Modelling HIV vaccination

-_-- ..

-I.--.~,..-.-"

1I REVIE"'S j

I

Modelling HIV vaccination Angela R. McLean and Sally M. Blower

T

Relatively recently, mathematical models vaccine can fail in different wo aspects of the biology ways: it might give complete of HIV raise particular have been applied to issues related to protection to some people and questions about the testHIV vaccination. Significant progress has been made towards understanding how none to others; alternatively, it ing and use of a prophylactic might reduce (but not elimivaccine. First, few, if any, people rather ineffective vaccines will perform in trials and in the community, but some nate) everybody'S probability mount an immune response of infection on exposure. They that is strong enough to clear areas still need research. show that, in calculating the their infection. It is therefore A.R. McLeall' is ill the Zoology Dept, vaccine efficacy, the approunlikely that a highly effective Oxford Ulliversity, So 11th Parks Road, Oxford, vaccine will be available soon. priate measure of incidence in UK OX1 3PS, alld also ill the Lahoratoire des Second, HIV is mostly spread dYllamiqlles lymphoc)'taires, Illstitllt Pastel/r, 25 TIle vaccinated and unvaccinated groups is determined by the through sexual intercourse. Its dll Doctellr ROllx, 75724 Paris Cedex 15, France; S.M. Blower is ill the Dept of Epidemiology alld manner in which the vaccine rate of transmission in a comfails. For a vaccine that community thus depends strongly Biostatistics, Ulliversity of California Sail Frallcisco, Sail Frallcisco Gelleral Hospital, Sail Frallcisco, pletely protects some people on the sexual behaviour within CA 94143-1347, USA. 'tel: +33145688582, that community. While moland does nothing for others, fax: +33 1 45688639, e-mail: amc/[email protected] ecular immunologists and virolthe appropriate measure is the ogists have been busy constructtotal number of cases over the ing candidate vaccines, mathematical epidemiologists course of the trial (also called the cumulative incihave been constructing models to investigate their po- dence). For a vaccine that gives only partial protectential impact. All the models grapple with questions tion to everybody, the appropriate measure is the raised by the two special properties of HIV. These number of cases per susceptible person per unit of time questions fall into two groups: those relating to the (also called the 'force of infection' or 'hazard'; see design and interpretation of clinical trials, and those Table I). Halloran and coworkers2 have called these two relating to the community-wide impact of a vaccine. types of vaccine 'all-or-nothing' and 'leaky' (Table I), Imperfect vaccines and efficacy trials and have calculated examples of how much difference The goal of a vaccine-efficacy trial is to estimate how it would make if the incorrect definition of incidence well a vaccine works. This is done by comparing the was used in a trial. Figure 1 summarizes one set of incidence of infection in a vaccinated group with that such calculations. The correct definition of incidence in a control group. The standard definition! of vaccine gives the true efficacy of the vaccine; using the incorefficacy, E, is: rect definition yields estimates of the vaccine efficacy that diverge away from the true value over time. E = 1- ( incidence rate in vaccinated group ) incidence rate in unvaccinated group

For example, if there were five cases among the vaccinated group for every 100 cases among the control group, the efficacy of the vaccine would be estimated as 95%. In a very influential paper (that was apparently the outcome of a class exercise), Smith et al.! discuss how different mechanisms of vaccine failure ought to be detected in clinical trials. They recognize that a

Herd immunity and vaccine impact The impact of a vaccine in the community is determined by more than just the efficacy measured in vaccine trials. The duration of vaccine-induced immunity is important, as are any differences in the natural history of HIV infection in vaccine failures. One way to summarize the impact of a vaccine in a community is to calculate the reproductive rate of the infection in a community receiving a given coverage of vaccination 3 • The basic reproductive rate is the number of secondary

Table 1. Terminological equivalents in three different models for vaccination against HIV Appropriate measure of incidence for vaccine efficacy

