KSperm: Simulate a p-value for the significance of the...

In LocalControlStrategy: Local Control Strategy for Robust Analysis of Cross-Sectional Data

Simulate a p-value for the significance of the Kolmogorov-Smirnov D-statistic from confirm().

Description

For a given confirm() output object, KSperm() simulates the NULL distribution of LTDs or LRCs resulting from Purely Random Clusterings of experimental units within the parent data.frame. This NULL distribution is discrete because Local Effect-Size estimates are TIED within-clusters. The observed D-Statistic from confirm() is compared with new NULL order statistics computed by KSperm(), again using stats::ks.test. When KSperm() is called immediately after confirm() and the seed value used in confirm() is known, then both the simulated p-value and the additional NULL KS-D order statistics generated by KSperm() will all be reproducible.

Usage

KSperm(x, reps=100)

Arguments

x	An output object from confirm().
reps	This is the number of new NULL KS-D statistics to generated. Each experimental unit is used at most once within each full replication. No clusters will be empty, but some may be "uninformative".

Details

The observed value of the Kolmogorov-Smirnov D-statistic from confirm() is used here, but its "p.value" from ks.test() is not because it is badly biased downwards. This bias results because the distribution of LTDs or LRCs across clusters is always discrete, due to TIED values within clusters that typically also vary in size. Thus, KSperm() generates "reps" additional, independent, NULL values of KS-D and saves their order statistics. Finally, KSperm() compares the Observed KS-D from confirm() with its simulated NULL order statistics to estimate an appropriately "adjusted" p-value, pv.adj. Note that the simulated pv.adj value estimate cannot be less than 1/(reps).

Value

An output list object of class KSperm:

hiclus	Hierarchical clustering object created by the designated method.
dframe	Name of data.frame containing X, t & Y variables.
trtm	Name of numerical treatment/exposure variable.
yvar	Name of numerical y-Outcome variable.
Type	1 ==> LTDs, otherwise LRCs.
reps	Number of overall Replications, each with the same number, K, of requested clusters.
nclus	Number of clusters requested.
units	Number of experimental units or patients.
obsD	Observed numerical value of KS D-statistic from confirm()
Dvec	Vector of order statistics for simulated NULL KS D-statistics.
pv.adj	Simulated p-value adjusted for TIES within discrete LTD/LRC distributions.

Author(s)

Bob Obenchain <[e-mail]>

References

Obenchain RL. (2010) Local Control Approach using JMP. Chapter 7 of Analysis of Observational Health Care Data using SAS, Cary, NC:SAS Press, pages 151-192.

Obenchain RL. (2019) LCstrategy_in_R.pdf http://localcontrolstatistics.org

See Also

confirm, ltdagg and lrcagg.

LocalControlStrategy documentation built on Nov. 10, 2022, 5:49 p.m.