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`lStatistical Centerf0I HIV/AIDS Research and Prevention, Fred Hutchinson CaneeIResearch Center and
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`Department of Biostatistics, University of Washington, Seattle, WA 98105, U. S A.
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`~Department of Statistics, Florida State University, Tallahassee, FL 32306, U S. A.
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`3Harvard AIDS Institute and Department of Immunology and Infectious Diseases, Harvard School of Public
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`Health, Boston, MA 02115, USA.
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`4Laboratoire de Bactériologie- Viiologie, UIIiveIsité CIIeIkh Anta Diop, Dakar, Senegal
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`SUMMARY
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`From a prospective cohort study of I948 initially human immunodeficiency virus (HIV) uninfected'fe—
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`male commercial sex workers followed between 1985 and 1999 in Dakar, Senegal, the authors compared
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`the male to female per infectious sexual exposure ’transmission probability of HIV types one (HIV-1)
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`and two (HIV-2). New nOn-parametric competing risks failure time methods were used, which mini-
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`mized modelling assumptions and controlled for risk factors for HIV infection. The HIV—1 versus HIV-2
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`.infectivity ratio over time was estimated by the ratio of smoothed non-parametric kernel estimates of
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`the HIV-1 and HIV-2 infection hazard functions in sex workers, adjusted by an estimate of the relative
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`HIV-l versus HIV—2 prevalence in the partner population. HIV-l was found to be significantly more-
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`infectious than HIV-2 throughout the follow-up period (P<0.001): The HIV-1/HlV-2 infectivity ratio
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`was inferred to be approximately constant over time, with estimated common value 3.55.'The finding
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`' of greater HIV-1 infectivity persisted in sensitivity analyses and in covariate-adjusted analyses, with
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`. adjusted infectivity ratio estimates ranging between 3.40 and 3.86. Understanding the mechanisms by
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`which HIV-I infects more efficientlythan HIV-2 may be useful in the development of HIV-1' vaccines.
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`Additionally, the methodology developed here may be useful for analysing other data sets. Copyright
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`© 2003 JohnWi‘ley & Sons, Ltd;
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`KEY WORDS:
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`cause specific hazard rates; competing risks; HIV transmission, infectious diseases,
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`sexually transmitted diseases; survival analysis
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`* Correspondence to: Peter Gilbert, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue North, MW-
`500, P. O. Box 19024, Seattle, WA 98109, U. S. A.
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`i E-mail. pgilbert@scharp.org
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`Contract/grant sponsor: National Institutes of Health, contract/grant numbers: A124643, AI46703—01.
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`Contract/grant sponsor: US. Army Medical Research, contract/grant numbers: C-70,72 17-C—0138, 17-95—5005,
`P01 A1 30795.
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`Contract/grant sponsor: National Science Foundation; contract/grantlnumber: DMS-9971784.
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`. Received July 2001
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`Accepted April 2002
`Copyright © 2003 John Wiley & Sons, Ltd.
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`EXHIBIT 2051
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`*
`IPR2018
`Biogen Exhibit 2051 .
`,
`April 24:10:33
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`Mylan V- Biogen
`Page 1 of 21
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` ' cc“ RPR CRR
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`. meewmhouns IPR 2018-01403
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`STATISTICS 1N MEDICINE
`' Statist Med. 2003; 22:573593 (DOI:
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`IO 1002/sim. 1342)
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`Comparison of HIV-1' and HIV-2 infectivity frOm a'
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`prospective cohort study in Senegal
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`Peter B. Gilbert1’*’l, Ian W. McKeagueZ, Geoffrey Eisen3, Christopher'Mullins3,
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`Aissatou Guéye-NDiaye“, Souleymane Mboup4 and Phyllis J. Kanki3
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`1
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`Biogen Exhibit 2051
`Mylan v. Biogen
`IPR 2018-01403
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`Page 1 of 21
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`

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`574
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`_ P. B. GILBERT ET AL.