Smith et al. 1

Halloran et al,2

McLean and BlowerS

Interpretation

Modell

Leaky

Degree

Vaccine protects everyone partially

Force of infection or hazard

Model 2

AII·or-nothing

Take

Vaccine protects a fraction completely

Cumulative incidence

o

t 995 Else,·ier Science Ltd 0966842X1951$09.50

TRENDS IN MICROBIOLOGY

458

VOl.. 3

No. 12

DECEl\.1BER

1995

REVIE'W"S

0.6

Hazard for all-or-nothing

i~ l--~o=====::::::====================~~~~~~~::~~~::::~~~ 0.5

______ - ________________________________________c_o_r_r_e_ct_m __e_a_s_u_re______

>

Cumulative incidence for leaky

'tJ III

~

0.4

iii

w

0.3

+-----------~----------.---------_,._---------.-----------.

o

2

4

8

6

10

Time (years)

cases caused by one infectious case introduced into a community where everybody else is susceptible. If we denote by Ro the basic reproductive rate for an unvaccinated person when everyone else is susceptible, and by Rp the reproductive rate in a community where a fraction p has been vaccinated\ we can express Rp in terms of Ro and parameters describing the properties of the vaccine. Three different types of vaccine failure can be combined into a single summary measure that we call 'vaccine impact', cp (Ref. 5). Like Smith et a/. I , we consider the case of vaccines working in some people, but not in others (this we call 'take'). We also consider the case of the vaccine giving incomplete protection (that is, reducing the degree of susceptibility) to those in whom it takes (this we call 'degree'). We add the possibility that vaccine-induced immunity might wane over time (this we call 'duration'). We have shown that, for a vaccine that takes in a fraction E, gives a degree of protection \jf (that is, reduces the per-exposure probability of infection by an amount \jf), and gives protection that lasts, on average, for a time 1/0), in a population in which individuals have a mean duration of sexual activity 1/1!, the overall measure of vaccine impact, , is: ¢=E\jfl!/ (I! + 0))

The vaccinated reproductive rate, Rp, for a population that receives this vaccine with a coverage p (that is, a fraction p are vaccinated) is then: Rp=(1-CPp)Ro

Impact, is the amount by which vaccine coverage should be reduced when calculating the impact a vaccine will have on transmission in the community. It is therefore a generalization of the well-established concept of vaccine efficacy, which includes the possibility that vaccine-induced immunity might not be permanent. Below, we show how to calculate ¢ when vaccine failures have a different natural history of HIV infection from people who have never seroconverted. As ¢ de-

TRENDS IN MICROmOLOGY

459

Fig. 1. Implications of vaccine failures for trials. Trials that use an inappropriate design could yield very poor estimates of the true effect of a vaccine. For a leaky vaccine (where everyone is somewhat protected). a trial based on the force of infection (also called the hazard) is appropriate. For an all-or-nothing vaccine (where everybody is either fully protected or not at all). cumulative incidence is the appropriate measure .. This example is from Halloran et al.9. and assumes a background force of infection of 0.05 per susceptible person per year and a true vaccine efficacy of 50%.

pends linearly on E and \jf, vaccines that are imperfect in take or degree of protection have a lower populationlevel impact than that of an ideal vaccine in an intuitively obvious way. The relationship between the duration of protection and the population-level impact is not so intuitively clear. As illustrated in Fig. 2, vaccine impact is very sensitive to the duration of protection. A vaccine that gives perfect protection that wanes with a half-life of 10 years is only as good as a vaccine that fully protects 30% of people for the rest of their lives. Rp can be used to calculate the theoretical vaccination coverage needed to eradicate an infection. It can also be used as a broader measure of the effect that a given level of intervention will have even if eradication is not achieved. Vaccines with the same impact (and hence the same coverage required for eradication) will reduce the reproductive rate in a vaccinated population, Rp, by the same amount if given at the same coverage. Interestingly, this does not necessarily lead to identical seroprevalence levels. Figure 3 shows how four vaccines with the same impact lead to different seroprevalence levels over time. Even the equilibrium levels are different for vaccines in which the degree of protection is less than one. \Y/e have extended vaccine impact, , to include the possibility that vaccine failures might have a different natural history of HIV infection from people who have never been vaccinated. Under these circumstances, the duration element is removed from the calculations, as we assume that anybody in whom the vaccine takes has an altered course of infection (if they become infected). To evaluate the potential effects of vaccines that decrease infectiousness, the potential trade-off between decreased infectiousness and increased duration of infectiousness must be examined explicitly6. This tradeoff can be expressed in terms of a basic reproductive rate for those vaccinated successfully, R,.. Reduced infectiousness makes Rv smaller than Ro, but a longer infectious period makes it larger. It is easy to show (Box 1) that, for a population where a fraction p have

VOL.

