The IAIPWE was developed for arbitrary K stage SMART and subsumes both IPWE and AIPWE. To implement the IPWE, q_list should be NULL and the t_s should be set to the maximum available time of the outcome observed. To implement the AIPWE, t_s should be set to the maximum available time of the outcome observed.
Arguments
- df
A data frame containing the data. It should include columns for the treatment assignments, response status, covariates, and outcomes.
- pi_list
A list of
modelObjobjects of length K specifying the propensity score model at each stage.- q_list
A list of
modelObjobjects of length K specifying the outcome regression model at each stage, orNULLfor IPW-only estimation.- regime_all
A list of length equal to the number of regimes to be estimated. Each element is a list with two components:
regime, an n x K matrix of treatment assignments each individual would receive under that regime, andregime_ind, an n x K indicator matrix of whether each individual was consistent with that regime at each stage.- feasible_sets_indicator
A logical value indicating whether feasible sets are present in the trial design. If
TRUE, some treatments are assigned deterministically based on response status; ifFALSE, all stages have random treatment assignment.- t_s
A numeric value indicating the time point at which the analysis should occur.
- B
A positive integer specifying the number of empirical bootstrap samples to use for variance estimation, or
NULL(default) to use the asymptotic sandwich variance estimator.
Value
A list with the following components:
- values
A numeric vector of estimated regime values.
- se
A numeric vector of standard errors for the regime values.
- covariance
The estimated L x L covariance matrix of the regime value estimators.
- params
A numeric vector of all estimated parameters.
- nus
A list of estimated stage arrival probabilities, as returned by
get_nu().- q_all
A list of fitted Q-function objects for each regime.
- regime_all
The input regime list, returned for convenience.
- dfs
A list of value term matrices for each regime.
- variance_choice
A character string indicating the variance estimation method used (
"Asymptotic"or"Bootstrap").- chi_square
A list with
Statistic(the chi-squared test statistic for equality of regime values) andp_value.