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`1-. INTRODUCTION
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`'The human immunodeficiency virus (HIV) can be classified as, types one (HIV-1.) and two ~
`(HIV-2). HIV-I accounts for the vast majority of HIV in the world, with HIV-2 present
`mainly in Western Africa. Laboratory studies and cohort studies have shown that the HIV types
`likely differ in various in vivo and in vitro phenotypic properties including replicative capacity
`[1—3], cytopathicity [4,5], pathogenicity [6—8], perinatal infectivity [9—1 1] and heterosexual
`infectivity [12]. Here, we are interested in evaluating differential male to female infectivity,
`where infectivity is defined as the per sexual contact probability of transmission from an
`HIV infected male to an HIV uninfected female. To address this, we considered long-term
`follow-up data from a cohert of female commercial sex workers .in Dakar, Senegal, where
`both HIV-1 and HIV-2 have been circulating since at least the mid-eighties.
`Donnelly e! a].
`[12] evaluated the question 'of dilTerential male to female infectivity by
`analysing the Dakar cohort of 780 initially HIV seronegative sex workers followed between
`February 1985 and December 1989. Their conclusion, at about the oneper cent significance
`level, was that HIV-l
`infectivity was greater than HIV-2 infectivity. We re-evaluated this
`question by analysing the most recent data set of 1948 initially HIV uninfected sex workers
`followed through. November 1999. The time is ripe for a reanalysis,'since the number of
`evaluable participants with an HIV infection event has matirred to 196, compared to 29 for
`the. earlier analysis; We applied new non-parametric competing risks failure time methods,
`which rely onfewer modelling assumptions than the methods used by Donnelly et a]. [12].
`Unadjusted and covariate-adjusted analyses provide evidence that HIV-l
`is more infectious
`than HIV-2 (P<0.001 in each analysis), with HIV—1 estimated to be 3.55-fold more infectious
`than HIV—2 in the unadjusted analysis, and 3.40—3.86-fold more infectious in the covariate-
`. adjusted analyses.
`
`2. DATA
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`,
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`the Senegalese government established a public health programme whereby self-
`In 1970,
`identified female sex workerswere required to register and regularly attend a health clinic,
`which provides regularmedical evaluation and free treatment for sexually transmitted diseases.
`In 1985,
`the Inter-University Convention for the Prevention of AIDS began a‘prospective
`natural history study that involved regular HIV testing from‘consenting sex workers [13, I4].
`' For the present study, the population consisted of registered sex workers in Dakar who agreed
`to participate and were initially HIV seronegative. Sex workers were followed for varying time
`intervals between 7 February 1985 and 1 November 1999, with clinic visits scheduled every
`six months. At each clinic visit, women were teSted for HIV-1 positivity and for HIV-2
`positivity, using immunoblot antibody assays, HIV specific peptides, and HIV specific PCR
`[14,15]. Seroconversions were confirmed using all available samples from individuals [14].
`The time of seroconversion was estimated as the midpoint between the last 'seronegative visit
`date‘W[WWIIWWW
`‘
`-
`an HIV-2 serostatus data at each clinic visit were available from a
`wor
`rs.
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`Information on nationality, age,.date of cohort entry, and years of registered prostitution were
`available from' greaterthan 99 per cent of the sex wor > :, nd information on the average
`v
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`”number of sexual partners per week was available fro (@er cent of the cohort. In total,
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`. ,
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`\
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`Copyright © 2003 John Wiley & Sons. Ltd.
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`_
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`’
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`Stylist. Merl. 2003; 221573—593
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`Page 2 of 21
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`COMPARING HIV—l AND HIV-2 INFECTIVITY
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`.
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`' 575
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`Annual prevalence by HIV type
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`12.0
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`10.0
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`‘D
`2 3.0
`U0
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`E 6 o
`g
`n.
`{3
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`4‘0
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`2.0
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`0.0
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`.
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`_
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`-l - HIV-1
`+ HIV-2
`- e- HIV-Dual
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`In
`O5
`._
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`(D
`0"
`.—
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`R Q a: D
`0’1
`65
`0')
`..
`.—
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`.—
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`N l') v Ifl W 7‘
`01
`0’:
`a! a O Ch
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`.—
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`.—
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`w 8
`0’:
`0)
`-
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`(a)
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`Incidence
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`Year
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`-I— HIV-2
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`- A- HIV-Dual
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`xgsgaasg gases
`Year
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`(b)
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`as
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`incidence of HIV-1 and HIV-2 infection among sex
`((1) Annual prevalence and (b) annual
`Figure l.
