- Email: [email protected]
Can we reduce the dose of a vaccine?
ELSEVIER
Can We Reduce the Dose of a Vaccine? Gerd Rosenkranz, PhD Behrinperke
AG, Liederbach,
FRG
ABSTRACT: This paper describes the planning, implementation,
and analysis of a clinical trial to develop a pediatric vaccine against the tick-borne encephalitis virus. The trial was primarily a dose-finding study with the following objectives: the protein content of the vaccine should be lower than that of the vaccine for adults (which was already approved) in order to reduce reactogenicity, especially the rate of fever reactions, in children. At the same time, the protein content had to be high enough so that the immunogenic@ of the pediatric vaccine would be at least equivalent to that of the vaccine for adults. We discuss in detail the definition of the equivalence criterion and the considerations
concerning sample size calculation. The methods described in this paper are also useful for designing clinical trials for the development of combined vaccines. 0 1997 Elsevier Science Inc. Controlled Clin Trials 1997;18:4%53
KEY WORDS: Vaccine trial, equivalence study, dose finding INTRODUCTION Tick-borne encephalitis (TBE) is the most important tick-transmitted human viral disease occurring in endemic areas of at least 13 European countries 111. In Slovakia, the Czech Republic, Austria, and Hungary, TBE represents a major health problem. In southern Germany, some 100 cases are reported annually. In 1991, a newly highly purified inactivated TBE virus particle vaccine was registered in Germany. The vaccine was shown to be immunogenic and safe in two immunization schedules: a conventional scheme with vaccinations on days 0, 28, and 300, and an abbreviated scheme with vaccinations on days 0, 7, and 21. During the first year after market launch many side effects such as headache, tiredness, joint pain, and, especially in children, elevated temperatures and fever were spontaneously reported. These adverse reactions were most prominent after the first vaccination [2]. A closer inspection of the available clinical data led to the conclusion that the antigen itself might be responsible for the side effects mentioned above. In this case, reducing the amount of antigen could lower the reactogenicity of the vaccine. On the other hand, antigen reduction could also diminish the vaccine’s immunogenicity. According to a dose-finding study in adults, the seroconversion rate reaches a plateau if the vaccine contains at least 1 bg of TBE protein 131. Seven days after the third vaccination according to the abbreviated schedule, the geometric mean titers
Address reprint requests to: Gerd Rosenkranz, PhD, SANDOZ Pharma Ltd., Biomedical Operations/ Biostatistics, Building 386, Room 1219, CH-4002 Basel, Switzerland. Received October 14, 1994; revised August 23, 2995, October 26, 1995. Controlled Clinical Trials 18&t53 (1997) 0 ELsevier Science Inc. 1997 655 Avenue of the Americas, New York, NY 10010
0197-2456/97/$17.00 SSDI 0197-2456(95)00261-8
G. Rosenkranz
44
(GMT) ranged from 3000 to 4100 for a protein content between 1 and 2 pg 141. In a group of 27 TBE convalescents who suffered from meningoencephalitis and encephalitis, a GMT of 12,125 has been recorded [5]. Since the protein content of the vaccine is 1.5 t.Lg,a reduction did not seem possible, in general; however, the immunogenic reaction of children was more pronounced than that of adults. In children aged under 14 years the induced antibody titer was about twice as high as those in adults after vaccination according to the abbreviated schedule. In addition, fever reactions were also observed more often in children. Therefore, it was decided to develop a pediatric vaccine by reducing the amount of TBE antigen if feasible. A clinical trial was planned with the primary objective of testing whether vaccination of children with lower doses induces antibody titers equivalent to those obtained in adults with the approved dose. The secondary objective was to investigate whether the rate of adverse reactions in the low-dose groups is lower than in the high-dose group of children. Two new doses for children (0.4 and 0.75 Fg) were tested because little was known about the dose-response relationship of TBE vaccines in children. The trial included two further groups of vaccinees as internal standards: a group of adults to deliver the reference value for the antibody titer, and a group of children vaccinated with the approved dose to provide the baseline for the occurrence rate of side effects. This latter group was necessary because event rates based on spontaneous reports while the vaccine is on the market are generally lower than those reported during a clinical trial. A possible reduction of side effects due to reduction of protein content might not be detected by comparing clinical trial data with data from routine annual safety reports. The following sections describe the biostatistical considerations during the planning phase of the trial, especially the formulation of the equivalence criterion and the sample size calculation, the recording and documentation of the main efficacy and safety variables, and the results of the trial. The methods described in this paper are also useful for designing clinical trials for the development of combined vaccines. In those studies one wants to show that combining several antigens within a single formulation yields equivalent or even better results with respect to immunogenicity and reactogenicity than administering the components separately. FORMULATION
OF THE EQUIVALENCE
CRITERION
At least three approaches to the equivalence problem are relevant to vaccines. One can formulate an equivalence criterion in terms of vaccine efficacy, seroconversion rate, or immunogenicity. The approach of vaccine efficacy requires large clinical trials under field conditions, the so-called household studies. For example, some thousands of vaccinees have been enrolled in studies that investigated the equivalence of the efficacy of whole-cell and acellular vaccines against pertussis (whooping cough) [6,7]. Because incidence of TBE is low even in endemic regions and because the disease cannot be transmitted from person to person, megatrials would be necessary to prove equivalence of efficacy. Seroconversion means that the immune system responds to an antigen stimulus by producing antigen-specific antibodies. Because seroconversion itself does not provide any information concerning the strength of the immunogenic reaction, we considered it to constitute only a weak criterion for equivalence.
Can We Reduce the Dose of a Vaccine?
