*! version 1.0.0 02dec2023

Title

multiauc - Calculation of correlated areas under the receiver operating
characteristic curves and their differences.

Syntax

multiauc
groupvar
varlist
[if] [in],
[options]

options

Options
idvar(idvar) specify a numeric ID variable for the
observations in the dataset

citype(multiauc##citypes:citype) specify the
transformation method to use when constructing confidence intervals for
individual score AUC estimates.

cilevel(cilevel) specify the two-sided significance level
to construct confidence intervals.

keepdvalues keeps the calculated D-values in a separate frame.

onlydvalues computes the D-values only and stops
exection. Must be used with option keepdvalues.

citypes

Options
normal uses Normal (Wald-type) method to calculate the
confidence interval (no transformation).

logit uses a logit transformation. This is the default.

atanh uses Fisher's Z (atanh) transformation.

Description

multiauc is intended to produce point estimates and confidence intervals
for the AUC for two or more correlated scores (or prognostic values). In
addition, it will also compute all pair-wise contrasts and their confidence
intervals.

groupvar is the binary (0/1) indicator of the outcome. It is assumed
that the AUC is to estimate the win probability of group==1 over
group==0.

varlist are the scores (or prognostic indices). For each score, higher
values are assumed to be associated with group==1, that is, higher values
indicate the condition of interest. A minimum of 2 scores are required.

citype() applies only the specified confidence interval type to the
AUC for the individual scores. The confidence intervals for the pair-wise
contrasts of AUC values are always constructed with Fisher's Z (atah)
transformation.

keepdvalues retains the calculated D-values in a a frame named
_Dvalues. If this frame exists, it will be replaced.

onlydvalues stops execution of this program after calculating the
D-values. It must be used with keepdvalues.

Examples

Using the De Long, et al. (1988) data, compute the correlated AUCs and
their differences.

. use delong1988

. multiauc group tp alb kg, idvar(pid)

Stored results

The following results are stored in r():

Scalars

r(level) Confidence interval level.

Macros

r(group) Group variable for condition of interest.

r(scores) Score variables as chosen in varlist.

r(auc_citype) Method of construction of CI for each AUC.

r(delta_citype) Method of construction of CI for AUC contrasts.
This is always "atanh".

Matrices

r(N_obs) Number of valid observations from each score in
estimation sample.

r(auc) AUC estimates for each score.

r(SE_auc) Standard errors for each AUC.

r(CI_auc) Confidence intervals for each AUC.

r(V_auc) Multivariate normal estimate of variance-covariance
matrix of the AUCs.

r(delta) Pair-wise estimates of the contrast (difference)
between correlated AUC values.

r(SE_delta) Standard errors for the AUC contrasts.

r(CI_delta) Confidence intervals for the AUC contrasts.

Author

Leonardo Guizzetti

leonardo.guizzetti@gmail.com

Acknowledgements

Thanks to Guangyong Zou for the encouragement to write this program.

References

DeLong ER, DeLong DM, Clarke-Pearson DL.
Comparing the areas under two or more correlated receiver operating
characteristic curves: A nonparametric approach.
Biometrics. 1988; 44: 837–845. doi: 10.2307/2531595

Zou L, Choi Y-H, Guizzetti L, Shu D, Zou J, Zou G.
Extending the DeLong algorithm for comparing areas under correlated
receiver operating characteristic curves with missing data.
Statistics in Medicine. 2024; 43(21): 4148-4162.
doi: 10.1002/sim.10172