3

No. 12 DECEJ'l.lBER 1995

REVIE"'\VS

Fig. 2. Implications of vaccine failures in the community. The impact of a vaccine at the community level is very sensitive to the duration of protections. The comparison with a vaccine that gives complete lifelong pretection is easily made because. for such a vaccine. vaccine impact is equal to take. So. for example. a vaccine that gives complete protection in everybody and that has a half·life of 10 years is only as good as a vaccine that takes in 30% of people. but protects them fully for the rest of their lives (dashed line).

0.6

z-

'e

0.5

:J

E

.S 'E

0.4

Q)

.r:. c:

o 0.3 U co c.

E 0.2 Q)

c:

'u o

g

0.1

0.0

~--------.-------~---------.--------.---------r--------'

o

5

10

20

15

30

25

Half-life of vaccine-induced immunity (years)

received a vaccine (which takes in a fraction E and protects to degree '1'), the appropriate average of Rv and R o is: Rp=(l-Ep)R o+ (l-'I')EpR v

A nice biological interpretation of this mathematical linear stability result is that Rp is the number of tertiary cases per secondary case (in the absence of densitydependent constraints). Halloran and colleagues7 derived this relationship for the special case in which everyone has been vaccinated (p = 1). Furthermore, if Rv= (l-1;)Ro, that is, vaccination reduces the lifetime infectiousness of a vaccine failure by an amount 1;, the new summary measure of vaccine imperfection is:

This has the reassuringly commonsensical biological corollary that reductions in susceptibility and reductions in infectiousness are interchangeable in their population-level impact. Altered levels of infectiousness among vaccine recipients have important implications for the design of vaccine trials. In particular, methods to detect such an effect are needed; this is an aspect of trial design that is under intense study at the moment (I. Longini, pers. commun.). Behavioural change during trials

The most obvious application of mathematics to the design of vaccine trials is in calculating how large the trial needs to be. Smith and colleagues have explained how this is done s; t4e required study size is a function of the ra te of HIV transmission in the community where

1.0

Fig. 3. Vaccines with the same impact. delivered at the same coverage. can lead to different levels of seroprevalence at coverage levels below those required to eradicate infection. The figure shows the sereprevalence over time for four vaccines that all have the same impact (¢=0.31) and are administered at the same noneradicating coverage (p= 80%). One vaccine gives only tem· porary protection (duration ro=0.069). one works only in some people (take E= 0.31). one gives all reCipients incomplete protection (degree 'V=0.31) and one combines all three types of imperfection (ro=0.02. E=0.6 and 'V=0.85).

0.9 0.8

Degree

Q)

> :;:::: 'iii

0.7

0

c. 0.6

e

Degree + take + duration

Q)

en c: 0

t

0.5

Take

0.4

0

c.

e

a..

0.3

Duration

0.2 0.1 0.0 0

20

40

60

80

100

120

140

Time (years)

TRENDS IN MICROBIOLOGY

460

VOl..

3

No. 12

DECEl\.lBER

1995

----- -

-- - ....

---

-_.

~

... -..

-

--

---- ...... -.-"":""2:"II..~

REVIE"WS

Box 1. Deriving Rp Rp is the reproductive rate in a population where a fraction p have received a vaccine. Rp=l is the eradication criterion. The normal definition of Ro is the number of secondary cases per primary case in a susceptible population. We need to know what kind of primary case it is.

Definitions The vaccine takes in a fraction E and gives a degree of protection \jI to those in whom it takes. Ro is the basic reproductive rate: the number of new cases generated by one person who is never successfully vaccinated if everyone that he or she meets is unvaccinated. Rv is the basic reproductive rate for vaccine failures. Vaccine failures are defined as people in whom the vaccine took, but who subsequently became infected. Secondary cases caused by a primary case Each primary case will cause Rj (l-Ep) cases among unprotected people, and R,(l- \jI)Ep cases among successfully vaccinated people, where i 0 if the primary case is unvaccinated, and i=v if the primary case is vaccinated.

