Vol.2, No.3, 51-56 (2013) Modern Chemotherapy
http://dx.doi.org/10.4236/mc.2013.23006
CIMAvax®EGF vaccine therapy for non-small cell
lung cancer: A weighted log-rank tests-based
evaluation
Carmen Viada Gonzalez1*, Jean-François Dupuy2, Martha Fors López3,
Patricia Lorenzo Luaces1, Gisela González Marinello1, Elia Neninger Vinagera4,
Beatriz García Verdecia1, Tania Crombet-Ramos1
1Clinical Trials Department, Center of Molecular Immunology, Havana, Cuba; *Corresponding Author:
2National Institute of Applied Sciences of Rennes, Rennes, France
3National Coordinator Center of Clinical Trial, Havana, Cuba
4Hermanos Ameijeiras Hospital, Havana, Cuba
Received 2 January 2013; revised 12 February 2013; accepted 1 March 2013
Copyright © 2013 Carmen Viada Gonzalez et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
Time-to-event has become one of the primary
endpoints of many clinical trials. Comparing
treatments and therapies using time-to-event (or
“survival”) data requires some care, since survi-
val differences may occur either early or late in
the follow-up period, depending on various fac-
tors such as the initial po tency or the duration of
efficacy of the drugs. In this work, we investi-
gate the effect of the CIMAvax®EGF vaccine the-
rapy on the survival of patients with non-small
cell lung cancer, using stratified and unstratified
weighted log-rank tests. Weighted log-rank tests
are designed to identify early and late survival
differences between treatments. Using these tests,
we conclude that the vaccine is more efficient
than the standard therapy among patients less
than 60 years of age.
Keywords: Log-Rank Test; Fleming-Harrington
Test; Stratified Tests
1. INTRODUCTION
The Center of Molecular Immunology (CIM) is one of
the centers of the Scientific Pole in Cuba devoted to the
research, development, and manufacturing of human
biotechnological products. The CIMAVax®EGF vaccine,
developed at CIM. Investigating the effect of the CI-
MAVax ®EGF vaccine on patients with NSCLC can be
based on comparing the survival functions under CI-
MAVax ®EGF and a control therapy. The log-rank test is
the classical tool that comes to mind for such an analysis.
However, this test is not appropriate for detecting a de-
layed separation of the survival curves that may occur
due to some late effect of one of the treatments. Previous
studies suggest that such an effect exist for the CIMA
Vax®EGF vaccine. Moreover, the log-rank test is useful
when each treatment group is homogeneous, in the sense
that the survival distribution is the same for every patient
in the group. Again, previous studies suggest that an
evaluation of CIMAVax®EGF efficacy should be strati-
fied over age, since homogeneity only holds within the
two subpopulations of patients under (respectively over)
60 years of age. Stratified weighted log-rank tests, such
as the stratified Fleming-Harrington’s family of tests, can
be used to deal simultaneously with the issues of late
effects and stratification. In this work, we apply these
tests to survival data arising from two clinical trials that
were conducted to evaluate the CIMAVax®EGF vaccine
in patients with NSCLC. The first study is a finished
phase II trial that included 80 patients, the second is an
on-going phase III trial including 356 patients. Both tri-
als were randomized and controlled with two treatment
arms, one arm receiving the CIMAVax®EGF vaccine and
a standard therapy, the other (control group) receiving
only the standard therapy. In both trials, the primary
endpoint of interest was the overall survival, measured as
the duration between inclusion in the trial and death of
the patient.
2. PURPOSE
The purpose of this work is to analyze survival data
from patients with NSCLC with standard therapy com-