`workers participating in the Dakar, Senegal, prospective cohort study. Prevalence rates were calculated
`from all registered sex workers visiting the clinic in the index year regardless of HIV serostatus at
`cohort entry (data from 3l41 sex workers used in the calculations). Incidence rates were calculated
`'from the cohort of registered sex workers HIV-seronegative at the beginning of the index year (data
`from 1951 sex workers used in the calculations).
`Incident dual
`infection events included transitions
`from HIV uninfected to dual infected and from infection with one .HIV type to dual
`infected.
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`199 of the 1951 initially HIV uninfected sex workers became HIV infected during the 15
`year observation period, 127 with HIV- 1 only, 66 with IIIV.—2 only, and six with both types
`Among dual-infected women,
`three had the first seropositive test reactive for both viruses;
`these women were assumed to have simultaneous HIV- 1 and HIV- 2 seroconversion dates. For
`' reasons given in the Methodology section, we removed these three subjects from the analysis;
`thus the analysed cohort consisted .of 1948 sex workers, of whom l96 became HIV infected.
`For calculating annual point prevalences of the viruses in sex workers, da .
`re used
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`from all sex workers registered during the year under consideration. A total 0*women.
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`contributed data to the prevalence calculations, including the 1951 initially uninfe -- - women
`plus 1190 sex workers who entered the cohort with HIV infection. The data demonstrated
`a relative plateau of HIV-2 prevalence, with HlV'-l prevalence. surpassing that of the more
`endemic virus, HIV-2, by the end of the observation. period (Figure 1(a)). Incidence data
`
`Copyright © 2003 John Wiley & Sons, Ltd.
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`i
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`Stalis‘l. Merl. 2003; 22:573—593
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`Page 3 of 21
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`II.I
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`...:--j'~,=p.B.O1L1315RTETAIL._-
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`-.I576,:-‘
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`showed a steady increase in Hqu incidence over time, with HIV-ZI-incidence remaining
`fairly stable and then gradually decreasing after 1994 (Figure l(b)). These data’indicate that
`,the epidemic curves fOr these two related viruses differ. One explanation would be greater .
`infectivity of- HlV- 1 compared to HlV-2, which we evaluate here
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`'3. METHODOLOGY
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`if
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`kill.
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`ZVarious authors have eStirInated' the infectivity probability of HIV-1, by‘tii‘odelhng infection
`risk as a function of the number-Of sexual contacts within sexual partnerships. Commonly
`the models have been formulated for studies Of monogamous individuals with HIV- 1
`infected
`partners [16— l8], or for studies of non-mOnogamous individuals with multiple partners of
`known HIV- ] prevalencé [l6, I9 20] H11 et (1/ [2]] reviewed methodologiesand challenges
`‘for comparing the infectivity of HIV variants.
`Donnelly er a1. [12] modelled the infectivity probabilities r, for HIV- 1 and_r3 fOr HIV-2 as
`functions of the reported number of sexual contacts and the partner prevalences _p1 of HIV- 1,
`p3 of HIV-2, and p13 of dual HIV-1 and I-llV- 2 infection. The partner prevalence
`were
`ass
`d known and constantover time. :Probabilities of becommg- 1n ected with either type,
`both, or ne1
`presse
`in terms of the estima
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`-
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`the parameters ri,r3, pl, p3, p13. The resulting pa1ametrie likelihood was maximized under an
`independent competing risks assumption using standard methods to obtain Ipoint estimates and
`variance estimates of r. and I2 [22]. Then, inference about diflerential infectivity was made -
`by testing r. :13 with a Wald statistic.
