near the boundary of the covariate space.

Usage

InferenceIncidRiskDiff$compute_asymp_confidence_interval(alpha = 0.05)

Arguments

alpha

Two-sided miscoverage rate; the returned interval has nominal coverage \(1-\alpha\).

---

InferenceIncidRiskDiff$compute_asymp_two_sided_pval()

Two-sided Wald test of \(H_0: \beta_T = \delta\) vs. \(H_1: \beta_T \neq \delta\), via the Wald statistic \((\hat\beta_T - \delta) / \hat s(\hat\beta_T)\) (\(\hat s\) the Huber-White sandwich SE) referred to a standard normal distribution – same \(z\), not \(t\), reference as $compute_asymp_confidence_interval(), for the same reason (no residual degrees of freedom are ever cached for this class).

Usage

InferenceIncidRiskDiff$compute_asymp_two_sided_pval(delta = 0)

Arguments

delta

Null risk-difference value under \(H_0\) (default 0, no treatment effect).

---

InferenceIncidRiskDiff$compute_estimate_with_bootstrap_weights()

Refits the linear-probability model by weighted least squares (stats::lm.wfit()) under subject/block resampling weights (nonparametric-bootstrap replicate weights or Bayesian-bootstrap Dirichlet weights, both expanded to row weights via expand_subject_or_block_weights_to_row_weights()) and returns the re-estimated treatment coefficient. Rows with non-finite or non-positive weight are excluded; if too few positive-weight rows remain to identify the design, the replicate estimate is NA_real_.

Usage

InferenceIncidRiskDiff$compute_estimate_with_bootstrap_weights(
  subject_or_block_weights,
  estimate_only = FALSE
)

Arguments

subject_or_block_weights

Numeric weights, one per subject or per resampling block (matched pair/cluster), as produced by the bootstrap or Bayesian-bootstrap resampling machinery.

estimate_only

Accepted for interface compatibility; standard errors are never computed for a single bootstrap replicate regardless of this flag (only the point estimate is used to build the bootstrap distribution).

---

InferenceIncidRiskDiff$clone()

The objects of this class are cloneable with this method.

Usage

InferenceIncidRiskDiff$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

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$add_all_subject_responses(rbinom(10, 1, 0.5))
inf = InferenceIncidRiskDiff$new(seq_des)
inf$compute_estimate()
#> [1] -0.4046069
# }