=

Tertiary cases caused by secondary cases Each case in a previously unprotected person will cause Ro(l- \jIEp) tertiary cases. Each case in a previously successfully vaccinated person will cause Rv(l-\jIEp) tertiary cases. Tertiary cases per secondary case Total secondary cases =Rj (l-\jIEp) Total tertiary cases =R,(l-Ep)Ro(l-\jIEp) + R,(l-\jI)EpRv(l-\jIEp) Rp= (l-Ep)Ro+ (l-\jI)EpRv = number of tertiary cases per secondary case

the study is based 8 • Smith et al. point out that it is ethically necessary to counsel all participants in a study about reducing risky behaviour (a euphemism for unprotected sexual intercourse). Successful counselling reduces transmission, thus reducing the chance of detecting any effect of the vaccine in the study. This 'catch-22' implies that trials need to have a larger sample size, so that expected decreases in exposure resulting from successful counselling do not jeopardize the chance of detecting a beneficial effect of the candidate vaccine. Successful counselling, leading to reductions in risky behaviour, poses one set of problems for trials. Unsuccessful counselling, leading to increases in risky behaviour, poses another. If everybody in a trial (both vaccinees and controls) increases their risky behaviour equally, the estimated efficacy of the vaccine should be unchanged. But what if trial participants get themselves tested for HIV and then act differently depending on the result of that test? Itwould be reasonable for trial participants who test HIV positive to assume that they are in the vaccine arm of the trial. If they then increase their risky behaviour while those receiving the placebo do not, the chances of the trial giving an accurate estimate of the efficacy of the vaccine are again jeopardized. Halloran and coworkers 9 have calculated just how wrong the estimates might be for varying levels of behavioural change (Fig. 4). They point out that a trial that records exposure in some way would be much less prone to such problems. Halloran et aU analyse in some depth the extent to which ill-designed trials might give a 'wrong' answer. The following factors are allowed to vary: the 'true' efficacy of the vaccine, its mode of action, the extent to which risky behaviour increases and the fraction of participants that change their behaviour. The authors summarize their findings: 'A good vaccine will look

0.7 0.6 >.

u

C'Cl

0.5

~

0.4

(!)

0.3

Qj

c:

·u u

C'Cl

0.2

"'0

0.1

I

>

(!)

co

I

0 .§ iii w -0.1 -0.2 -0.3 0.5

1.5

2

2.5

Increase in contacts (factor)

TRENDS IN MICROBIOLOGY

461

VOl..

3

No. 12

DECEJ\.lBER

Fig. 4. Implications of changes in behaviour for trials. Trials that fail to record exposure (sex acts, number of partners or some combination) are very vulnerable to changes in behaviour leading to increased exposure among the vaccinated group of the trial. This example from Halloran et al. 9 assumes a background force of infection of 0.05 susceptible people per year (that is, each year 1 in every 20 susceptible people becomes infected) and a true vaccine efficacy of 50%. The vaccine is assumed to protect all recipients partially. The model trial uses the appropriate measure of incidence and has a thousand people in each group. All vaccinated individuals are assumed to increase their risky behaviour by the factor shown. The figure shows estimates of vaccine efficacy and 95% confidence intervals at 3 years (open circles) and 10 years (filled circles) after vaccination.

1995

~~

-----

REVIE-WS

c

1.0

~ (.)

0.9

0

Fig. 5. Implications of changes in behaviour in the community. Behavioural change in the wider community might be expected if a vaccine became widely available lO • If exposure was reduced (as a consequence of counselling at the time of vaccination), there would be a synergistic effect with the vaccine. However, if exposure was increased, some of the benefits of the vaccination programme would be abrogated, and it would become very difficult to eradicate infection. In the figure, the model community has Ro= 5 and so, with no behavioural change, a perfect (¢= 1) vaccine would eradicate infection at 80% vaccine coverage (dashed line).

'6

... ... Cll

Q)

0.8

.E

0.7

c 0

'E 0 c.

0.6

ec.

