*! version 1.0.0 10jul2015 Long Hong

help survgini

Title

survgini -- Non-parametric restricted Gini for survival data

Syntax

survgini time failure treatment [if] [in] [,
nolastevent nolinearrank noasymptotic
nopermutation m(integer)]

Variables

Variables

time Time-to-event variable. Note that when there are
zero-valued observations, the command will change
those values to 1.0e-06 to ease computation during the execution.
The original value will be restored after the execution.

failure Censoring indicator; failure=0 if the observation
is right-censored and failure=1 otherwise

treatment Treatment group; please use treat=1 for
the first group and treat=2 for the second group

* Only three numeric variables are allowed and the
order is fixed.

Options

Options

nolastevent Represents the longest follow-up time until
which we integrate in the computation of the restricted Gini index.
Choosing nolastevent means integrating until the last observation
censored or not. Default setting allows integrating until the last event
non-censored.

nolinearrank Default setting computes the linear rank tests
(log-rank test and Wilcoxon test). This option inactivates the tests.

noasymptotic Default setting computes the asymptotic Gini
test. This option inactivates the test.

nopermutation Default setting computes the permutation Gini
test. This option inactivates the test.

m(integer) The number of replications for permutation
sampling; the default is 500. The number cannot exceed your version of Stata's matrix size
limit. See matsize for more information.

Description

survgini The Gini concentration test for survival data is a
nonparametric test based on the Gini index for testing the equality of
two survival distributions from the point of view of concentration.
The package compares different nonparametric tests
(asymptotic Gini test, permutation Gini test,
log-rank test, and Wilcoxon test) and computes their p-values
and test statistics (Bonetti, et al., 2009; Gigliarano and Bonetti, 2011).

Example

We will use the survival data from the Eastern Cooperative Oncology Group
(ECOG)'s phase III clinic trial E1690, which accrued patients from 1991 to 1995
and was unblinded in 1998. This trial was aimed at comparing the effect of
Interferon alpha-2b chemotherapy (IFN) to observation only in patients affected
by high-risk melanoma. Trial E1690 was a randomized three-arm clinical trial
that compared high dose IFN, low dose IFN, and control. To illustrate
survgini, we use relapse-free survival (RFS) data from the treatment group
with high dose IFN and that from the control group (215 and 212 patients,
respectively).

One can use survgini by inputting the three variables of the
interest in orders as shown below. Please note that when the sample size
is relatively large, we shall inactive the permutation test, which is mainly
for the case when the sample size is small.

. survgini failtime failcens trt, noperm

Comparison among GiniAs Log-rank and Wilcoxon tests

| pGiniAs pLR pW

+

pval | .0526 .05391 .03506
stat | 3.7565 3.7154 4.4421

It could also be argued that the sample size is not large enough to
produce reliable asymptotic results from Asymptotic Gini, Log-rank, and Wilcoxon
tests. One can use the permutation test instead by inactive the rest of the
tests as shown below.

. set seed 20171121

. survgini failtime failcens trt, nolin noas

Gini Permutation Test

| pGiniPerm

+

pval | .05
stat | .0037

However, one may have to pay attention to the following three direct
consequences of the fact that the permutation test involves replications of
permutation sampling. First, it will significantly slow down the speed of the
programming, especially when m(integer) is set to be large. Second, the
result can change slightly every time it is executed. We strongly recommend
users can use the seed function before using the permutation test for
replication purpose. Finally, the test statistics is not comparable to the rest
of the tests whose test statistic follows an asymptotic Chi-square
distribution.

Saved Results

survgini saves the following in r()

Scalars

r(pGiniAs) p-value of the asymptotic Gini test

r(pGiniPerm) p-value of the permutation Gini test

r(pLR) p-value of the Log-Rank test

r(pW) p-value of the Wilcoxon test

r(statGiniAs) test statistic of the asymptotic Gini test

r(statGiniPerm) test statistic of the permutation Gini test

r(statLR) test statistic of the Log-Rank test

r(statW) test statistic of the Wilcoxon test

Author

Long Hong

Department of Economics

University of Wisconsin - Madison

Madison, WI, USA

long.hong@wisc.edu

References

Bonetti, M., Gigliarano, C. and Muliere, P. (2009). The Gini
concentration test for survival data. Lifetime Data Analysis, 15,
493-518.

Gigliarano, C. and Bonetti, M. (2011). The Gini test for survival data
in presence of small and unbalanced groups. In press, Biomedical Statistics
and Clinical epidemiology.