Computes the An matrix, defined as \(-\partial \Psi / \partial \theta\), where \(\Psi\) is the stacked estimating equations vector. The estimating equations are ordered to match Bn: \(\pi_1, \ldots, \pi_K\), \(\nu_1, \ldots, \nu_{K+1}\), \(\beta^{(\ell)}_1, \ldots, \beta^{(\ell)}_K\) 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_an(
df,
pis,
p_fits,
nus,
q_all,
values,
regime_all,
dfs,
feasible_sets_indicator,
q_list
)Arguments
- df
A data frame containing the trial data, including treatment assignments, covariates, outcomes, and a
kappacolumn.- pis
A data frame of estimated propensity scores with columns
pi1, ..., piK, one column per stage.- p_fits
A list of fitted propensity score model objects (one per stage), each a
modelObjfit object.- nus
A list as returned by
get_nu, containing the estimated stage probabilitiesnu, the sample sizens, andnd.- 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.- values
A numeric vector of estimated regime values.
- regime_all
A list of regime objects, each containing a
regimematrix and aregime_indindicator matrix.- dfs
A list of data frames of value term components for each regime, as returned by
estimate_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).