45
Immunogenicity is measured in terms of levels of antibody titers determined from serially diluted blood samples. In our case, immunogenicity was evaluated by assaying the antibodies in an enzyme-linked immunosorbent assay (ELISA) 181. Though antibody titers are recorded on an ordinal scale, for statistical analysis of titer equivalence we assumed that the distribution of the antibody titers can be approximated by a log normal distribution. Titer equivalence was formulated in terms of the geometric mean titers. The GMTs ?A and yc of adults and children, respectively, were considered to be equivalent, if their ratio yA/ yc did not exceed the dilution factor which was 2 in our case, i.e., if 1ogZYA
-
lo&
YC
c
1
This criterion is reasonable because a variation of titer determinations of this range is regarded to be within the accuracy of the measuring process. Note that our equivalence criterion was one-sided in that it allowed yc to be larger than Y,+ This reflected our intention to look for doses that produce immunogenicity in children to be at least as strong as that in adults with the approved dose and not to look for equivalence in a strict (two-sided) sense. In the following, the term “equivalence” will be used for “at least equivalence” throughout. TESTING
FOR EQUIVALENCE
OF IMMUNOGENICITY
A test for equivalence was constructed using the usual confidence interval for the difference of means of normally distributed variables. This approach is similar to that described in Blackwelder [9] for testing equivalence for binary data. Let X,‘, . . ., X,’ denote the antibody titers of children and Y;, . . ., Yk those of adults. Furthermore let Xi = log, Xl and Yj = log, Y{ denote the respective log titer values. We assume that Xi and Yj are independently normally distributed with means 5 = log2 yc and 3 = log,? YAand a common variance I$. Then p = 2” is called the scatter factor of the distribution of the Xl and Y,‘. Note that because HX,
=Zrc] = P[Xi c 51 = l/2
the GMT of Xl is also the median of Xi. A similar relation holds for Y,’ and YA. To test for at least equivalence of immunogenicity we try to reject the hypothesis of nonequivalence: Ho: 7-j - 5 2 1 in favor of the alternative
of having equivalence:
H,: 7) - 5. < 1 Let
x =$:-,x,,Y = $;"=]Y,, where u = m + n lOO(1 - a) confidence
s = ~r~:‘=,(x; - X)’ + &(Y,
- Y)2]
2, the degrees of freedom of S2. The one-sided limit U of 0 = q - 5 is given by
upper
46
G.
Rosenkranz
Here tcr$ denotes the OLfractile of a t distribution with k degrees of freedom. Rejecting the hypothesis of nonequivalence if U < 1 gives an unbiased level OLtest for HO.This can easily be seen from the power function of this test, namely,
Y-X-0
T(0) = P&l < 11 = PO
[
SJ(m
P,JA] denotes the probability For 8 2 1 we find that
IT(e) s PO i
Similarly,
SAMPLE
Y-X-e
SJ(m
1-e
<
+ n)/mn
SJ(m
+
L;,
+ n)/mn
1
of the event A if 0 is the true parameter
I [
< t,;, = PO + n)/mn
Y-X
S&m
value.
1
< t,;, = a
+ n)/mn
for 0 < 1, ~(0) > OLholds, which proves our assertion.
SIZE CONSIDERATIONS: Since S -
IMMUNOGENICITY
can be approximated cr almost surely for n - 03,QT
d(e) = FL
i
a&m
1-e
+ L;,
+ n)/mn
with #defined by
i
where FL denotes the distribution function of a tdistributed random variable with k degrees of freedom. Let 1 - P be the required power for the equivalence test. Then one way to determine the required sample size of the trial is to postulate that equality of immunogenicity will be detected with a probability of 1 - S, i.e., e(O) = 1 - l3. Obviously, this requirement does not take into account the slope of the power function which declines from 1 - S at 61 = 0 to 01 at 8 = 1. As a consequence, the probability of detecting equivalence may be low when 8 lies near the border of the equivalence region. This is one of the major differences between equivalence trials and ordinary comparison trials. In the latter, the preassigned power is guaranteed over all parameter values of clinical importance, whereas in the former power may be low in regions of interest. To circumvent this problem, we can select a value 0 < f& < 1 that we want to classify as lying within the equivalence region with a sufficiently high probability 1 - POand calculate the sample size from $(0,) > 1 - So or 1 -
aJ(m
00 +ta;, 24-p,,
+ n)/mn
For fixed k = m + n, the left-hand side of the equation above is maximal for m = n. In this case, the number of vaccinees per group is given by
kf;Z(k-1) + $3,?,-I) 1 -
00
The following calculations always assume equal numbers of vaccinees enrolled into each experimental group. From previous studies we found that o = 1.4. To detect equality of immunogenicity with 90% power and a significance level of 5%, 35 vaccinees per group are required. If the true value of 0 is l/2, which lies just in the middle of the
Can We Reduce the Dose of a Vaccine?
47
0.8
0.6 $ 2 z
0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
Tie
0.5
0.4
0.6
0.7
0.8
0.9
1.0
difference of log-GMTs
1Sample size per group: Power of the test for equivalence
Figure 1
of immunogenicity
of vaccines.
equivalence region, equivalence of the GMTs can only be found with a probability of 40%. To protect ourselves against such a substantial loss of power, we required that *(l/2) = 0.8. A sample size of 98 vaccinees per group is necessary to satisfy this condition. Note that then equality of the GMTs could be detected with a probability of almost 1. The power functions for a trial with 35 and 98 vaccinees are plotted in Figure 1. Since a loss to follow-up rate of 30% was supposed, it was planned to enroll 150 vaccinees per group.
TESTING
EQUIVALENCE
BETWEEN
MORE THAN TWO GROUPS
So far we have proposed a solution for the equivalence problem for the case of two groups of vaccinees. Because in the present study equivalence had to be shown between two groups and a control, the issue of multiple comparisons arose. In general, some sort of cx adjustment is necessary in order to keep the overall error probability of falsely deciding in favor of equivalence below some preassigned bound. In the present situation, however, we can assume a monotone dose-response relationship, i.e., the higher of the two doses under study can be
G.
