CIMAvax<sup>®</sup>EGF vaccine therapy for non-small cell lung cancer: A weighted log-rank tests-based evaluation

doi:10.4236/mc.2013.23006

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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: [email protected]

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

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

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:



j iijijiiiii

i1, D

WtYY1YYYdY 1d,

j1, ,K













and the covariance of Zj() and Zg() is:

C. V. Gonzalez et al. / Modern Chemotherapy 2 (2013) 51-56 53

 

jjj iijiigiiiii

i1, D

SWtYYYYYdY1









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

 

Zι,,Zι



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:



 



 



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:

 

p,qii 1i 1

ˆˆ

Wt St1St,p0,q0





 

 (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

 



 



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.

4. RESULTS

We analyzed the data obtained from the phase II and

C. V. Gonzalez et al. / Modern Chemotherapy 2 (2013) 51-56

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)

9 7 6.77 (1.57, NA)

p = 0.407

Y V

23 19 10.47 (3.20, 31.80)

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)

9 7 6.77 (1.57, NA) p = 0.182

Y V

23 19 10.47 (3.20, 31.80)

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)

60 49 7.53 (5.39, 9.68)

p = 0.123

Y V

107 77 11.8 (8.18, 15.42)

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)

60 49 7.53 (5.39, 9.68)

p = 0.233

Y V

107 77 11.8 (8.18, 15.42)

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.

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

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.

OPEN ACCESS

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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