Surrogate (version 1.7)

Test.Mono: Test whether the data are compatible with monotonicity for S and/or T (binary endpoints)

Description

For some situations, the observable marginal probabilities contain sufficient information to exclude a particular monotonicity scenario. For example, under monotonicity for \(S\) and \(T\), one of the restrictions that the data impose is \(\pi_{0111}<min(\pi_{0 \cdot 1 \cdot}, \pi_{\cdot 1 \cdot 1})\). If the latter condition does not hold in the dataset at hand, monotonicity for \(S\) and \(T\) can be excluded.

Usage

Test.Mono(pi1_1_, pi0_1_, pi1_0_, pi_1_1, pi_1_0, pi_0_1)

Arguments

pi1_1_

A scalar that contains \(P(T=1,S=1|Z=0)\).

pi0_1_

A scalar that contains \(P(T=0,S=1|Z=0)\).

pi1_0_

A scalar that contains \(P(T=1,S=0|Z=0)\).

pi_1_1

A scalar that contains \(P(T=1,S=1|Z=1)\).

pi_1_0

A scalar that contains \(P(T=1,S=0|Z=1)\).

pi_0_1

A scalar that contains \(P(T=0,S=1|Z=1)\).

References

Alonso, A., Van der Elst, W., & Molenberghs, G. (2015). Validation of surrogate endpoints: the binary-binary setting from a causal inference perspective.

Examples

# NOT RUN {
Test.Mono(pi1_1_=0.2619048, pi1_0_=0.2857143, pi_1_1=0.6372549, 
pi_1_0=0.07843137, pi0_1_=0.1349206, pi_0_1=0.127451)
# }