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Computes the Bn matrix, defined as \(n^{-1} \sum_{i=1}^{n} \Psi_i \Psi_i^T\), the empirical variance of the estimating equations. Each row of the individual-level estimating equation matrix corresponds to one subject, with columns ordered as \(\pi_1, \ldots, \pi_K\), \(\nu_1, \ldots, \nu_{K+1}\), \(\beta^{(\ell)}_1, \ldots, \beta^{(\ell)}_K\) for each regime \(\ell\), and the value estimating equations \(V_1, \ldots, V_L\). Based on Section 7 of Boos and Stefanski for the robust sandwich matrix.

Usage

get_bn(df, p_fits, nus, q_all, dfs, values, feasible_sets_indicator, q_list)

Arguments

df

A data frame containing the trial data, including treatment assignments, covariates, outcomes, and a kappa column.

p_fits

A list of fitted propensity score model objects (one per stage), each a modelObj fit object.

nus

A list as returned by get_nu, containing the estimated stage probabilities nu, the sample size ns, and nd.

q_all

A list of fitted outcome regression objects for each regime, as returned by estimate_values. Can be an empty list when using IPW estimation.

dfs

A list of data frames of value term components for each regime, as returned by estimate_values.

values

A numeric vector of estimated regime values.

feasible_sets_indicator

A logical value indicating whether feasible sets are present in the trial design (i.e., some treatments are deterministic based on response status).

q_list

A list of outcome regression model specifications (one per stage), used to determine the number of Q-function models at each stage (e.g., separate models for responders and non-responders).

Value

A numeric matrix representing the Bn component of the sandwich variance estimator, with dimensions equal to the total number of estimated parameters.