C. V. Gonzalez et al. / Modern Chemotherapy 2 (2013) 51-56
52
pared with patients vaccinated with CIMAVax®EGF.
3. PATIENTS AND METHODS
3.1. Study Design and Treatment
A phase II clinical trial including 80 patients (under a
balanced design), and a Phase III trial including 356 pa-
tients (under an unbalanced design 1:2 and still ongoing)
are analyzed, first separately, and then by combining the
data from both trials. Both trials are controlled, with two
treatment arms: one group received the CIMAvax®EGF
vaccine plus standard therapy and the other the standard
therapy. Based on previous studies, the statistical analy-
ses were stratified according to the age of the patients
(the patients under 60 years were assigned to a stratum,
the patients over 60 years to another stratum. In the se-
quel, these strata are respectively referred to as “younger”
and “older”). Ta bl e 1 provides a brief description of the
data. The overall survival, defined as the duration be-
tween inclusion in the trial and death was the primary
endpoint of interest. Some other variables were also as-
sessed but their analysis falls beyond the objective of the
present. The ethics boards of all the participant institu-
tions approved the protocols, and all the patients pro-
vided a written informed consent. The data were col-
lected, managed, and analyzed at CIM and CENCEC.
3.2. Eligibility Criteria
Included patients had histologic or cytological evi-
dence of NSLC (Adenocarcinome and Non Adenocarci-
nome), ECOG performance status 0, 1, or 2, stage IIIb
and IV, and adequate hematologic, renal, and hepatic
functions.
3.3. Statistical Analysis
3.3.1. Weighted Log-Rank Tests for Two or
More Samples
We consider the problem of comparing the hazard
rates of K (K ≥ 2) treatment groups that is, we consider
the testing problem:
 
01 2K
H:h ththt,foralltι  (1)
versus
Table 1. Disposition of patients for Phase II and Phase III clini-
cal trials.
Trial Phase II Phase III*
Stratum Vaccine Control Vaccine Control Total
Older 17 (42%) 10 (25%) 138 (56%) 60 (54%) 198 (56%)
Younger 23 (58%) 30 (75%) 107 (44%) 51(46%) 158 (44%)
Total 40 (100%) 40 (100%) 245 (100%) 111 (100%) 356 (100%)
HA: at least one of the hj is different from the others
for some tι

where hj(t) is the hazard rate in the j-th
group and  denotes the largest time at which some pa-
tients are still at risk in each group. The alternative hy-
pothesis is global in the sense that one rejects the null
hypothesis if at least one of the populations differs from
the others. The available data for solving this testing
problem consist of independent durations, possibly right-
censored, obtained from the K treatment groups. In the
sequel, we let 12 D
tt t

 denote the distinct death
times in the K pooled groups, dij be the number of deaths
at time ti in the j-th group, and Yij be the number of pa-
tients at risk at ti in the j-th group (j1, ,K

,
i1, ,D

). Let iij
j1, K
dd

 and iij
j1, K
YY


be the numbers of deaths and patients at risk in the com-
bined K groups at time ti, i = 1, ···,D.
Weighted log-rank tests of H0 are based on weighted
differences between the Nelson-Aalen estimators of the
cumulative hazard rates in the K groups and the Nelson-
Aalen estimator obtained in the pooled groups that is,
under H0 (see [1,2], for example). Using data from the
j-th group, the hazard function can be estimated by dij/Yij.
If the null hypothesis H0 holds, an estimator of the com-
mon hazard rate is the pooled groups estimator di/Yi.
Now, Wj(t) be a positive weight function for the j-th
group. This weight function is chosen so as to detect
early or late differences between the treatment groups.
Finally, the weighted log-rank statistic for testing H0
against HA is defined as:






jjiijijii
i1, D
ZιWtd YdY,j1,,K



 (2)
If all the Zj() (j1, ,K

) are close to zero, then
there is little evidence to believe that the null hypothesis
in (1) is false, whereas if one of the Zj() is far from zero,
then there is evidence that the j-th treatment group has a
hazard rate differing from that expected under the null
hypothesis. Although the mathematical theory allows for
general weight functions in (2), in practice, all the com-
monly used test statistics have weight Wj(ti) = Yij W(ti),
where W(ti) is a common weight shared by the K groups.
Zj() then becomes:




jiijij ii
i1, D
ZιWtdYd Y,j1,,K




 (3)
In this case, Zj() can be interpreted as the sum of the
weighted differences between the observed numbers of
deaths and the expected number of deaths under H0 in the
j-th sample. The variance of Zj() in (3) is given by:
  
jj
2
j iijijiiiii
i1, D
ˆ
S
WtYY1YYYdY 1d,
j1, ,K






and the covariance of Zj() and Zg() is:

C. V. Gonzalez et al. / Modern Chemotherapy 2 (2013) 51-56 53
 
2
jjj iijiigiiiii
i1, D
ˆ
SWtYYYYYdY1
jg





d,
The quantities are linearly depen-
dent since j1
, K is zero. Therefore, the test
statistic is constructed by selecting any K − 1 of the j
 
1K
Zι,,Zι

j
Zι
Zs

(the first K1, say). The estimated variance-covariance
matrix of the resulting vector is given by the (K − 1) x (K
− 1) matrix  formed by the appropriate jg . Finally,
the test statistic is given by the quadratic form:
ˆ
SS

     
t
1
1K1 1K1
Zι,,ZιZι,,Zι


 X



If the null hypothesis H0 is true and the sample size is
large, X is approximately distributed as a chi-square with
K − 1 degrees of freedom. An α-level test of H0 thus re-
jects the null hypothesis when X is greater than the upper
α-quantile of this chi-square. In particular, when K = 2,
as is the case in our data set, X should be distributed as a
chi-square with 1 degree of freedom under H0.
A variety of weight functions have been proposed in
the literature (see [4-8], and [3] for a review). The most
common and widely used test has W(t) = 1 for all t. This
test is referred to as the Mantel-Haenszel or log-rank test,
and is available in any modern statistical software. It has
optimum power to detect alternatives where the hazard
rates in the K treatment groups are proportional to each
other.
Fleming and Harrington proposed (see [3]) a very
general class of tests that includes the Mantel-Haenszel
test as a special. Let Ŝ(t) be the Kaplan-Meier estimator
of the common survival function under H0, based on the
combined treatment groups. The weight function in the
Harrington-Fleming’s test is, at time ti:
 
q
p,qii 1i 1
ˆˆ
Wt St1St,p0,q0
p


 
 (4)
Here, the survival function at the previous death time
is used as a weight for mathematical reasons (this en-
sures that these weights are known just prior to the time
at which the comparison is to be made). Letting p = q = 0
in (4) results in the Mantel-Haenszel test. Letting p = 1
and q = 0 results in a version of the Mann-Whitney-
Wilcoxon test. When p > 0 and q = 0, Wp,q give the most
weight to early departures between the hazard rates in the
K groups, whereas when p = 0 and q > 0, the corre-
sponding tests give most weight to departures which oc-
cur late in time. By an appropriate choice of p and q, one
can construct tests which have the greatest power against
alternatives where the K hazard rates differ over any de-
sired region.
We applied this methodology to our data sets. Flem-
ing-Harrington test (with p = 0.5 and q = 0.5) is more
sensitive to detect differences when the curves have a
delayed separation in time that is why sometimes the
results are significant. Mantel-Haenszel test is appropri-
ate when there is a proportional separation of curves.
3.3.2. Stratifi ed Test
As mentioned above, the log-rank tests test is useful
when each treatment group is homogeneous that is, when
the survival distribution is the same for every patient
within a group. A violation of this homogeneity usually
indicates that one needs to adjust the analysis for some
other (than the treatment group) covariate. For example,
previous studies suggest that an evaluation of CIMA
Vax®EGF efficacy should be stratified over age, since
homogeneity only holds within the two subpopulations
of patients under (respectively over) 60 years of age. One
possible approach to this issue is to base the decision on
a stratified version of one of the tests discussed above.
This approach is feasible when the covariate we adjust
for is categorical and its number of levels is not too large,
or when it is continuous but can be discretized into a
workable number of levels. In the sequel, we discuss
how such stratified tests are constructed, and how they
can be used to analyze our data.
Suppose that the covariate we need to adjust for is
discrete (or continuous and discretized), with M levels.
Then, we wish to test the hypothesis