0.5

c 0

0.4

c

0.3

~

'u

¢=\.O

(.)

Cll

0.2

~

0.1

> 'iii

0

0.0 0

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

2

Relative level of risky behaviour

good under a variety of circumstances, while a poor vaccine will easily look worse than it is.'

could be very difficult to identify which people should be targeted. It is essential that these findings are taken into account when discussing targeted vaccination.

Behavioural issues during vaccine use

If a prophylactic vaccine was to complete a large-scale vaccine-efficacy trial successfully, it would presumably be used rapidly in high-risk communities (at least in developed countries). What would be its impact? We modelled the impact of a vaccine in a community using parameters derived from population-based studies of the homosexual community in San Francisco, USA5,lo,ll. As discussed above, we first addressed questions about the control, without eradication, of HIV in San Francisco (Fig. 3). We then went on to consider what would happen if people increased their risky behaviour because of a false sense of security endowed by the licensing of a vaccine. Figure 5 shows the relationship between vaccine impact, <1>, behavioural change and the proportion of the community that would need to be vaccinated to eradicate HIV in San Francisco. We have also derived an expression to estimate the circumstances under which it would be possible for increases in risky behaviour to overwhelm the beneficial effects of a vaccine completely. For example, consider the case of a vaccine that gives 50% protection and is given to 60% of people. If they respond with a 40% increase in their risky behaviour, the epidemic would get worse, not better. The great heterogeneity that exists in risky behaviour suggests that a vaccine might be targeted towards highrisk individuals and thus have a disproportionate effect 12 • Heterogeneity in sexual behaviour and risk of infection changes the impact of a nontargeted vaccination programme, and the pattern of mixing in the population is crucial to the impact of a targeted campaign. However, careful longitudinal studies of risky behaviour show that membership of high-risk groups is not stable over timeIJ, and that the risk of acquiring HIV infection is very dependent on the sexual networks to which an individual belongs '4 . This means that it

TRENDS IN MICROBIOLOGY

462

Conclusions

HIV, its treatment and prevention are rarely out of the news. Hopes rise and fall as vaccine and drug trials are announced or postponed. Basic science, too, provides sometimes hopeful, sometimes discouraging insights. The announcement early this year that some Gambian prostitutes have lymphocytes that might make them immune to infection with HIVI5 was tremendously encouraging to everyone hoping for a preventative vaccine. The news that there are some people with apparent protective immunity to infection is an extremely important boost to confidence that one day there will be vaccines to protect against infection with HIVI6. Now, while such vaccines are in development, is a good time to use mathematical models to question how they should be tested and, ultimately, how they should be used 17,lS. Acknowledgements

A.R.M. is funded by the Royal Society, S.M.B. by NIDA and NIAID. References

1 Smith, P.G., Rodrigues, L.c. and Fine, P.E.~1. (1984) Int. J. Epidemiol. 13, 87-93 2 Halloran, M.E., Haber, ~1. and Longini, I.R. (1992) Am. J. Epidemiol. 136, 328-343 3 Anderson, R.M. and May, R.~1. (1991) Infectious Diseases of Humans: Dynamics and Control, Oxford University Press 4 Longini, 1.11., Halloran, M.E. and Haber, M. (1993) Math. Biosci. 117,271-281 5 McLean, A.R. and Blower, S.~1. (1993) Proc. R. Soc. LOlldOIl SeT. B 253, 9-13 6 Anderson, R.~1., Gupta, S. and },!ay, R.M. (1991) NatllTe 350, 356-359 7 Halloran, ~I.E., Watelet, L. and Struchiner, c.J. (1994) Math. Biosci. 121, 193-225

VOL.

