Fano.BinBin: Evaluate the possibility of finding a good surrogate in the...
In Surrogate: Evaluation of Surrogate Endpoints in Clinical Trials

Fano.BinBin

R Documentation

Evaluate the possibility of finding a good surrogate in the setting where both `S` and `T` are binary endpoints

Description

The function Fano.BinBin evaluates the existence of a good surrogate in the single-trial causal-inference framework when both the surrogate and the true endpoints are binary outcomes. See Details below.

Usage

Fano.BinBin(pi1_,  pi_1, rangepi10=c(0,min(pi1_,1-pi_1)), 
fano_delta=c(0.1), M=100, Seed=1)

Arguments

`pi1_`	A scalar or a vector of plausibel values that represents the proportion of responders under treatment.
`pi_1`	A scalar or a vector of plausibel values that represents the proportion of responders under control.
`rangepi10`	Represents the range from which `\pi_{10}` is sampled. By default, Monte Carlo simulation will be constrained to the interval `[0,\min(\pi_{1\cdot},\pi_{\cdot0})]` but this allows the user to specify a more narrow range. `rangepi10=c(0,0)` is equivalent to the assumption of monotonicity for the true endpoint.
`fano_delta`	A scalar or a vector that specifies the values for the upper bound of the prediction error `\delta`. Default `fano_delta=c(0.2)`.
`M`	The number of random samples that have to be drawn for the freely varying parameter `\pi_{10}`. Default `M=1000`. The number of random samples should be sufficiently large in relation to the length of the interval `rangepi10`. Typically `M=1000` yields a sufficiently fine grid. In case `rangepi10` is a single value: `M=1`
`Seed`	The seed to be used to sample the freely varying parameter `\pi_{10}`. Default `Seed=1`.

Details

Values for \pi_{10} have to be uniformly sampled from the interval [0,\min(\pi_{1\cdot},\pi_{\cdot0})]. Any sampled value for \pi_{10} will fully determine the bivariate distribution of potential outcomes for the true endpoint. The treatment effect should be positive.

The vector \bold{\pi_{km}} fully determines R^2_{HL}.

Value

An object of class Fano.BinBin with components,

`R2_HL`	The sampled values for `R^2_{HL}`.
`H_Delta_T`	The sampled values for `H{\Delta T}`.
`PPE_T`	The sampled values for `PPE_{T}`.
`minpi10`	The minimum value for `\pi_{10}`.
`maxpi10`	The maximum value for `\pi_{10}`.
`samplepi10`	The sampled value for `\pi_{10}`.
`delta`	The specified vector of upper bounds for the prediction errors.
`uncertainty`	Indexes the sampling of `pi1\_`.
`pi_00`	The sampled values for `\pi_{00}`.
`pi_11`	The sampled values for `\pi_{11}`.
`pi_01`	The sampled values for `\pi_{01}`.
`pi_10`	The sampled values for `\pi_{10}`.

Author(s)

Paul Meyvisch, Wim Van der Elst, Ariel Alonso

References

Alonso, A., Van der Elst, W., & Molenberghs, G. (2014). Validation of surrogate endpoints: the binary-binary setting from a causal inference perspective.

Examples

# Conduct the analysis assuming no montonicity
# for the true endpoint, using a range of
# upper bounds for prediction errors 
Fano.BinBin(pi1_ = 0.5951 ,  pi_1 = 0.7745, 
fano_delta=c(0.05, 0.1, 0.2), M=1000)


# Conduct the same analysis now sampling from
# a range of values to allow for uncertainty

Fano.BinBin(pi1_ = runif(n=20,min=0.504,max=0.681), 
pi_1 = runif(n=20,min=0.679,max=0.849), 
fano_delta=c(0.05, 0.1, 0.2), M=10, Seed=2)

Surrogate documentation built on Sept. 25, 2023, 5:07 p.m.