48
Rosenkranz
expected to induce higher antibody titers than the lower one. Let & (&J denote the GMT induced by the lower (higher) experimental dose administered to children. Under the above-mentioned assumption, the set of hypotheses
is a family of hypotheses closed under intersection in the sense of Marcus et al. [lo]. This is easily seen since & s F;* implies I-l,, rl Ho2 = Ho2. In this case both hypotheses can be tested with a level CYtest without violating the significance level of the experiment if testing is done sequentially: H,,, is only tested if Ho2 has been rejected. Thus, for showing equivalence for more than two groups in the setting of a dose-response study, no additional vaccinees per group are required. SAMPLE
SIZE CONSIDERATIONS:
REACTOGENICITY
The sample size considerations made above only cover the issue of proving equivalence of immunogenicity with some preassigned power. It should be kept in mind, however, that the reason for conducting the trial was the unexpected reactogenicity of the vaccine. Reactogenicity consists of a mixture of symptoms of a more or less subjective nature like headache, pain, or tiredness. The only symptom that is measurable quite objectively is fever. Since fever was the most prominent side effect in children, we selected rise of body temperature as the main criterion in the evaluation of reactogenicity. Fortunately, severe fever reactions (over 39°C) have only been observed in less than 5% of the vaccinated children. An improvement of tolerance could hardly be shown in terms of the frequency of severe fever reactions if only about 100 volunteers per group were enrolled into the trial. We therefore decided to use raised temperatures over 38°C as a surrogate criterion. With this definition, fever rates of about 15% were reported in children in previous studies. Because these reactions occurred mainly after the first vaccination, a comparison of fever rates between the highdose and the low-dose groups can be based on the total number of vaccinees enrolled in each group (i.e., 150). A reduction of the rate from 15% to 5% could then be detected with a power of 80% by means of Fisher’s exact test 1111. INVESTIGATIONAL
PLAN
Healthy children aged between 18 months and 14 years received three vaccinations of 0.5 ml vaccine according to the abbreviated immunization schedule on days 0, 7 + 1, and 21 2 1, with “2“ denoting predefined time windows. Each child was randomized to one of the three treatment groups. The vaccine in each group contained 0.4,0.75, and 1.5 pg TBE protein, respectively. Neither the physicians nor the vaccinees knew which dose was administered. According to the sample size considerations of the previous section, 450 children should be enrolled. A group of 150 adults who received the approved dose of 1.5 kg was also included as an internal standard for the GMT to which the GMTs of the children were compared. Blood samples for titer determination were taken from each vaccinee before the first vaccination and on day 42 (time window: 25 days), i.e., about 21 days after the third vaccination. The serum from these samples was assayed by
Can We Reduce the Dose of a Vaccine?
49
ELISA. To check the validity of the results we used an additional test system. Specifically, 40% of the sera from children and 20% of the sera from adults were also investigated with a neutralization test.
DOCUMENTATION
OF ADVERSE
EFFECTS
To be able to show any improvement of tolerance in the low-dose side effects had to be reported and documented in a standardized achieve this, the subjects-in the case of the children, their parents guardians-were asked to look for the following symptoms after each tion and to document the findings on a specially prepared sheet: l l
groups, way. To or legal vaccina-
Local reactions: reddening, swelling, or pain at the vaccination site General reactions: body temperature (measured rectally), tiredness, pain, headache, nausea, or vomiting
joint
Other reactions not listed were to be recorded in a separate space on the form. The exact time of the observations had to be noted. The target variable for tolerance was the frequency of temperatures raised above 38°C on the first 3 days after the first vaccination. The body temperature was measured rectally in the evening after each vaccination and in the morning and the evening of the following 2 days. Electronic thermometers were supplied to all of the subjects. To exclude lot effects, the study medication was obtained from a single lot, which was diluted to get the respective doses. The vaccinees’ (or their parents’) reports were entered by the investigator on the case record forms as adverse events. The study monitors checked completeness and correctness of this data transfer.
RESULTS:
STUDY
POPULATION
Between March 1993 and July 1993, 713 persons to be vaccinated were enrolled in 41 centers in Germany. The sizes of the three dosage groups were 173,175, and 174. The proportion of subjects older than 12 years ranged from about 9% to 16%, whereas the other age groups accounted for 40-50% of subjects. Thirteen of the children were younger than 2 years in the 0.4~kg dosage group; the corresponding figures for the 0.75q.g and the 1.5~kg dosage groups were 11 and 7, respectively. The distribution of sex, height, and weight was similar across groups. The age range for enrollment of adults was 18-60 years. The upper limit was chosen because the performance of the immune system decreases with increasing age. About 66% of the adults were between 20 and 40 years of age, and about 31% were between 40 and 59 years old. There were 95 male and 96 female subjects. A total of 6 subjects, 3 children and 3 adults, were considered dropouts, i.e., they did not complete the study according to protocol, in most cases because of intercurrent illnesses. Many of the protocol violations (about 20% of the subjects enrolled) were due to nonadherence to vaccination or blood sampling schedule, problems with obtaining serum and storage, or violation of the age limits. If possible, we included these vaccinees into an intention-to-treat analysis.
50
G.
12600
Rosenkranz
.
1 I
;
6400
;
3200
1
$ 1
.
16001
I
_
800
f 8
400
: I
200
i I
100
.
c Number: Group:
._.__~
n=169 Children
0.4ug
n=169
Children
O.?Sug
rl=169 Children
I
IT=178
1.5ug
Adults
1.5ug
Upper dashed Ilna: Median tlhr of adults Lowar dashed Ilne: Lowar limit of saroconverslon
Figure 2
Box-plots of TBE antibody titers (ELISA) after the 3rd vaccination.
IMMUNOGENICITY This section reports only the results of the intention-to-treat analysis because the results of the per-protocol analysis were nearly identical. The results obtained by ELISA and the neutralization test were highly correlated. The adults achieved a GMT of 1123 [scatter factor (SF) = 2.2; n = 1781, the children given 1.5 kg a GMT of 2009.4 (SF = 2.1; n = 169), the children given 0.75 kg a GMT of 1426.9 (SF = 2.1, n = 1691, the children given 0.4 kg a GMT of 1011.1 (SF = 2.3, n = 169). Hence, according to the equivalence criterion specified above, the GMTs in the children in the middle and the lowest dose group were equivalent to the adult GMT: the upper confidence limit for the comparison of the adult group with the middle (U = -0.12) and the lowest (U = 0.36) children’s dose group were both smaller than 1. The medians reflect the equivalence of the mean titers even more clearly (Figure 2): the median in the middle and in the lowest dosage group were the same as the median in the adult group. The median in the highest children’s dosage group was twice as high as the adult value, which confirms the results of former investigations that the immunogenicity of the vaccine is higher in children. REACTOGENICITY The most important criterion in the assessment of tolerance was the frequency of raised temperature. The use of antipyretics was allowed if body temperature
51
Can We Reduce the Dose of a Vaccine? 30
25
2
1 -~
3
0.40 -
7
2
+
0.75
~Fever ("C) Figure 3
3 -
z%%z38-39
1 -
2
3
7.50 >39
Number of vaccination Dose (ug)
I
Proportion of vaccinees with fever reactions possibly associated with the vaccine.
rose above 38.5”C, which did occur in 20 subjects. Therefore, the severity of fever cannot be judged perfectly and the number of cases with raised temperature higher then 39°C may have been underestimated. Despite this, the following conclusions can be drawn from the results displayed in Figure 3: l
l
At all dosages, most cases of raised temperature occurred after the first vaccination. The frequency of raised temperature was much lower on the middle dose than on the highest dose, but no further decrease can be observed after the application of the lowest dose.
