Resume : Estimation of HIV infected individuals using a model with competing risks of diagnosis and illness onset (Theory of Biomathematics and Its Applications XII : Mathematical and experimental approach to clarify patterns in a transition process)

Resume: Estimation ofHIV infected individuals usinga model with competing risks of diagnosis and illnessonset

HiroshiNishiura

Infectious DiseaseEpidemiology Department ofGlobal Health Policy

Graduate School of Medicine The University ofTokyo

Resumeof forthcomingarticle

As

an

original study isexpected to be printed elsewhere, _herewith

_a

Resumeofthe study is provided for this proceedings.

Background

Acquired immunodefieiency syndrome(AIDS) is

a

disease of immunocompromised host with anumber ofopportunistic infections,caused the human immunodeficienty virus(HIV). Following infection with HIV, it takes

on

average 10 yearsto develop AIDS. OncedevelopingAIDS, its diagnosis is properlymade by AIDS expert and certainly reported in industrialized countries including Japan where there

are a

number ofAIDS specialized healthcare facilities.Nevertheless, unless infected individuals undertake voluntary blood testing, the infection statuswith HIV is unrecognized before developingAIDS.

Since the reported dataset ofAIDS

cases

captures the

transmission

dynamics of

some

10 years

ago, we

cannot objectively understand ifthe epidemic is downward

or

upward trend at present only bylooking$at$ AIDS

cases.

Backcalculation method is

a

well-known statistical method that haspermitted

us

to estimate$HlV$ incidence.using the

AIDScasedata and the incubation period distribution. Namely, the incidenceofAIDS

cases

is written

as a

convolution ofthe HIV incidence(i.e.

new

infections with HIV) and the probability density function ofthe incubation period ofAIDS, and

deconvolution procedure has helped

us

toestimateHIV incidence from such relationship.

While the backcalculation method hasbeenuseful and

was

widely applied to different settings, the AIDS incidence in Japanhas notreflectedthe entire number of AIDS diagnoses from 1999, duetocessation of reporting previously diagnosed $HlV$

infected individuals that progressed toAIDS. Forthisreason, all AIDS

cases

have not beencounted in Japan, making it unrealisticto apply the simple convolution equationto

数理解析研究所講究録

the observedAIDS

case

data. Moreover, in additionto AIDScases, there havebeen reports ofdiagnosed HIV infection statusamong blood donors and

a

statistical method that could offerestimatesofHlV incidence using both AIDS

cases

and HIVdiagnoses hasbeen called for.

A multistate model

was

proposed

as

ideal method to be$al$)pliedtothe Japan dataset. In additionto such

a

well parameterized model, the present study aimedto develop

a

model that capturesthe data generating processofHIV/AIDS _in

_a

_simpleryet

general

manner

using

a

competing riskmodel. Employing the competing riskmodel,_the

interplay between HIV diagnosis and onsetofAIDS is captured.

Method

Basicmodelstructure

A competingrisk model that captures thedata generatingprocess ofHlV diagnosisand onset ofAIDS has been mathematicallyformulated (Figure). Therate ofHIVdiagnosis

was

modeled

as a

function ofcalendartime, while the illness onset ofAIDS

was

assumedtobe regulated by $an$ independently and identicallydistributed incubation

period distribution.

Figure. Competing risk model

as

applied toHIV/AIDS

Available data

HIVAIDS surveMance record in iapan: Bimonthly $(]984$ -2000$)$

or

quarterly $(200$]$-$

$P^{lesent)}$numbersofHIV infectionand AIDS diagnosis

are

obtained. AmongAIDS

diagnosis, informationwithregard to previous HIV diagnosis isnotavailable. Reporting interval in surveillance system is revised duetothe different law (AIDS Prevention Law

1989-1999

and theNational Epidemiological Surveillance of Infectious Diseases from Mar. I999). Registration system ofAIDS excluded those who

were

diagnosed

as

HIV-infected afterthe revision.

We obtained themaximum likelihood estimates of unknown parameters including the HIV incidence and the rate ofdiagnosis. Likelihood function

was

explicitly derived from

McKendrick

equation system. Assuming that

the

$HlV$incidence

ischaracterized byanon-homogeneous Poisson process, both the resulting HIV diagnosesand AIDS incidence

were

assumedto follow Poisson distributions.

Results/Discussion

Estimated number of people living with HIV/AIDS (PLWHA)

was

on

_{the order of}

26000as oftheend of2014. Theestimates werecomparable to those obtained using a three-stage multistate model that

was

employed in the past. As

an

advantage ofthe proposedmodel, itwas shown that the forecast

can

be obtained in real-time accounting forboth parameteruncertainty and demographic stochasticity. As

a

visualconfirmation ofthe goodness-of-fit, observed andexpected cumulative numbers ofHIV infections

and AIDS

cases were

compared.

A genera/representation ofHIV/AIDS _{model in Japan} was_{considered. The}

proposed competing risk mode/permits

a

simpler sensitivity analysis ofthe model estimatestodifferent incubation periods.

Address forcorrespondence:

Department of Global Health Policy Graduate School ofMedicine

The University of Tokyo Tokyo 113-0033

JAPAN

$E$-mail address: [email protected]

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