3

No. 12 DECEMBER 1995

"

5

REVIE"W"S

8 Smith, P.G., Hayes, R.J. and Mulder, D.W. (1991) AIDS 5 (Suppl. 2), S107-S113 9 Halloran, M.E. et al. (1994) Stat. Med. 13,357-377 10 Blower, S.M. and McLean, A.R. (1994) Science 265, 1451-1454 11 Blower, S.M. and McLean, A.R. (1995) Science 267, 1253-1254 12 Anderson, R.M., Swinton,J. and Garnett, G.P. (1995) Proc. R. Soc. London Ser. B 261, 147-151

13 Blower, S.M., van Griensven, G.J.P. and Kaplan, E.H. (1995) Epidemiology 6, 238-242 14 Service, S.K. and Blower, S.M. (1995) Proc. R. Soc. London Ser. B 260, 237-244 15 Rowland-Jones, S. et al. (1995) Natllre Med. 1,59-64 16 McLean, A.R. (1995) Proc. R. Soc. London Ser. B 261, 389-393 17 Mclean, A.R. (1995) Lancet 345, 272 18 Mclean, A.R. and Anderson, R.M. (1988) Epidemiol. Infect. 100,419-442

Bacterial superantigens in human disease: structure, function and diversity Robert G. Ulrich, Sina Bavari and Mark A. Olson All bacterial superantigens use common structural strategies to bind to major histocompatibility complex class II receptors, while binding the T cell antigen receptor in different ways. Overstimulation of the immune response is responsible for the acute pathological effects, while reactivation of developmentally silenced T cells might result in autoimmune disease. Certain diseases might be controlled with superantigens or genetically attenuated vaccines.

Mouse mammary tumor viruses (MMTVs) express a second class of superantigens that crete a variety of biologiwere first discovered as minor cally active proteins. Among lymphocyte-stimulating (Mis) these products are the 23determinants responsible for 29 kDa staphylococcal enteroT cell responses among MHCtoxins, the toxic-shock syndrome toxin (TSST-1) and matched mouse strains5• No human equivalent has yet been certain streptococcal proteins, identified. These retroviral which are collectively referred proteins may be more peptideto as superantigens (SAgs) belike in nature, as a proteolytic cause of their profound effects processing event is required for on the immune system!. The them to act as SAgs (Refs 6,7). Mycoplasma arthritidis mitoR.G. Ulrich· is ill the Dept of Immll1l010gy alld The SAgs of MMTV do not gen (MAM) is also an SAg, Moleclllar Biology, and S. Bavari and M.A. Olsoll but is unrelated to the staphyinteract with the same MHC are ill the Dept of Cell Biology and Biochemistry, lococcal enterotoxins or to class II protein surfaces as do Army Medical Research Institllte of Illfectiolls bacterial SAgs (Ref. 8), and diTSST-1 in primary structure Disease, Bldg 1425, Frederick, MD 21702, USA. ·tel: +1301 6194232, fax: +1301 6192348, rect receptor binding has been (B.C. Cole, pers. commun.). e-mail: [email protected] difficult to demonstrate. FurThe normal function of major histocompatibility comthermore, MMTV SAgs appear plex (MHC) class II molecules is to bind and present to have no sequence similarity with bacterial SAgs, peptide antigens to T cells. The MHC class II molecule suggesting that the viral products are an entirely sep(consisting of a and p subunits) is usurped by SAgs as arate class of proteins. a specific cellular receptor2 (Fig. 1), and the complex of MHC class II molecule and SAg stimulates a substan- Associations with human disease tially greater number of T cells than does an antigen- The effects of bacterial SAgs fall loosely into two catspecific response. Moreover, SAgs stimulate lympho- egories: (1) acute responses, for example, toxic-shock cytes expressing distinct T cell antigen receptor (TCR) syndrome and food poisoning, and (2) chronic autoimmune-related responses. The majority of menstrual Vp subsets. For example, human VpS-expressing T cells3 respond preferentially to the SAg staphylococcal and nonmenstrual-associated toxic-shock syndrome enterotoxin B (SEB), while those responding to staphy- cases are linked to TSST-1, and the remaining cases lococcal enterotoxin A (SEA) include VpS.3, 6.3 and are caused by staphylococcal enterotoxins 9 and 9.1. Free SAgs also have a I.ow binding affinity for the streptococcal pyrogenic exotoxins (SPEspo. A severe form of streptococcal pneumonia with accompanying TCR, independent of the MHC molecule 4 •

taPhytocoCCllS allrells and Streptococcus pyogeltes se-

S

ro 1995 Elsevier Science Ltd TRENDS IN MICROBIOLOGY

463

0966842X1951$09.50

VOL. 3

No.

12

DECEMBER 1995