`3
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`The analysis was conducted under six sets of assumptions, for twospecifications of partner
`prevalences crossed with three ways of imputing values for the average number of sexual
`contacts per week for the3th1 a missing value
`The infectivity ratio estimate ri/rz ranged between 5.8 and 8.9 for thesixIIanalyses, and the
`two-sided pI-values for testing r1 —r3 ranged between 00064 and 0013.-
`Rather than estimating r. and r3 separately and then comparing the estimates to evaluate :
`difie1e11tial infectivity, our approach estimated the 1atio rl/r3 directly and assessed if it signif— j
`icantly differed from one Targeting inference on the infectivity ratio conceptually addresses
`the differential infectivity question more directly. In addition, estimating the infectivity ratio
`-.ea11 be done with gieatel aeeu1acy than estimating the type-specific infectivities sepa1ately,
`since the inference procedure does not rely on havin accurate measurement on the number
`0 sexual conta s as
`escr1 e
`eow; see equations (1) and (2)) Th e
`ther advanta es
`Web First, it does not assume that the HIV-1 and HIV-Z partner prevalences
`Mr estimates were used and their uncertainty was partially accOunted for. Sec-I
`ondly,
`the l-llV- l and HIV- 2 partner prevalences were allowed to vary with calendar time
`,1.
`This is important because the HIV- 1 prevalence in sex workers varied substantially between '8
`1985 and 1989 (Figure 1(a)), and the sex worker prevalence is closely related to the partner
`= "
`prevalence. Thirdly,
`it allows the HIV- 1 and HIV-2 infectivities r.(t) and r3(t) to vary with
`I time rather than assuming they are fixed constants. The infectivity ratio coillId vary over time", '3
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`" .fOr example, if HIV 1 and HIV-2 underwent difierent evolutionary pathways towards more or'
`less infectious phenotypes. Fourthly,
`it. adjusts for several risk factor covariates. IFifthly, the '
`testing procedu1e used to assess differential infectivity makes no modelling assumptions about
`the hazard rates of HIVI- l and HlV-2 infection over time, and requires no assumptions about
`\
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`Copyright © 2003 John Wiley & Sons, Ltd.
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`stain-1. Med. 2003;22:573-593 ‘
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`the nature of dependence between the competing risks. Not requiring independent competing
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`, risks is important becausethe risks likely were dependent (for example, because sex workers
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`at high risk for infection with one type of HIV may also have been at high risk for infection
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`with the other type). Limitations of the methods are discussed in the Discussion
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`3.1. Non-parametric Competing risks failure time methods
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`We Viewed the two Virus types as competing. risks of infection,a framework also used
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`(somewhat diiTeIently) by 1eferencc [23]
`fOI comparing tiansmissibility of HIV- l subtypes
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`in Thailand, and applied non-parametric statistical methods to compare the HIV- 1 and HIV— 2'
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`infection hazard rates The outcome measures on each subject were the time and type of the
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`first HIV infection. Since a fist HIV infection may modify the 1isk of a second HIV infection
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`(for example, analyses of the Dakar cohort have suggested that infection with HIV-2-partially
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`protects against subsequent superinfection with HIV-1 [15,24]), no data on sex workers were
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`considered beyond first infection events. Thus, HIV-l
`infections censored HIV-2 infections,
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`and vice versa Since very few superinfection events occurred (a total of three), ignoring these
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`events did not appreciably affeet the statistieal powei of the analysis.
`The competing risks approach does not allow for the possibility of simultaneous co——infection
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`'with competing virus types. To accommodate this, we removed the three subjects from the
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`analysis who were simultaneously co——infectcd by the definition of seroconveision time we
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`.used Since only three subjects had this endpoint,
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`is unlikely that an alternative anal-
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`ysis that retained these subjects (for example, an analysis that considers simultaneous type .
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`and 2 co-i-nfection as
`a third competing 1isk of infection) would affect
`the 1esults ,
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`appreciably.
`The time to infection was measured as the time from entry into the cohort until seroconver-
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`sion. All analyses were based 011 this time scale, ‘study time’, although the calendar time scale
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`,was also used for adjusting HIV-1 and HIV—2 hazard estimates by' HIV-1 and HIV-2 partner
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`prevalences, as described below. Sex workers Who were never observed to be infected were
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`censored with censoring time equal to the time interval of follow-up. An alternative analysis
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`based on calendar time would accommodate the possibility that the infectivities’vary more
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`with calendar time than with study time. We chose the studytime scale because it allows the '
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`use of relatively simple survival analysis methods (a calendar time scale would require that
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`the methods account for the left truncation of survival times resulting from staggered entry),
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`and because our approach provides a way to adjust for the effects of calendar time.