Comparison of the total number of cases of raised temperature higher than 38°C after the first vaccination of the approved dose (32.4%) and the two other dosages (21.1% and 20.1%) showed a significant difference in the one-sided
G. Rosenkranz
52
Fisher’s exact test (p = 0.0066 and 0.012, respectively). These figures, compared with the rate of 15% estimated from previous studies, show that even taking lot variations into account, substantial underreporting of adverse events can occur in clinical trials if the events are not carefully asked for and documented in a standardized manner. The improved tolerance achieved by decreasing the amount of antigen administered was also observed for the general reactions: halving the dose resulted in a marked improvement, and the further reduction is only a marginal, additional benefit. In the assessment of local reactions, no dependence on the dose or on whether the first vaccination was compared with subsequent ones was evident.
DISCUSSION The objective of the study was to investigate whether reducing the amount of antigen in a TBE vaccine would improve tolerance in children while guaranteeing adequate immunogenicity. The aim of achieving equivalent immunogenicity to the 1.5+g dose in adults was fulfilled by both dosages tested in this study. Since halving the dose improved tolerance markedly but further reduction of the dose yielded only marginal additional benefit, an amount of 0.75 pg antigen per dose was chosen for the pediatric vaccine. Since young people aged over 12 years reacted nearly like adults, the upper age limit for the administration of the vaccine was set to 12 years. With this recommendation the Federal Institute for Sera and Vaccines (Paul Ehrlich Institute), Germany, approved the vaccine in February 1994. We want to make some comments on the equivalence test applied to this study. Since an equivalence criterion in terms of the GMT is very intuitive, we performed a test for equivalence based on a confidence interval for normally distributed random variables though the distribution of the titer values is discrete. We think that our approach can be justified because the usual t test with which our equivalence test is closely related is sufficiently robust under deviations from normality if sample size is large (see [121). A nonparametric approach for the equivalence problem at hand is also possible for example by using the upper 95% confidence limit U’ of the Hodges-Lehmann estimator for the shift of the distribution of the log titer values between children and adults [13,14]. Assuming this model, an equivalence region can be defined in the same way as it was done in the analysis of the present study. We performed the calculations without correction for ties and obtained U’ = 0 (U’ = 0.42) for the comparison of the titers of the adults with those of the children being vaccinated with the middle (low) dosage. Since the upper confidence limit is < 1 for both comparisons, the results of this nonparametric analysis support the results of the parametric analysis of the present study. It should be mentioned, however, that the sample size calculation would not be as straightforward as it was under the normal model. A more general but less intuitive approach would be to state equivalence in terms of the probability that the titers in children are lower than those in adults. In this setting, equivalence can be assumed if this probability is close to one half. The probability in question can be consistently estimated by the Mann-Whitney form of the Wilcoxon Rank Sum Test statistic. (It should be noted that this parameter is different from the shift of two distributions which
Can We Reduce the Dose of a Vaccine?
53
is estimated by the Hodges-Lehmann estimator mentioned above.) We did not work this out in detail because an easily interpretable equivalence region cannot be defined in such a straightforward way as described above. Equivalence studies for the immunogenicity studies of vaccines are becoming more and more important because so-called combined vaccines are now under development. Before these new vaccines can be approved and widely applied it has to be shown that the combination of several antigens within a single formulation is at least as protective as the components administered separately or consecutively. In those cases where a protective antibody titer is identified, these equivalence trials can be evaluated in terms of immunogenicity and the methods used in the present study can be applied. The author thanks his colleagues A. Berghout, MD, and O.-E. Girgsdies, PhD, for many stimulating discussions and a critical review of the manuscript. Also the comments of the editor and two referees helped very much to further improve the paper and are gratefully acknowledged.
REFERENCES 1. WHO. Tick-borne
encephalitis and haemorrhagic fever with renal syndrome in Europe. Report on a WHO meeting, Baden, 1983. Euro Reports and Studies N. 104, 1986.
2. Quast U, Fescharek R, Rosenkranz G, Franke V, Theobald K. Vertraeglichkeit FSME-Vakzine Behring. Der Kinderarzt. 1993;24:193-199.
der
3. Bock HL, Klockmann U, Juengst C, Schindel-Kuenzel F, Theobald K, Zerban R. A new vaccine against tick-borne encephalitis: initial trial in man including a doseresponse study. Vaccine. 1990;8:22-24. 4. Harabacz I, Bock HL, Juengst C, Klockmann U, Praus M, Weber R. A randomized phase II study of a new tick-borne encephalitis vaccine using three different doses and two immunization regimens. Vaccine. 1992;10:145-150. 5. Klockmann U, Bock HL, Kwasny H, Praus M, Cihlova V, Tomkova E, Krivanec K. Humoral immunity against tick-borne encephalitis virus following manifest disease and active immunization. Vaccine. 1991;9:4246. 6. Ad hoc group for the Study of Pertussis Vaccines. Placebo controlled trial of two cellular pertussis vaccines in Swedenprotective efficacy and adverse events. The Lancet. 1988;1:995-960. 7. Storsaeter I, Blackwelder WC, Hallander HO. Pertussis antibodies, protection and vaccine efficacy after household exposure. Am J Dis Child. 1991;146:167-172. 8. Heinz FX, Berger R, Tuma W, Kunz C. A topological and functional model of epitopes on the structural glycoprotein of tick-borne encephalitis virus defined by monoclonal antibodies. Virology. 1983;126:525-538. 9. Blackwelder WC. “Proving Trials. 1982;3:345-353.
the null hypothesis”
in clinical trials. Controlled
Clin
10. Marcus R, Peritz E, Gabriel KR. On closed testing procedures with special reference to ordered analysis of variance. Biometrika. 1976;63:655-660. 11. Casagrande JT, Pike MC, Smith PG. The power function of the “exact” test for comparing two binomial distributions. App Sfat. 1978;27:176-180. 12. Lehmann EL. Testing Statistical Hypotheses. 2nd Ed. New York: John Wiley; 1986. 13. Hodges JL, Lehmann Stat. 1963;34:598-611.