 
0,strat 1s2sKs
H:htht ht,
for s1,M andtι



 (5)
against the alternative that at least one of the hjs is dif-
ferent from the others for some s and some t  . A strati-
fied test is constructed similarly as in (2) and (3) (for the
weighted version of the test), except that all quantities
are calculated by using only the data from the s-th stra-
tum, yielding Zjs() and s. The same weight functions as
in the previous section can be used for the stratified tests.
A global test of H0,strat in (5) is obtained by summing all
the within-stratum quantities, such as: Zj() = s = 1,···,M
Zjs() and ŝjg = s = 1,···,M ŝjgs. Finally, the stratified test sta-
tistic is defined as
 

 

t
1
1K1 1K1
ι,, ιZι,,ZιZZ 


strat
X
where  is the (K − 1) x (K − 1) matrix obtained from
the ŝjg's. If the null hypothesis H0,strat in (5) is true, and
the sample size is large, strat is approximately distrib-
uted as a chi-square with K − 1 degrees of freedom. An
α-level test of H0 thus rejects the null hypothesis when
strat is greater than the upper α-quantile of this
chi-square. In particular, when K = 2, as is the case in our
data set, strat should be distributed as a chi-square
with 1 degree of freedom under H0,strat.
X
X
X
4. RESULTS
We analyzed the data obtained from the phase II and

C. V. Gonzalez et al. / Modern Chemotherapy 2 (2013) 51-56
54
phase III trials described above, using the methodology
described in the previous section.
It was first analyzed both trials separately, and then
performed a single analysis by combining both data sets
(such a combination is appropriate here, since both stud-
ies had similar characteristics: inclusion and exclusion
criteria, schedule of treatment, ···).
We performed the Mantel-Haenszel test and the Flem-
ing-Harrington test with p = 0.5 and q = 0.5. We used the
stratified versions of both tests, and refining the results
by testing the hypothesis of no differences between CI-
MAVax ®EGF vaccine and standard therapy within each
stratum.
The results are summarized in Ta bl e 2 (for the phase
II trial), Tabl e 3 (for the phase III trial), and Tab le 4 (for
the combined data).
In Table 2 it is observed the median of survival for
both groups of phase II study (one patient with missing
data). The younger patients that received the vaccination
has the highest value (10.47 months) while the rest of
patients did not reach more than 7 months.
When age is not taken into account in the stratified
Table 2. Comparison of the results using two different approa- ches for Phase II study.
Mantel-Haenszel test
Strata Group N Events Median (0.95 CI) Stratified Model By Stratum
O V 17 17 5.63 (4.53, 8.53)
C
9 7 6.77 (1.57, NA)
p = 0.407
Y V
23 19 10.47 (3.20, 31.80)
C
30 29 5.33 (3.20, 8.20)
p = 0.25
p = 0.0493*
Fleming-Harrington test with p = 0.5 and q = 0.5
Strata Group N Events Median (0.95 CI) Stratified Model By Stratum
O V
17 17 5.63 (4.53, 8.53)
C
9 7 6.77 (1.57, NA) p = 0.182
Y V
23 19 10.47 (3.20, 31.80)
C
30 29 5.33 (3.20, 8.20)
p = 0.37
p = 0.0383*
*p < 0.05 O: Older, Y: Younger, V: Vaccine, C: Control.
Table 3. Comparison of the results using two different approaches for Phase III study.
Mantel-Haenszel test
Stra-tum Group N Events Median 0.95 CI Stratified Model By Stratum
O V
138 98 10.83 (8.80, 12.87)
C
60 49 7.53 (5.39, 9.68)
p = 0.123
Y V
107 77 11.8 (8.18, 15.42)
C 51 40 7.17 (7.90, 11.31)
p = 0.049*
p = 0.045*
Fleming-Harrington test with p = 0.5 and q = 0.5
Stratum Group N Events Median 0.95 CI Stratified Model By Stratum
O V
138 98 10.83 (8.80, 12.87)
C
60 49 7.53 (5.39, 9.68)
p = 0.233
Y V
107 77 11.8 (8.18, 15.42)
C
51 40 7.17 (7.90, 11.31)
p = 0.108
p = 0.282
*p < 0.05 O: Older, Y: Younger, V: Vaccine, C: Control.