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`We defined r,(t), i: 1,2, as the average type 17 infectivity among the population of all sex
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`workers 1 years into follow-up. Our goal was to estimate rl(t)/r2(t) non—parametrically for t.
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`ranging over the follow-up period 0 to 14.73 years. To this end,
`let 2,0),
`i=.1,2, represent
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`the hazard of type i
`infection for a sex worker at study time 1. Each hazard function has
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`‘crude’ inteipretation as the instantaneous type—specific infection risk in the presence of both
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`circulating Viruses [25]. Consider calendartim'es ranging between the opening and closmg
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`of the study, 7 February 1985 to l November
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`number of years since 7 February 1985. At time 't, the weekly risk of HIV-1 infection, 2.1(1‘),
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`of sexual contacts during the week with a client infected with either virus type, 0(1), times
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`'the proportion 7n of these infected clients who are infected with HIV- 1
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`2. A similar formula holds for the weekly risk of HIV-2 infection. This key relationship
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`Impliesthat'-
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`‘1‘,”“7 .-‘
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`j:
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`.-'M
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`' MI) _r-I(t)><c(z)>‘<n.(zc,g+z).
`. MI)
`r(t)xc(t)x7t2(lcj+t)
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`I
`where ch denotes the calendar time at which the jth sex worker entered the study, so that
`7rI(tc,~ +1) is the proportion of infected clients who were HIV-1 sIeroprevalent at calendar
`time (c, +1. We refer to IrI( ) as the partner relative prevalence of HIV-1 versus HIV—2.
`Since the contact rate c(I) cancels in the numerator and denominator. of (1), the ratio of
`type-specific infection hazards ,lI(I )/J2(t) depends only on the infectivity ratio rI(t)/r2(t) and
`on the partner relative prevalence ratio I'rI(IcII + t)/1r2(tcj + t). Consequently, in our approach
`it is not necessary to estimate contact rates of sex workers, an important advantage given the
`difficulty of this task. For all analyses, we assumed that for any given calendar tim'e lc, all? ,~
`sex workers at risk for HIV infeétion'at that time had the same partner relative'prevalencef.‘
`F
`initial. analyses that did not incorporate covariates, we also assumed that the product of_
`the” typespe '
`'e'c‘t'iVity ana’he contact rate, nlt')clt I, was common for all sex workers
`‘,..
`i=1, 2, and based estimationof IrI(tI_)/r2(t) on the formula resulting from expression (1)I:
` no)_='i.‘”(z)/m(zr,~+z)
`.
`i2)
`'i—'_'.-.
`.- ° .'
`"_ II'2(I'I)II'IJtz(t)/1tg(tcj+l)
`'_
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`For analyses that included covariates; a common infectivity ratio I'I(t|z)/I2(I|z) Was assumed .-
`for all sex workers with covariate vector 2, and was estimated using model (I3), as. described
`..r.
`laterIn this section.
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`.—
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`:1.
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`32. Estimation and (oizfidehw iIIIIterah
`To estimate II(t)/r2(t) via equation- (-2), we estimated each i;,(I) Withadjustment at each
`event time for each sex worker by an estimate of the reciprocal of the HIV-1‘ partner relative
`prevalence. Specifically, we estimated an adjusted version of J.,(t) JIMJU), by smoothing the
`non-parametric Nelson-Aalen estimate A,-(I) of the cumulative HIV-i hazaIdI function AI(I)
`[26,27], with the integrand corresponding to the HIV-i infection counting process for the jth
`sex worker divided by an estimate of IrI(ch + I) (see Appendix). The adjustment elTectivelIy
`prorates the amount of person-years exposed to HIV-i so that the estimated function J.Iadj(t)Is
`I proportional to II(I). The adjusted hazard JIM-(I) has interpretation as the HIV-i infection rate
`in women had all exposures with infected clients been to type i HIV. The ratio of the ‘relative-
`. prevalence adjusted’ estimates ,iIaIII-(I) and Jim-(II) was then used to estimate )‘I(I)/r2(l).
`.
