Gittins {RARtrials}

Gittins Indices

Description

Gittins can provide Gittins indices for binary reward processes and normal reward processes with known and unknown variance for certain discount factors. Binary reward process can handle scenarios with up to 2000 participants in a trial, while normal reward process can handle scenarios with up to 10000 participants in a trial.

Usage

Gittins(Gittinstype, df)

Arguments

Gittinstype

type of Gittins indices, with choices from 'Binary', 'UNKV' and 'KV'. 'Binary' represents binary outcomes, 'UNKV' and 'KV' represent continuous outcomes with known and unknown variance respectively.

df

discount factor which is the multiplier for loss at each additional patient in the future. Available values are 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 0.99 and 0.995 for Gittinstype in 'UNKV' and 'KV'; 0, 0.5, 0.7, 0.99 and 0.995 for Gittinstype in 'binary'.

Details

Gittins indices for binary outcomes are generated from bmab_gi_multiple_ab function from gittins package with time horizon 100, 100, 100, 1000, 1000 for discount factor 0, 0.5, 0.7, 0.99 and 0.995 respectively. Gittins indices for continuous outcomes are obtained by linear extrapolation using Table 8.1 and Table 8.3 in (Gittins et al. 2011).

Value

A vector of Gittins indices for Gittinstype in 'UNKV' and 'KV'. A matrix of Gittins indices for Gittinstype in 'Binary'.

References

Gittins J, Glazebrook K, Weber R (2011). Multi-Armed Bandit Allocation Indices, 2nd Edition, volume 33. Hoboken,NJ:John Wiley & Sons. ISBN 9780470670026, doi:10.1002/9780470980033.ch8.

Examples

Gittins(Gittinstype='KV',df=0.5)

Gittins(Gittinstype='Binary',df=0.995)
Gittins(Gittinstype='UNKV',df=0.99)