tsml.cara.rct: Targeted Minimum Loss Covariate-Adjusted Response-Adaptive...
In achambaz/tsml.cara.rct: Targeted Sequential Minimum Loss CARA RCT Design and Inference

Description Usage Arguments Details Value Author(s) References See Also Examples

Simulates a targeted minimum loss covariate-adjusted response-adaptive RCT design and statistical analysis.

tsml.cara.rct(what = c("ATE", "MOR"), 
    flavor = c("parametric", "lasso"), ninit = 50, by = 25, nmax = 500,
    tm.init = oneOne, tm.ref = oneOne, learnQ,
    tm.model = formula(A ~ 1), tm.control = glm.control(maxit = 500), 
    Gmin = 0.01, Gexploit = Gmin, Gexplore = 0.01, Qmin = 0.01, 
    conf.level = 0.95, verbose = FALSE, piV = c(1/2, 1/3, 1/6), 
    family = c("beta", "gamma"), Qbar = Qbar1, Vbar = Vbar1, 
    Bn = 1e+05, slice.by = 1e+05)

`what`	A `character` indicating the parameter of interest to estimate. Either "ATE" for the Average Treatment Effect, the difference between the means under 'do(A=1)' and 'do(A=0)', or "MOR" for the Mean under the Optimal treatment Rule 'do(A=r(W))'.
`flavor`	A `character` indicating the 'flavor' of the procedure.
`ninit`	An `integer`, number of subjects to sample at initialization. Defaults to 50.
`by`	An `integer`, number of subjects to sample at each step after initialization. Defaults to 25.
`nmax`	An `integer`, maximum number of subjects to sample during the trial. Must be larger than 'ninit+by'. Defaults to 500.
`tm.init`	A `function` describing the initial treatment mechanism to be employed. Defaults to the balanced (1:1) treatment mechanism, ie, `function` `oneOne`.
`tm.ref`	A `function` describing the reference treatment mechanism to be employed. Defaults to the balanced (1:1) treatment mechanism, ie, `function` `oneOne`.
`learnQ`	A model {\cal Q} of conditional expectations of Y given (A,W) for both flavors 'parametric' and 'lasso', given as a `formula` or a `function` outputing formulas. Defaults to `formula(Y~1)` for flavors 'parametric' and 'lasso'.
`tm.model`	A parametric model {\cal G} of treatment mechanisms, used only when 'what' equals "ATE". The procedure targets the optimal treatment mechanism within this model. Defaults to `formula(A~1)`.
`tm.control`	A `list` of options for the targeting of the treatment mechanism within the model defined by argument 'tm.model'. Used only when 'what' equals "ATE", it defaults to `glm.control(maxit=500)`.
`Gmin`	A small positive `numeric`, with default value `1e-2`. When `what` equals 'ATE', it is the minimum value of elements of the parametric model {\cal G} of treatment mechanisms (see argument `tm.model`). The maximum value is `1-Gmin`. When `what` equals 'MOR', it is the minimum value of the conditional probability of A=r_n(W) given W.
`Gexploit`	A small positive `numeric`, with default value that of `Gmin`, or a function of sample size giving such small numbers, only used when `what` equals "MOR", in conjunction with `Gexplore`.
`Gexplore`	Either a small positive `numeric`, with default value `1e-2`, or a function of sample size giving such small numbers, only used when `what` equals "MOR", in conjunction with `Gexploit`.
`Qmin`	A small positive `numeric`, the minimum value of scaled outcomes Y. The maximum value is `1-Qmin`.
`conf.level`	A `numeric`, the confidence level of the resulting confidence interval.
`verbose`	A `logical` or an `integer` indicating the level of verbosity (defaults to 'FALSE').
`piV`	Marginal distribution of V. Defaults to `c(1/2, 1/3, 1/6)`.
`family`	A `character`, either "beta" (default) or "gamma", the nature of the law of outcome.
`Qbar`	A `function`, the conditional expectation of Y given (A,W). Defaults to `Qbar1`.
`Vbar`	A `function`, the conditional variance of Y given (A,W). Defaults to `Vbar1`.
`Bn`	An `integer`, the sample size used to estimate the true value of the data-adaptive parameter at each step of the procedure when 'what' equals 'MOR'. Defaults to 1e5.
`slice.by`	An `integer`. If it is smaller than argument 'n' of 'getSample', then the simulation is decomposed into 'n%/%slice.by' smaller simulations of 'slice.by' observations and one of 'n%%slice.by' observations. Defaults to 1e5 (hence, no decomposition if 'n' smaller than 4e5). Mainly for internal use.

Defines a lower-bound on the conditional probability of do(A=1-r_n(W)) given W.

Returns a TSMLCARA object which summarizes the TSMLCARA undertaken procedure.

Antoine Chambaz [aut, cre]

Chambaz, van der Laan, Zheng, Chapter 16, Modern Adaptive Randomized Clinical Trials: Statistical, Operational, and Regulatory Aspects, by A. Sverdlov (CRC Press, 2015).

update, targetPsi, getSample

##
log <- Arguments$getVerbose(-1, timestamp=TRUE)
set.seed(12345)

## ########################
## AVERAGE TREATMENT EFFECT
## ########################
tm.model <- formula(A~.)
psi.sd <- sqrt(getOptVar(n=1e5,
                         tm.model=tm.model,
                         piV=c(1/2, 1/3, 1/6),
                         family="gamma",
                         Qbar=Qbar1,
                         Vbar=Vbar1))
truth <- c(psi=91/72, psi.sd=psi.sd)

## parametric example
learnQ <- formula(Y~I(as.integer(A)):(U+V)+I(as.integer(1-A)):(U+V))
ATE.param <- tsml.cara.rct(what="ATE",
                           flavor="parametric",
                           ninit=200,
                           by=100,
                           nmax=400,
                           tm.init=oneOne,
                           tm.ref=oneOne,
                           learnQ=learnQ,
                           tm.model=tm.model,
                           conf.level=0.95,
                           piV=c(1/2, 1/3, 1/6),
                           family="gamma",
                           Qbar=Qbar1,
                           Vbar=Vbar1)
ATE.param
## Not run:
plot(ATE.param, truth=truth)
## End(**Not run**)

## See the vignette for more examples...