EL. Estimates
14. Lehmann EL. Nonparametric Stat. 1963;34:1507-1512.
of location based on rank tests. Ann Math
confidence intervals for a shift parameter.
Arm Math
Can We Reduce the Dose of a Vaccine? Gerd Rosenkranz, PhD Behrinperke
AG, Liederbach,
FRG
ABSTRACT: This paper describes the planning, implementation,
and analysis of a clinical trial to develop a pediatric vaccine against the tick-borne encephalitis virus. The trial was primarily a dose-finding study with the following objectives: the protein content of the vaccine should be lower than that of the vaccine for adults (which was already approved) in order to reduce reactogenicity, especially the rate of fever reactions, in children. At the same time, the protein content had to be high enough so that the immunogenic@ of the pediatric vaccine would be at least equivalent to that of the vaccine for adults. We discuss in detail the definition of the equivalence criterion and the considerations
concerning sample size calculation. The methods described in this paper are also useful for designing clinical trials for the development of combined vaccines. 0 1997 Elsevier Science Inc. Controlled Clin Trials 1997;18:4%53
KEY WORDS: Vaccine trial, equivalence study, dose finding INTRODUCTION Tick-borne encephalitis (TBE) is the most important tick-transmitted human viral disease occurring in endemic areas of at least 13 European countries 111. In Slovakia, the Czech Republic, Austria, and Hungary, TBE represents a major health problem. In southern Germany, some 100 cases are reported annually. In 1991, a newly highly purified inactivated TBE virus particle vaccine was registered in Germany. The vaccine was shown to be immunogenic and safe in two immunization schedules: a conventional scheme with vaccinations on days 0, 28, and 300, and an abbreviated scheme with vaccinations on days 0, 7, and 21. During the first year after market launch many side effects such as headache, tiredness, joint pain, and, especially in children, elevated temperatures and fever were spontaneously reported. These adverse reactions were most prominent after the first vaccination [2]. A closer inspection of the available clinical data led to the conclusion that the antigen itself might be responsible for the side effects mentioned above. In this case, reducing the amount of antigen could lower the reactogenicity of the vaccine. On the other hand, antigen reduction could also diminish the vaccine’s immunogenicity. According to a dose-finding study in adults, the seroconversion rate reaches a plateau if the vaccine contains at least 1 bg of TBE protein 131. Seven days after the third vaccination according to the abbreviated schedule, the geometric mean titers
Address reprint requests to: Gerd Rosenkranz, PhD, SANDOZ Pharma Ltd., Biomedical Operations/ Biostatistics, Building 386, Room 1219, CH-4002 Basel, Switzerland. Received October 14, 1994; revised August 23, 2995, October 26, 1995. Controlled Clinical Trials 18&t53 (1997) 0 ELsevier Science Inc. 1997 655 Avenue of the Americas, New York, NY 10010
0197-2456/97/$17.00 SSDI 0197-2456(95)00261-8
G. Rosenkranz
44
(GMT) ranged from 3000 to 4100 for a protein content between 1 and 2 pg 141. In a group of 27 TBE convalescents who suffered from meningoencephalitis and encephalitis, a GMT of 12,125 has been recorded [5]. Since the protein content of the vaccine is 1.5 t.Lg,a reduction did not seem possible, in general; however, the immunogenic reaction of children was more pronounced than that of adults. In children aged under 14 years the induced antibody titer was about twice as high as those in adults after vaccination according to the abbreviated schedule. In addition, fever reactions were also observed more often in children. Therefore, it was decided to develop a pediatric vaccine by reducing the amount of TBE antigen if feasible. A clinical trial was planned with the primary objective of testing whether vaccination of children with lower doses induces antibody titers equivalent to those obtained in adults with the approved dose. The secondary objective was to investigate whether the rate of adverse reactions in the low-dose groups is lower than in the high-dose group of children. Two new doses for children (0.4 and 0.75 Fg) were tested because little was known about the dose-response relationship of TBE vaccines in children. The trial included two further groups of vaccinees as internal standards: a group of adults to deliver the reference value for the antibody titer, and a group of children vaccinated with the approved dose to provide the baseline for the occurrence rate of side effects. This latter group was necessary because event rates based on spontaneous reports while the vaccine is on the market are generally lower than those reported during a clinical trial. A possible reduction of side effects due to reduction of protein content might not be detected by comparing clinical trial data with data from routine annual safety reports. The following sections describe the biostatistical considerations during the planning phase of the trial, especially the formulation of the equivalence criterion and the sample size calculation, the recording and documentation of the main efficacy and safety variables, and the results of the trial. The methods described in this paper are also useful for designing clinical trials for the development of combined vaccines. In those studies one wants to show that combining several antigens within a single formulation yields equivalent or even better results with respect to immunogenicity and reactogenicity than administering the components separately. FORMULATION
OF THE EQUIVALENCE
CRITERION
At least three approaches to the equivalence problem are relevant to vaccines. One can formulate an equivalence criterion in terms of vaccine efficacy, seroconversion rate, or immunogenicity. The approach of vaccine efficacy requires large clinical trials under field conditions, the so-called household studies. For example, some thousands of vaccinees have been enrolled in studies that investigated the equivalence of the efficacy of whole-cell and acellular vaccines against pertussis (whooping cough) [6,7]. Because incidence of TBE is low even in endemic regions and because the disease cannot be transmitted from person to person, megatrials would be necessary to prove equivalence of efficacy. Seroconversion means that the immune system responds to an antigen stimulus by producing antigen-specific antibodies. Because seroconversion itself does not provide any information concerning the strength of the immunogenic reaction, we considered it to constitute only a weak criterion for equivalence.
Can We Reduce the Dose of a Vaccine?