`To estimate IrI(II.) over the range of calendar times of the study, we first estimated the
`annual partner relative prevalence for each year_1985 to 1999Aby the ratio of the observed
`HIV-1 and HlV'(HlV-1 and-H1V-2 combined) prevalences in all female sex workers registered
`, during the given year. Dual infected women 1were counted as infected in both‘the numerator
`7 and denominator prevalences. These calculatiOns used data on sex workers HIV seronegative . I
`and seropositive at entry,
`totalling 3141 women. The annual relative prevalence estimates
`were then smoothed (using Iowess in S-plus) to obtain estimates of 7!](lc) for all intermediate
`calendar times. For the jth sex worker under observation at study time I, her partner relative
`prevalence of HIV- 1 at that time was simply estimated by irI(tC,- +1) (and her partner relative
`prevalence of HlV-2 was estimated by mug,- +II): 1— n|(thj + 1)).I-
`Copyright © 2003 John Wiley & Sons, Ltd.
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`COMPARING HIV-1 AND HIV-2 INFECTIVITY
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`A 95 per cent confidence interval (CI) for r.(t)/r2(t) was calculated using the delta method
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`applied to the asymptotic variances of ilade) and of 223W). To adjust the CI for the un-
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`certainty in the estimated partner-relative prevalence ratio, the CI was recalculated 100 times
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`using 100 randomly sampled partner relative prevalence estimates from its asymptotic normal
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`distribution (details provided in the Appendix). ‘Unadjusted’ 'and ‘adjusted’ CIs were Calcu—
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`lated, where unadjusted CIs assume the partner-relative prevalence ratio is known and equal
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`to the estimate, and the limits of the adjusted CIs span the 2.5th and 97 5th percentiles of
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`the 100 recalculated confidence limits. Note that the adjusted confidence limits donnot take
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`'into account uncertainty due to the assumption that the relative prevalence among clients is
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`the same as among sex workers Thus, though the adjusted CIs are wider than the unadjusted
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`CIs, they are likely still too narrow.
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`Since the non-parametric analysis suggested a common infectivity ratio rI/r22r1(t)/r_2(t)
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`over time, as shown in the Results, We estimated the common ratio. ‘ The common parame-
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`ter r1 /r2 was estimated by the average of the estimates of rl(tk)/r3(tk) over a discrete grid
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`of 132 evenly spaced study times tk spanning the follow--up period, with inverse-variance
`weighting.
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`I» 3.3. Evtimation and confidence intervals that adiuxt for covariates
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`If the sex workers had different‘risk factors for HIV-linfection than for HIV-2 infection,
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`in either direction or magnitude, then the estimator for the infectivity ratio considered above
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`could be biased. For example, bias could result if sex workers who became infected with’HIV-
`tended to have more sexual contacts with clients than women who became infected with
`1
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`HIV-2 To adjust the estimate of the infectivity ratio for covariates, we used the following
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`proportional hazards model:
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`11012)
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`)«2(le)
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`= exp[/)'0 + [3T2]
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`(3)
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`This version of the Cox model was studied by Lunn and McNeil [30] who showed that it
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`can be fit using existing software programs for the ordinary Cox model without competing
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`risks (for example, with the function coxph in S-p.-lus) SWasured\
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`on the clients of the sex workers we were unable to adjust the infectivity ratio estimates for
`clme assumed that at each calendar time the partner relative
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`prevalence 7:1(tc) was common among sex workers (as stated earlier).
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`At each event
`time t,
`the term exp[/i0 + [frz]
`in model (3) was multiplied by an esti-
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`mate of the relative prevalence ratio 7:1(tcj + t)/7t2(tcj + t), where j indicates the sex worker
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`who‘ had the event. This can be accomplished, for example, using the offset feature in the
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`S-plus function coxph. With this adjustment, under the assumption that the infectivity ratio
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`r1 /r2 was constant over time, exp[./)’0] from model (3) estimates r1 /r2 adjusted for thecovari-
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`ates 2 .at specified level 2:0. Continuous covariates were centredby their mean values so
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`that
`the adjustment conditions on central covariate values. The profile likelihood of model
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`(3) was used for producing a likelihood ratio test of the null hypothesis that the adjusted
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`rl/rz equalled one, and to construct a confidence interval for rl/rz. The validity Of the pro-
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`portional hazards assumption in model-(3) was assessed by the method of Grambseh and
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`'Therneau [28].
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`Copyright © 2003 John Wiley & Sons, Ltd.
