Description

Several of the statistical methods implemented in package DynTxRegime allow for subset modeling or limiting of feasible treatment options. This section details how this input is to be defined.

Details

In general, input fSet is used to define subsets of patients within an analysis. These subsets can be specified to (1) limit available treatments, (2) use different models for the propensity score and/or outcome regressions, and/or (3) use different decision function models for each subset of patients. The combination of inputs moPropen, moMain, moCont, fSet, and/or regimes determines which of these scenarios is being considered. We cover some common situations below.

Regardless of the purpose for specifying fSet, it must be a function that returns a list. There are two options for defining the function. Version 1 is that of the original DynTxRegime package. In this version, fSet defines the rules for determining the subset of treatment options for an INDIVIDUAL. The first element of the returned list is a character, which we term the subset 'nickname.' This nickname is for bookkeeping purposes and is used to link models to subsets. The second element of the returned list is a vector of available treatment options for the subset. The formal arguments of the function must include (i) 'data' or (ii) individual covariate names as given by the column headers of data. An example using the covariate name input form is

This function indicates that if an individual has covariate a1 > 1, they are a member of subset 'subA' and their feasible treatment options are {1,2}. If a1 <= 1, they are a member of subset 'subB' and their feasible treatment options are {3,4}.

A more efficient implementation for fSet is now accepted. In the second form, fSet defines the subset of treatment options for the full DATASET. It is again a function with formal arguments (i) 'data' or (ii) individual covariate names as given by the column headers of data. The function returns a list containing two elements: 'subsets' and 'txOpts.' Element 'subsets' is a list comprising all treatment subsets; each element of the list contains the nickname and treatment options for a single subset. Element 'txOpts' is a character vector indicating the subset of which each individual is a member. In this new format, the equivalent definition of fSet as that given above is:

Though a bit more complicated, this version is much more efficient as it processes the entire dataset at once rather than each individual separately.

The simplest scenario involving fSet is to define feasible treatment options and the rules that dictate how those treatment options are determined. For example, responder/non-responder scenarios are often encountered in multiple-decision-point settings. An example of this scenario is: patients that respond to the first stage treatment remain on the original treatment; those that do not respond to the first stage treatment have all treatment options available to them at the second stage. In this case, the propensity score models for the second stage are fit using only 'non-responders' for whom more than 1 treatment option is available.

An example of an appropriate fSet function for the second-stage is

for version 1 or for version 2

The functions above specify that patients with covariate responder = 0 receive treatments from subset 'subA,' which comprises treatments A = (1,2). Patients with covariate responder = 1 receive treatment from subset 'subB' or 'subC' depending on the first stage treatment received. If fSet is specified in this way, the form of the model object depends on the training data. Specifically, if the training data obeys the feasible treatment rule (here, all individuals with responder = 1 received tx in accordance with fSet), moPropen would be a "modelObj"; the propensity model will be fit using only those patients with responder = 0; those with responder = 1 always receive the appropriate second stage treatment with probability 1.0. However, if the data are from an observation study and the training data do not obey the feasible treatment rules (here, some individuals with responder = 1 received tx = 0; others tx = 1), the responder = 1 data must be modeled and moPropen must be provided as one or more ModelObjSubset() objects.

If outcome regression is used by the method, moMain and moCont can be either objects of class "modelObj" if only responder = 0 patients are to be used to obtain parameter estimates or as lists of objects of class "ModelObjSubset" if subsets are to be analyzed individually or combined for a single fit of all data.

For a scenario where all patients have the same set of treatment options available, but subsets of patients are to be analyzed using different models. We cane define fSet as

for version 1 or in the format of version 2

where all patients have the same treatment options available, A = (1,2), but different regression models will be fit for each subset (case 2 above) and/or different decision function models (case 3 above) for each subset. If different propensity score models are used, moPropen must be a list of objects of class "modelObjSubset." Perhaps,

If different decision function models are to be fit, regimes would take a form similar to

Notice that the names of the elements of regimes and the subsets passed to buildModelObjSubset() correspond to the names defined by fSet, i.e., 'subA' or 'subB.' These nicknames are used for bookkeeping and link subsets to the appropriate models.

For a single-decision-point analysis, fSet is a single function. For multiple-decision-point analyses, fSet is a list of functions where each element of the list corresponds to the decision point (1st element <- 1st decision point, etc.)