45
Immunogenicity is measured in terms of levels of antibody titers determined from serially diluted blood samples. In our case, immunogenicity was evaluated by assaying the antibodies in an enzyme-linked immunosorbent assay (ELISA) 181. Though antibody titers are recorded on an ordinal scale, for statistical analysis of titer equivalence we assumed that the distribution of the antibody titers can be approximated by a log normal distribution. Titer equivalence was formulated in terms of the geometric mean titers. The GMTs ?A and yc of adults and children, respectively, were considered to be equivalent, if their ratio yA/ yc did not exceed the dilution factor which was 2 in our case, i.e., if 1ogZYA
-
lo&
YC
c
1
This criterion is reasonable because a variation of titer determinations of this range is regarded to be within the accuracy of the measuring process. Note that our equivalence criterion was one-sided in that it allowed yc to be larger than Y,+ This reflected our intention to look for doses that produce immunogenicity in children to be at least as strong as that in adults with the approved dose and not to look for equivalence in a strict (two-sided) sense. In the following, the term “equivalence” will be used for “at least equivalence” throughout. TESTING
FOR EQUIVALENCE
OF IMMUNOGENICITY
A test for equivalence was constructed using the usual confidence interval for the difference of means of normally distributed variables. This approach is similar to that described in Blackwelder [9] for testing equivalence for binary data. Let X,‘, . . ., X,’ denote the antibody titers of children and Y;, . . ., Yk those of adults. Furthermore let Xi = log, Xl and Yj = log, Y{ denote the respective log titer values. We assume that Xi and Yj are independently normally distributed with means 5 = log2 yc and 3 = log,? YAand a common variance I$. Then p = 2” is called the scatter factor of the distribution of the Xl and Y,‘. Note that because HX,
=Zrc] = P[Xi c 51 = l/2
the GMT of Xl is also the median of Xi. A similar relation holds for Y,’ and YA. To test for at least equivalence of immunogenicity we try to reject the hypothesis of nonequivalence: Ho: 7-j - 5 2 1 in favor of the alternative
of having equivalence:
H,: 7) - 5. < 1 Let
x =$:-,x,,Y = $;"=]Y,, where u = m + n lOO(1 - a) confidence
s = ~r~:‘=,(x; - X)’ + &(Y,
- Y)2]
2, the degrees of freedom of S2. The one-sided limit U of 0 = q - 5 is given by
upper
46
G.
Rosenkranz
Here tcr$ denotes the OLfractile of a t distribution with k degrees of freedom. Rejecting the hypothesis of nonequivalence if U < 1 gives an unbiased level OLtest for HO.This can easily be seen from the power function of this test, namely,
Y-X-0
T(0) = P&l < 11 = PO
[
SJ(m
P,JA] denotes the probability For 8 2 1 we find that
IT(e) s PO i
Similarly,
SAMPLE
Y-X-e
SJ(m
1-e
<
+ n)/mn
SJ(m
+
L;,
+ n)/mn
1
of the event A if 0 is the true parameter
I [
< t,;, = PO + n)/mn
Y-X
S&m
value.
1
< t,;, = a
+ n)/mn
for 0 < 1, ~(0) > OLholds, which proves our assertion.
SIZE CONSIDERATIONS: Since S -
IMMUNOGENICITY
can be approximated cr almost surely for n - 03,QT
d(e) = FL
i
a&m
1-e
+ L;,
+ n)/mn
with #defined by
i
where FL denotes the distribution function of a tdistributed random variable with k degrees of freedom. Let 1 - P be the required power for the equivalence test. Then one way to determine the required sample size of the trial is to postulate that equality of immunogenicity will be detected with a probability of 1 - S, i.e., e(O) = 1 - l3. Obviously, this requirement does not take into account the slope of the power function which declines from 1 - S at 61 = 0 to 01 at 8 = 1. As a consequence, the probability of detecting equivalence may be low when 8 lies near the border of the equivalence region. This is one of the major differences between equivalence trials and ordinary comparison trials. In the latter, the preassigned power is guaranteed over all parameter values of clinical importance, whereas in the former power may be low in regions of interest. To circumvent this problem, we can select a value 0 < f& < 1 that we want to classify as lying within the equivalence region with a sufficiently high probability 1 - POand calculate the sample size from $(0,) > 1 - So or 1 -
aJ(m
00 +ta;, 24-p,,
+ n)/mn
For fixed k = m + n, the left-hand side of the equation above is maximal for m = n. In this case, the number of vaccinees per group is given by
kf;Z(k-1) + $3,?,-I) 1 -
00
The following calculations always assume equal numbers of vaccinees enrolled into each experimental group. From previous studies we found that o = 1.4. To detect equality of immunogenicity with 90% power and a significance level of 5%, 35 vaccinees per group are required. If the true value of 0 is l/2, which lies just in the middle of the
Can We Reduce the Dose of a Vaccine?
47
0.8
0.6 $ 2 z
0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
Tie
0.5
0.4
0.6
0.7
0.8
0.9
1.0
difference of log-GMTs
1Sample size per group: Power of the test for equivalence
Figure 1
of immunogenicity
of vaccines.
equivalence region, equivalence of the GMTs can only be found with a probability of 40%. To protect ourselves against such a substantial loss of power, we required that *(l/2) = 0.8. A sample size of 98 vaccinees per group is necessary to satisfy this condition. Note that then equality of the GMTs could be detected with a probability of almost 1. The power functions for a trial with 35 and 98 vaccinees are plotted in Figure 1. Since a loss to follow-up rate of 30% was supposed, it was planned to enroll 150 vaccinees per group.
TESTING
EQUIVALENCE
BETWEEN
MORE THAN TWO GROUPS
So far we have proposed a solution for the equivalence problem for the case of two groups of vaccinees. Because in the present study equivalence had to be shown between two groups and a control, the issue of multiple comparisons arose. In general, some sort of cx adjustment is necessary in order to keep the overall error probability of falsely deciding in favor of equivalence below some preassigned bound. In the present situation, however, we can assume a monotone dose-response relationship, i.e., the higher of the two doses under study can be
G.