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`580
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`3.4. Tests fof diflerenlial ' ill/activity
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`For testing'for’difierent infectivities of HIV-1 and HIV—2, we applied a test that was developed
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`for comparing two cause—specific hazard functions with adjustment for covariate effects [29]..
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`This test evaluates the null hypothesis 2.1(t|20(t))=2.2(t|‘zo(t)) for all t, for a specified covariate
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`level. z0(t). The. test statistic is based on a weighted average of differences betweennon-
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`parametric estimates of iti'(t|zo(t)) and 2.2(tlzo(t)) under the causc‘ specific Cox proportional
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`hazards model over time, with weights chosen to control
`instability in the beginning and
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`end of the observation period. By considering the logarithm of the estimated partner relative.
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`prevalence ratio 7t1(-)/7t2(-) as a time-dependent covariate with value fixed at zero, we applied
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`this procedure to test r1(z)=r2(t) for all
`t ver'sus'r1(t)>‘r2(t) with r'1(t)>r2(t) for some I
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`carried out l00 times for 100 randomly sampled partner relative prevalence ratios over time
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`(as described in the Appendix).
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`3.5. Tests/Or differential fit/activity that adjust/Or covariates
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`Cause specific Cox proportional hazards models were used to identify risk factors for HIV-
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`1
`infection and for HIV-2 infection, and the re--c0ded Cox model (3) was used to identify
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`- covariates that predicted a differential HIV- ] versus HIV—2 infection risk [30]. These analyses
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`identified risk .factors that were important
`to adjust for in assessing differential infectivity.
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`,The procedure of reference [29] was used for testing the null hypothesis of equal infectivities
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`under adjustment for a ‘covariate vector 2, that is, of Ho : r1(t|z)='r2(t|z) for all 1.
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`Nearly half of the sex workers in the study had no data on the covariate average number of
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`reported sexual contacts per week. To evaluate the robustness of the results to missing values
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`of this variable, we carried out the covariate-adjusted analyses described above using two sim-
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`~ ple techniques for handling this variable. These are: (i) a co
`'se analysis; (ii) an anal-
`lete-
`m ysis of all sex workers imputing the missing sexual contacts values to be equa to the mean.
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`3.6. Sensitivity analysis
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`‘ A main aSsumption of the approach was that the relative prevalence over time in sex workers
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`represented the relative prevalence over time in their partners. To evaluate sensitivity of the
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`results to misrepresentation, we re-did the unadjusted and covariate-adjusted analyses with
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`the estimated HIV-l/HIV-2 relative prevalence ratio nl(-)/7r2(~) increased at all times by a’(
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`multiplicative constant K> l, which made it more difficult to infer greater HIV—l
`infectivity.
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`The analysis was repeated for several values ofK> l.
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`4. RESULTS '
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`The analysed cohort included@sex Workers, of whom 196 had afirst HIV infection event,
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`, 4.1. Description of the cohort
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`-2. Figure 2'shows the HIV seronegativeobservation time of
`128 with HIV-1 and 68 with HI
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`the sex workers who seroconverted while under follow-up._.S'ex workers infected with HIV-1
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`had a median entry date of 13'October‘ 1988 and a median infection time of 3.30 years;
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`while sex workers'infected with HIV-2' had an earlier median entry date 30 September 1986
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`Copyright © 2003 John Wiley & Sons, Ltd.
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`COMPARING HlV-l AND HlV-2 lNFECTlVlTY
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`NumberInfected
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`08888883888888o3888885
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`HIV-1 Serooonverters
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`190519fi19871988 190919N1991 19921993199419951996199719981999 2000
`YOIf
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`Figure 2. Timing of HlV-l and HIV-2 infection (observation time and calendar time) for the 196
`initially HlV seronegative Dakar sex worker cohort participants who became infected while enrolled,
`between 7 February 1985 and l November 1999.
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`and a shorter median infection time of 2.58 years. Among all enrolees, the median period of
`follow-up was 3.33 years, with an interquartile range of l.33—7.42 years;
`l221 of 1948 (62.7
`per cent) of participants were never observed to seroconvert and were lost to follow-up prior
`to 1 January 1999. Participants completed a consultation form at a clinic visit at a median
`rate