Francisco Coutinho

Hepatitis-2015Orlando, USA

July 20 - 22 2015

Estimating the Size of the HCV Infection Prevalence: A Method Using the Incidence of Cases Reported to an Official Notification

SystemMarcos Amaku1,+, Marcelo Nascimento Burattini1,2, Francisco Antonio Bezerra

Coutinho1, Luis Fernandez Lopez1,3 , Fabio Mesquita4, Marcelo Contardo Moscoso Naveira4, Gerson Fernando Mendes Pereira4, Melina Érica Santos4, and Eduardo

Massad1,5,*

1 Faculdade de Medicina da Universidade de São Paulo, and LIM01-HCFMUSP, Brasil 2 Hospital São Paulo & Escola Paulista de Medicina, Universidade Federal de São Paulo, Brasil3Florida International University, Miami, Fl, U.S.A.4Departamento de DST, AIDS e Hepatites Virais¸ Ministério da Saúde do Brasil5London School of Hygiene and Tropical Medicine, London, UK+All the authors, with the exception of the corresponding, are listed alphabetically*Corresponding author - Av.Dr. Arnaldo 455, Sao Paulo, CEP 01246-903, edmassad@dim.fm.usp.br

•Hepacivirus•Hepacivirus is a genus of viruses, in the family Flaviviridae. Humans serve as natural hosts. There is currently only one species in this genus: the type species Hepatitis C virus. •Seven genotypes have been identified.•Lower classifications: Hepatitis C virus•Rank: Genus•Infects about 170 million people around the world

In untreated patients, the median expected time to cirrhosis is 30 years; 33% of patients have an expected median time to cirrhosis of less than 20 years and 31% will only progress to cirrhosis after more than 50 years, if ever.

There is no vaccine, and the available antiviral drugs are toxic, expensive and only partly effective .The combination of pegylated interferon with ribavirin, still the treatment for HCV infection in most countries, elicits long-term responses in less than 50% of the patients. Recently developed drugs, like Daclastavir, Simeprevir and Sofosbuvir are providing cure in a substantial proportion of treated patients. These modern antiviral drugs, however, are still extremely expensive (about US80,000 per treatment course) and inaccessible to most affected countries.

Reported Cases

Unreported Cases

The Problem

In Brazil, for instance, the prevalence of infection reported to the official notification system is around 160 thousand individuals , whereas the total number of HCV infected individuals in the country is currently estimated by the Brazilian Ministry of Health to be around 1.8 million people.

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In this work we calculate three quantities: the prevalence of notified cases to the official reporting system of the Brazilian Ministry of Health (called SINAN) database; the number of individuals in the Brazilian official liver-transplantation waiting list due to chronic HCV infection; and the total number of individuals infected with HCV. The first two variables produced by the model are compared with real data from SINAN and the national service of organ transplantation and the third is the main aim of this paper. We used two different approaches and show that both converge to the same result.

Individuals diagnosed as HCV infected in Brazil are reported to the National Reportable Disease Information System (Sistema de Informação de Agravos de Notificação [SINAN]) of the Brazilian Ministry of Health.

This database mirrors the official notification file which contains several variables related to each specific individuals. As the notification rate of HCV infection is approximately in steady-state in the last ten years, we analyzed the SINAN information between 2004 and 2012 with respect to age only, neglecting the small time-variation in that period.In addition to the number of HCV infected individuals reported to SINAN we also considered the Liver Transplantation Waiting List (LTWL) of the Brazilian Notification System of Organ Transplantation (Sistema Nacional de Transplantes, SNT) in order to estimate the list size for patients waiting for a liver transplantation in the period between 2004 and 2012. About 50% of all liver failures that lead to a transplantation in Brazil are due to HCV chronic infection (Chaib et al., 2010). Alongside the prevalence of patients notified to SINAN in 2012, the size of the liver transplantation waiting list at that year will be one of the quantities used to check the value of our estimations of the actual number of individuals infected with HCV in Brazil in the year 2012.

Figure 1. The number of HCV infected individuals reported per year. The reported rate is approximately constant in the period between 2004 and 2012.

Figure 2. The number of HCV infected individuals reported per year and age. The age distribution of the number of notifications is approximately the same for the

period analysed.