48
Rosenkranz
expected to induce higher antibody titers than the lower one. Let & (&J denote the GMT induced by the lower (higher) experimental dose administered to children. Under the above-mentioned assumption, the set of hypotheses
is a family of hypotheses closed under intersection in the sense of Marcus et al. [lo]. This is easily seen since & s F;* implies I-l,, rl Ho2 = Ho2. In this case both hypotheses can be tested with a level CYtest without violating the significance level of the experiment if testing is done sequentially: H,,, is only tested if Ho2 has been rejected. Thus, for showing equivalence for more than two groups in the setting of a dose-response study, no additional vaccinees per group are required. SAMPLE
SIZE CONSIDERATIONS:
REACTOGENICITY
The sample size considerations made above only cover the issue of proving equivalence of immunogenicity with some preassigned power. It should be kept in mind, however, that the reason for conducting the trial was the unexpected reactogenicity of the vaccine. Reactogenicity consists of a mixture of symptoms of a more or less subjective nature like headache, pain, or tiredness. The only symptom that is measurable quite objectively is fever. Since fever was the most prominent side effect in children, we selected rise of body temperature as the main criterion in the evaluation of reactogenicity. Fortunately, severe fever reactions (over 39°C) have only been observed in less than 5% of the vaccinated children. An improvement of tolerance could hardly be shown in terms of the frequency of severe fever reactions if only about 100 volunteers per group were enrolled into the trial. We therefore decided to use raised temperatures over 38°C as a surrogate criterion. With this definition, fever rates of about 15% were reported in children in previous studies. Because these reactions occurred mainly after the first vaccination, a comparison of fever rates between the highdose and the low-dose groups can be based on the total number of vaccinees enrolled in each group (i.e., 150). A reduction of the rate from 15% to 5% could then be detected with a power of 80% by means of Fisher’s exact test 1111. INVESTIGATIONAL
PLAN
Healthy children aged between 18 months and 14 years received three vaccinations of 0.5 ml vaccine according to the abbreviated immunization schedule on days 0, 7 + 1, and 21 2 1, with “2“ denoting predefined time windows. Each child was randomized to one of the three treatment groups. The vaccine in each group contained 0.4,0.75, and 1.5 pg TBE protein, respectively. Neither the physicians nor the vaccinees knew which dose was administered. According to the sample size considerations of the previous section, 450 children should be enrolled. A group of 150 adults who received the approved dose of 1.5 kg was also included as an internal standard for the GMT to which the GMTs of the children were compared. Blood samples for titer determination were taken from each vaccinee before the first vaccination and on day 42 (time window: 25 days), i.e., about 21 days after the third vaccination. The serum from these samples was assayed by
Can We Reduce the Dose of a Vaccine?
49
ELISA. To check the validity of the results we used an additional test system. Specifically, 40% of the sera from children and 20% of the sera from adults were also investigated with a neutralization test.
DOCUMENTATION
OF ADVERSE
EFFECTS
To be able to show any improvement of tolerance in the low-dose side effects had to be reported and documented in a standardized achieve this, the subjects-in the case of the children, their parents guardians-were asked to look for the following symptoms after each tion and to document the findings on a specially prepared sheet: l l
groups, way. To or legal vaccina-
Local reactions: reddening, swelling, or pain at the vaccination site General reactions: body temperature (measured rectally), tiredness, pain, headache, nausea, or vomiting
joint
Other reactions not listed were to be recorded in a separate space on the form. The exact time of the observations had to be noted. The target variable for tolerance was the frequency of temperatures raised above 38°C on the first 3 days after the first vaccination. The body temperature was measured rectally in the evening after each vaccination and in the morning and the evening of the following 2 days. Electronic thermometers were supplied to all of the subjects. To exclude lot effects, the study medication was obtained from a single lot, which was diluted to get the respective doses. The vaccinees’ (or their parents’) reports were entered by the investigator on the case record forms as adverse events. The study monitors checked completeness and correctness of this data transfer.
RESULTS:
STUDY
POPULATION
Between March 1993 and July 1993, 713 persons to be vaccinated were enrolled in 41 centers in Germany. The sizes of the three dosage groups were 173,175, and 174. The proportion of subjects older than 12 years ranged from about 9% to 16%, whereas the other age groups accounted for 40-50% of subjects. Thirteen of the children were younger than 2 years in the 0.4~kg dosage group; the corresponding figures for the 0.75q.g and the 1.5~kg dosage groups were 11 and 7, respectively. The distribution of sex, height, and weight was similar across groups. The age range for enrollment of adults was 18-60 years. The upper limit was chosen because the performance of the immune system decreases with increasing age. About 66% of the adults were between 20 and 40 years of age, and about 31% were between 40 and 59 years old. There were 95 male and 96 female subjects. A total of 6 subjects, 3 children and 3 adults, were considered dropouts, i.e., they did not complete the study according to protocol, in most cases because of intercurrent illnesses. Many of the protocol violations (about 20% of the subjects enrolled) were due to nonadherence to vaccination or blood sampling schedule, problems with obtaining serum and storage, or violation of the age limits. If possible, we included these vaccinees into an intention-to-treat analysis.
50
G.
12600
Rosenkranz
.
1 I
;
6400
;
3200
1
$ 1
.
16001
I
_
800
f 8
400
: I
200
i I
100
.
c Number: Group:
._.__~
n=169 Children
0.4ug
n=169
Children
O.?Sug
rl=169 Children
I
IT=178
1.5ug
Adults
1.5ug
Upper dashed Ilna: Median tlhr of adults Lowar dashed Ilne: Lowar limit of saroconverslon
Figure 2
Box-plots of TBE antibody titers (ELISA) after the 3rd vaccination.
IMMUNOGENICITY This section reports only the results of the intention-to-treat analysis because the results of the per-protocol analysis were nearly identical. The results obtained by ELISA and the neutralization test were highly correlated. The adults achieved a GMT of 1123 [scatter factor (SF) = 2.2; n = 1781, the children given 1.5 kg a GMT of 2009.4 (SF = 2.1; n = 169), the children given 0.75 kg a GMT of 1426.9 (SF = 2.1, n = 1691, the children given 0.4 kg a GMT of 1011.1 (SF = 2.3, n = 169). Hence, according to the equivalence criterion specified above, the GMTs in the children in the middle and the lowest dose group were equivalent to the adult GMT: the upper confidence limit for the comparison of the adult group with the middle (U = -0.12) and the lowest (U = 0.36) children’s dose group were both smaller than 1. The medians reflect the equivalence of the mean titers even more clearly (Figure 2): the median in the middle and in the lowest dosage group were the same as the median in the adult group. The median in the highest children’s dosage group was twice as high as the adult value, which confirms the results of former investigations that the immunogenicity of the vaccine is higher in children. REACTOGENICITY The most important criterion in the assessment of tolerance was the frequency of raised temperature. The use of antipyretics was allowed if body temperature
51
Can We Reduce the Dose of a Vaccine? 30
25
2
1 -~
3
0.40 -
7
2
+
0.75
~Fever ("C) Figure 3
3 -
z%%z38-39
1 -
2
3
7.50 >39
Number of vaccination Dose (ug)
I
Proportion of vaccinees with fever reactions possibly associated with the vaccine.