C. V. Gonzalez et al. / Modern Chemotherapy 2 (2013) 51-56 55
Table 4. Comparison of the results using two different approaches for combined trials.
Mantel-Haenszel test
Stra-tum Group N Events Median 0.95 CI Stratified Model By Stratum
O V 153 113 9.57 (7.44, 11.7)
C 69 57 7.17 (5.19, 9.15) p = 0.181
Y V 129 95 11.73 (8.64, 14.82)
C 79 67 6.4 (4.97, 7.83)
p = 0.002**
p= 0.001**
Fleming-Harrington test with p = 0.5 and q = 0.5
Stra-tum Group N Events Median 0.95 CI Stratified Model By Stratum
O V 153 113 9.57 (7.44, 11.7)
C 69 57 7.17 (5.19, 9.15) p = 0.447
Y V 129 95 11.73 (8.64, 14.82)
C 79 67 6.4 (4.97, 7.83)
p = 0.027*
p = 0.019*
*p < 0.05; **p < 0.005; O: Older, Y: Younger, V: Vaccine, C: Control.
F
igure 1. Kaplan Meier Survival curves for phase II, III and combined trials in each of the strata.

C. V. Gonzalez et al. / Modern Chemotherapy 2 (2013) 51-56
56
model p values are non-significant but in the stratum
analysis for the younger patients receiving CIMAVax
®EGF and for both methods p values are less than 0.05.
It is observed that there is a survival advantage for
younger patients with this vaccine.
P values for the older stratum were non-significant for
both approaches.
Tabl e 3 shows the results of Phase III trial. In case of
the Mantel Haenzel test p value was significant and again
the youngest people have an advantage (approximately 4
months) if they receive the vaccine with the overall sur-
vival greater than those patients in the standard therapy.
Regarding the analysis of Non proportional hazard rate
p values were non-significant.
In Table 4 the combined data of Phase II and Phase III
studies are shown, for both methods performed without
taking into account the age p values are less than 0.05,
and considering the age, younger stratum is benefit if
they are vaccinated with CIMAVax®EGF.
There is an advantage regarding median values for the
patients under 60 years (5 months with a significant cli-
nical and statistical relevance)
From the Figure 1, the survival curves in the CI-
MAvax®EGF vaccine group and standard therapy group
diverge (at least in the younger stratum) after some time
has elapsed, which suggests that a Fleming-Harrington
test with q > 0 (that is, for detecting a delayed difference)
is appropriate.
It is observed that survival curves from the younger
stratum are clearly separated, so the vaccinated group has
an advantage over the group that only received the stan-
dard therapy while for the older patients for both groups
of treatment the benefit is the same. In all the survival
curves regarding the youngest patients vaccinated (the
last column of Figure 1) it is observed that the separation
of the curves occurs early in time however patients over
60 years the effect of the vaccine is seen later (central
column of the figure)
5. CONCLUSION
According to the results of the finished phase II trial,
we conclude that the group that received the CIMAVax
®EGF vaccine has a better response in the younger stra-
tum. The analysis of the phase III trial data also corrobo-
rates these results which contributes to obtain the sani-
tary registration of this vaccine. When both studies phase
II and III are combined, we also infer that the vaccine-
tion with CIMAVax®EGF is more efficient in younger
subjects since the median survival was of eleven months
which is a remarkable figure for patients with NSCLC.
6. ACKNOWLEDGEMENTS
This work has been supported by a UICC International Cancer
Technology Transfer Fellowship. We thank: Monitor Group: Bárbara
Wilkinson Brito, MSc. Clinical Laboratory; Liana Martínez, MSc. Ex-
perimental Pharmacology; Mayelin Troche de la Concepción, BSc.
Nursing; Aymara Fernandez Lorente, Medical Doctor; Data Manage-
ment Group: Yanela Santiesteban González, Informatic Technique,
Yuliannis Santiesteban González, Informatic Technique; Mabel Álvarez
Cardona, Informatic Technique; Aliuska Frías Blanco, Informatic
Technique.
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