# Pairwise.DiagTest3Grp.Test: Do pairwise statistical test on the summary measure (VUS or... In DiagTest3Grp: Diagnostic test summary measures for three ordinal groups

## Description

Do pairwise statistical test to compare the summary measure (VUS or Youden) estimates between a pair of markers among multiple markers assuming that the marker follows normal distribution in each diagnosis group, for both independent samples and paired samples.Resulting p-values can be adjusted for mulltiple testing. The function returns a nice upper-triagnular graphical display and print matrix on pairwise comparisons.

## Usage

 1 2 3 4 Pairwise.DiagTest3Grp.Test(dat,paired=FALSE,type=c("VUS","Youden"),p=0,q=0,mu=0, conf.level=0.95, alternative=c("two.sided","less","greater"), p.adjust.method=c("none","holm","hochberg","hommel","bonferroni","BH","BY","fdr"), digits=3,...)

## Arguments

 dat For unpaired data (data measured on different independent sets of samples), dat is a list of K (=number of markers) components, each corresponding to a marker. Each component of the list should be a data frame of number of observation by two columns:(1) group (note:must be at the 1st column) with the three levels of D^-, D^0 and D^+ (corresponding to increasing disease severity respectively); (2)numeric marker measurements at the 2nd column. for paired data, dat should be a data frame with observations at row and group/markers at column (group must be at the 1st column) with the three levels D^-, D^0 and D^+(corresponding to increasing disease severity respectively), followed by markers at the 2nd to the last column. paired A logic value TRUE/FALSE, indicating whether all markers are measured on the same set (paired=TRUE) or not (paired=FALSE). type A character value. type=“VUS” or “Youden”, indicates which summary measure (VUS or Youden) will be used to indicate the discriminative ability of the three-group diagnostic tests. Allows unique argument matching,i.e., can use unique abbreviations such as “V” or “Y”. p A numeric value. To test on partial VUS satisfying specificity >=p and sensitivity >=q, set p, q to desired value. default=0 for full VUS. q A numeric value.To test on partial VUS satisfying specificity >=p and sensitivity >=q, set p, q to desired value. default=0 for full VUS. mu A numeric value. The hypothesized true difference between two markers. Default mu=0 but can be changed to a nonzero value. conf.level a numerica value. The confidence interval. default=95%. The confidence interval on point estimate of abs diff between two markers's summary measures will be returned. For >=3 markers, this will be NA. alternative A character value. Now is fixed as "two-sided". p.adjust.method A vector string specifying multiple testing adjustment method.Default=“none”. digits A numeric integer. The number of digits for p-value print ... Other arguments that can be input into heatmap.2() function in R package gplots.

## Details

see p.adjust for details on multiple testing adjustment on p-values. and see DiagTest3Grp.Test for statistical test between two markers.

## Value

Besides a heatmap illustrating the mulitple testing adjustment corrected P-values from pairwise comparisons in a upper-triangular display, the function also returns a list of two components:

 print.matrix A data frame. If K markers are analyzed, the data frame will have K-1 row and K-1 columns. The first column contains the IDs of markers 1:(K-1) while the column names are ID for marker 2:K.The entries in column 3 and following are stat (t statistic), raw P (raw P value) or adjusted P from testing two markers. The 2nd column indicates whether the matching row indicate stat (z-statistic), raw P (raw P value) or adjusted P. So this output basically presen the results in an upper triangular matrix format. pval.matrix More detailed output. A data frame with the columns: index of marker 1, index of marker 2, ID of marker1,summary measure estimated for marker 1, ID of marker2,summary measure estimated for marker 1, the lower limit of the resulting CI on the difference between the summary measure estimates (marker1-marker2), the upper limit of the CI, z-statistic, raw P value and adjusted P value.

## Warning

The bootstrapping to obtain the variance on the nonparametric VUS estimate may take a while.

## Note

Bug reports, malfunctioning, or suggestions for further improvements or contributions can be sent to Jingqin Luo <[email protected]>.

Jingqin Luo

## References

Xiong, C. and van Belle, G. and Miller, J.P. and Morris, J.C. (2006) Measuring and Estimating Diagnostic Accuracy When There Are Three Ordinal Diagnostic Groups. Statistics In Medicine 25 7 1251–1273.

Ferri, C. and Hernandez-Orallo, J. and Salido, M.A. (2003) Volume under the ROC Surface for Multi-class Problems LECTURE NOTES IN COMPUTER SCIENCE 108–120. Xiong, C and Van Belle, G. and Miller, J.P. and Yan, Y. and Gao, F., and Yu, K, and Morris, J. (2007) A Parametric Comparison of Diagnostic Accuracy with Three Ordinal Diagnostic Groups. Biometrical Journal 5, 682-693

Luo, J and Xiong, C. (2012) Youden Index and Associated Optimal Cut-point for Three Ordinal Groups. Communications In Statistics-Simulation and Computation(in press).

Jingqin Luo, Chengjie Xiong (2012). DiagTest3Grp: An R Package for Analyzing Diagnostic Tests with Three Ordinal Groups.Journal of Statistical Software, 51(3), 1-24.URL http://www.jstatsoft.org/v51/i03/.