rose above 38.5”C, which did occur in 20 subjects. Therefore, the severity of fever cannot be judged perfectly and the number of cases with raised temperature higher then 39°C may have been underestimated. Despite this, the following conclusions can be drawn from the results displayed in Figure 3: l
l
At all dosages, most cases of raised temperature occurred after the first vaccination. The frequency of raised temperature was much lower on the middle dose than on the highest dose, but no further decrease can be observed after the application of the lowest dose.
Comparison of the total number of cases of raised temperature higher than 38°C after the first vaccination of the approved dose (32.4%) and the two other dosages (21.1% and 20.1%) showed a significant difference in the one-sided
G. Rosenkranz
52
Fisher’s exact test (p = 0.0066 and 0.012, respectively). These figures, compared with the rate of 15% estimated from previous studies, show that even taking lot variations into account, substantial underreporting of adverse events can occur in clinical trials if the events are not carefully asked for and documented in a standardized manner. The improved tolerance achieved by decreasing the amount of antigen administered was also observed for the general reactions: halving the dose resulted in a marked improvement, and the further reduction is only a marginal, additional benefit. In the assessment of local reactions, no dependence on the dose or on whether the first vaccination was compared with subsequent ones was evident.
DISCUSSION The objective of the study was to investigate whether reducing the amount of antigen in a TBE vaccine would improve tolerance in children while guaranteeing adequate immunogenicity. The aim of achieving equivalent immunogenicity to the 1.5+g dose in adults was fulfilled by both dosages tested in this study. Since halving the dose improved tolerance markedly but further reduction of the dose yielded only marginal additional benefit, an amount of 0.75 pg antigen per dose was chosen for the pediatric vaccine. Since young people aged over 12 years reacted nearly like adults, the upper age limit for the administration of the vaccine was set to 12 years. With this recommendation the Federal Institute for Sera and Vaccines (Paul Ehrlich Institute), Germany, approved the vaccine in February 1994. We want to make some comments on the equivalence test applied to this study. Since an equivalence criterion in terms of the GMT is very intuitive, we performed a test for equivalence based on a confidence interval for normally distributed random variables though the distribution of the titer values is discrete. We think that our approach can be justified because the usual t test with which our equivalence test is closely related is sufficiently robust under deviations from normality if sample size is large (see [121). A nonparametric approach for the equivalence problem at hand is also possible for example by using the upper 95% confidence limit U’ of the Hodges-Lehmann estimator for the shift of the distribution of the log titer values between children and adults [13,14]. Assuming this model, an equivalence region can be defined in the same way as it was done in the analysis of the present study. We performed the calculations without correction for ties and obtained U’ = 0 (U’ = 0.42) for the comparison of the titers of the adults with those of the children being vaccinated with the middle (low) dosage. Since the upper confidence limit is < 1 for both comparisons, the results of this nonparametric analysis support the results of the parametric analysis of the present study. It should be mentioned, however, that the sample size calculation would not be as straightforward as it was under the normal model. A more general but less intuitive approach would be to state equivalence in terms of the probability that the titers in children are lower than those in adults. In this setting, equivalence can be assumed if this probability is close to one half. The probability in question can be consistently estimated by the Mann-Whitney form of the Wilcoxon Rank Sum Test statistic. (It should be noted that this parameter is different from the shift of two distributions which
Can We Reduce the Dose of a Vaccine?
53
is estimated by the Hodges-Lehmann estimator mentioned above.) We did not work this out in detail because an easily interpretable equivalence region cannot be defined in such a straightforward way as described above. Equivalence studies for the immunogenicity studies of vaccines are becoming more and more important because so-called combined vaccines are now under development. Before these new vaccines can be approved and widely applied it has to be shown that the combination of several antigens within a single formulation is at least as protective as the components administered separately or consecutively. In those cases where a protective antibody titer is identified, these equivalence trials can be evaluated in terms of immunogenicity and the methods used in the present study can be applied. The author thanks his colleagues A. Berghout, MD, and O.-E. Girgsdies, PhD, for many stimulating discussions and a critical review of the manuscript. Also the comments of the editor and two referees helped very much to further improve the paper and are gratefully acknowledged.
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der
3. Bock HL, Klockmann U, Juengst C, Schindel-Kuenzel F, Theobald K, Zerban R. A new vaccine against tick-borne encephalitis: initial trial in man including a doseresponse study. Vaccine. 1990;8:22-24. 4. Harabacz I, Bock HL, Juengst C, Klockmann U, Praus M, Weber R. A randomized phase II study of a new tick-borne encephalitis vaccine using three different doses and two immunization regimens. Vaccine. 1992;10:145-150. 5. Klockmann U, Bock HL, Kwasny H, Praus M, Cihlova V, Tomkova E, Krivanec K. Humoral immunity against tick-borne encephalitis virus following manifest disease and active immunization. Vaccine. 1991;9:4246. 6. Ad hoc group for the Study of Pertussis Vaccines. Placebo controlled trial of two cellular pertussis vaccines in Swedenprotective efficacy and adverse events. The Lancet. 1988;1:995-960. 7. Storsaeter I, Blackwelder WC, Hallander HO. Pertussis antibodies, protection and vaccine efficacy after household exposure. Am J Dis Child. 1991;146:167-172. 8. Heinz FX, Berger R, Tuma W, Kunz C. A topological and functional model of epitopes on the structural glycoprotein of tick-borne encephalitis virus defined by monoclonal antibodies. Virology. 1983;126:525-538. 9. Blackwelder WC. “Proving Trials. 1982;3:345-353.
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14. Lehmann EL. Nonparametric Stat. 1963;34:1507-1512.
of location based on rank tests. Ann Math
confidence intervals for a shift parameter.
Arm Math