The HCV infection dynamics is described by a simple SIR model as follows:

With boundary conditions:

and total population size (constant):

Figure 3. Diagram representing the model's dynamics

The prevalence of reported cases is given by the integration of :

and the incidence of reported cases is given by :

The first approach

The real incidence of HCV infection is unknown by the reasons described in theintroduction. To estimate the incidence, we modeled the age-dependent force ofinfection as a function with the "Gaussian" form:

Figure 4. Fitting the SINAN data to a continuous function (equation 3).

Table 1. Biological significance and value of the parameters used in the first approachParameter Biological Significance Value

Scale parameter 0.00263 years-1

Age of maximum incidence 44.64 yearsWidth of age-dependent

incidence function386.89 years2

Rate of incidence increase 0.15 years-1

Initial age of infection 15 yearsNatural mortality rate (assumed constant for

simplicity)

0.0133 years-1

Recovery rate (assumed negligible)

0 years-1

HCV induced mortality rate

years-1

HCV infection notification rate

0.0125 years-1

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2c

3c

4c

5c

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)(a 1))45(1.0exp(115.0 a

The second approach

In the second approach, we fitted a continuous curve directly to the SINAN data.For this we choose the following function

The quantities to be compared

The prevalence of reported cases

The first quantity used to check the model's reliability was the prevalence of HCV cases notified to SINAN in the year 2012. The SINAN database contains the age distributed number of newly HCV infections notified per year, that is, the reported incidence of infection. From this it is possible to estimate the prevalence of HCV cases notified to the SINAN. To estimate this prevalence based on SINAN data, in which age is recorded in one year intervals, we used the following equation:

The size of the liver transplantation waiting list

The second quantity used to check the model's reliability was the number of patients in the list of liver transplantation who have liver failure due to chronic HCV infection. The size of the liver transplantation list was estimated by Chaib et al.(2014) who calculated expected number of patients in the liver transplantation list for the State of Sao Paulo. This State is responsible for about 30% of the number of transplantation carried out in the whole country (Chaib et al., 2014). In addition the liver transplantation due to liver failure by HCV infection represents about 50% of the cases (Chaib et al., 2014). From this we estimated the size of the liver transplantation for the entire country.

Waiting list dynamics in the state of Sao Paulo, Brazil

The aim of this study is to demonstrate the performance of our state liver transplantation program and analyze when the number of liver transplantation will meet the demand of our waiting list.

Year Tr I D1997 631998 160 553 3211999 188 923 4142000 238 1074 5482001 244 1248 6042002 242 1486 7252003 289 1564 7232004 295 1500 671

The data related to the actual number of liver transplantation, Tr, the incidence of new patients in the list, I, and the number of patients who died in the waiting list, D, in the State of São Paulo since 1997 as:

Tr =107.07ln(year) + 72.943

We next projected the size of the waiting list, L, by taking into account the incidence of new patients per year, I, the number of transplantations carried out in that year, Tr, and the number of patients that died in the waiting list, D. The dynamics of the waiting list is given by the difference equation:

that is, the list size at time t+1 is equal to the size of the list at the time t, plus the new patients getting into the list at time t, minus those patients who died in the waiting list at time t, and minus those patients who received a graft at time t. The variables I, and D, from 2004 onward were projected by fitting an equation by maximum likelihood, in the same way that we did for Tr.

Year Tr I D2006 349 1566 8952007 330 1022 7342008 454 1213 4902009 609 1287 4552010 671 1415 4032011 609 1577 4702012 501 1488 441

The data related to the actual number of liver transplantation, Tr, the incidence of new patients in the list, I, and the number of patients who died in the waiting list, D, in the State of São Paulo since 2006 is now:

Tr =500ln(year) + 184.7

We next projected the size of the waiting list, L, by taking into account the incidence of new patients per year, I, the number of transplantations carried out in that year, Tr, and the number of patients that died in the waiting list, D. The dynamics of the waiting list is given by the difference equation:

that is, the list size at time t+1 is equal to the size of the list at the time t, plus the new patients getting into the list at time t, minus those patients who died in the waiting list at time t, and minus those patients who received a graft at time t. The variables I, and D, from 2006 onward were projected by fitting an equation by maximum likelihood, in the same way that we did for Tr.

Calculating the age of infection from the model

From table 3 it is possible to calculate the proportion of the 93 individuals with 12 years old in 2012 (that has been reported since 2001) that had been reported when aged 8 years (that is those reported when aged 8 years in 2008 and, therefore have acquired the infection any time between 2001-2008, that is when aged between 0 and 8 years). They were 5/93 (0.054).

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