amd {varoc}

AMD: above mean difference

Description

Summary measures to evaluate the continuity performance of biomarkers, diagnostic tests, or risk prediction models.

Usage

amd(y,x,fpf=0.3,pval="no",alternative="greater",B=2000,conf.level=0.95)

Arguments

y

binary output, where y=1 if disease (or case) and y=0 if non-disease (or control).

x

continuous score, e.g. biomarker, diagnostic test, risk score.

fpf

false positive fraction at which above mean difference is cacluated.

pval

"yes" for bootstrap p-value and bootstrap confidence interval.

alternative

alternative hypothesis: "greater"" (default), "less", "two.sided".

B

number of bootstrap samples.

conf.level

confidence level of bootstrap confidence interval.

Details

The amd function summarizes a continuity performance of x at each cutoff c as: i) above mean difference (AMD) and ii) intergrated AMD (IAMD). For i), AMD(c) is true positive mean(TPM)(c) minus false positive mean(FPM)(c), where TPM(c) is E(x>c|y=1) and FPM(c) is E(x>c|y=0). For ii), IAMD is a global measure of evaluating continuity performance of x over all thresholds.

These measures can be viewed as continuous versions of ROC curve-based measures. Specifically, TPM(c) and FPM(c) are continuous versions of true positive fraction(TPF)(c) (or sensitivity(c)) and false positive fraction(FPF)(c) (or one minus specificity(c)), where TPF(c)=P(x>c|y=1) and FPF(c)=P(x>c|y=0). The useful (or useless) x has TPF(c)-FPF(c)>0 and AMD(c)>0 (or TPF(c)-FPF(c)=0 and AMD(c)=0). Similiarly, useful (or useless) x has area under the ROC curve(AUC)>0.5 and IAMD(c)>0 (or AUC=0.5 and IAMD(c)=0).

The bootstrap p-value and confidence interval are computed under the null hypthesis: AMD(c)\leq0 or IAMD(c)\leq0, when pval="yes" and alterantive="greater".

The threshold c is determined by setting an acceptable fpf, i.e. FPF(c)=fpf. Thus, i) is interpreted as AMD at a FPF of fpf, ii) is interprted as IAMD (or average AMD) at a FPF range of 0 and 1. The varoc and jdp functions visualize them.

Value

df

data frame with y and x.

fpf

false positive fraction at which above mean difference is cacluated.

res

data frame with tpf, fpf, tpm, fpm, amd, lcl, ucl, zAMD, pvalue at each threshold (th)), where lcl (lower confidence limit), ucl (upper confidence limit), zAMD (test statistics) and pvalue (one-sided p-value) are for amd.

amd

data frame with tpf, fpf, tpm, fpf, amd, lcl, ucl, zAMD, pvalue at FPF(th)=fpf, where lcl, ucl, zAMD and pvalue are for amd. Here, empierical estimator of FPF is used, and amd$fpf could be different from the fpf value in the augument.

iamd

data frame with auc, itpm, iftm, iamd, lcl, ucl, zIAMD, pvalue, where lcl, ucl, zIAMD and pvalue are for iamd.

Author(s)

Yunro Chung [aut, cre]

References

Danielle Brister and Yunro Chung, Value added receiver operating characteristics curve (in-progress)

Examples

set.seed(3)

n1=50
n0=50

#1. marker 1 (useless biomaker)
y1=c(rep(1,n1),rep(0,n0))
x1=abs(c(rnorm(n1,0,1),rnorm(n0,0,1)))

#1.1.amd
fit1=amd(y=y1,x=x1,fpf=0.3)
print(fit1)

#1.2. varoc
varoc(fit1)

#1.3. jdp
jdp(fit1)

#2. marker 2 (useful biomarker)
y2=y1
x2=abs(c(rnorm(n1,1,1),rnorm(n0,0,1)))

#2.1. amd
fit2=amd(y=y2,x=x2,fpf=0.3)

#2.2. varoc for marker 1 vs marker 2
mzr.min=min(c(fit1$res$amd,fit2$res$amd))
mzr.max=max(c(fit1$res$amd,fit2$res$amd))

varoc(fit1,mzr="zAMD",mzr.min=mzr.min,mzr.max=mzr.max)
varoc(fit2,mzr="zAMD",mzr.min=mzr.min,mzr.max=mzr.max)

#2.3. varoc for marker 1 vs marker 2
min=min(c(x1,x2))
max=max(c(x1,x2))
jdp(fit1,min=min,max=max)
jdp(fit2,min=min,max=max)