An Estimation and Projection Package for Multiple Groups and Epidemics

The UNAIDS/WHO EPP

Tim BrownEast-West Center/Thai Red Cross Society

Collaboration on HIV Modeling, Analysis & Policy

April 2003

The ultimate objective• To develop a simple model that

– Allows countries to estimate current HIV burden– Permits short term projections (5-year)– Is epidemiologically plausible– Can reproduce real world trends in HIV– Can be applied in-country

• Ideally a simple single curve that fits all situations, but….

To paraphrase Willy Fowler:

One of the great tragedies of modern

epidemiology is the murder of elegant

models by cold, ugly data

We try to fit simple models, but it never

quite fits……

Nasty lessons from the real world

• Dynamics of real world HIV epidemics is complex

• Never a “single” HIV epidemic

• Each consists of multiple sub-epidemics– Affecting different sub-populations– In different geographic areas– Evolving at different rates

Nasty lessons from the real world

• Modeling large countries requires geographic decomposition– Unclear picture of the largest countries,

e.g., China, India and Indonesia

• Generalized epidemics often vary greatly between urban and rural settings – Vary in intensity– Vary in timing

Nasty lessons from the real world

• Concentrated epidemics differ radically from country to country– Varying contributions from sub-populations– Differences in timing of epidemic take-off– Variable rates of sub-epidemic evolution

So we need a tool that….• Can deal with geographic diversity• Can incorporate sub-population

epidemics• Can obtain different fits for each

observed geographic and sub-population HIV trend

• Simplifies the process of combining sub-epidemics into “the” national epidemic

The approach

• Start with existing HIV trend data

• Fit a model through the data – Test possible epidemiological parameters– Choose a set minimizing least squares

• Project future course based on the fitted parameters

Fitting an epidemic

0

10

20

30

40

50

60

70

% H

IV+

Why not use the gamma function?

• Epimodel is based on a gamma function modified for HIV mortality, but….

• Incidence always goes to zero, so the gamma function cannot reproduce endemic epidemics– Short term fits will generally underestimate long

term prevalence trends and always show declining trends

– With more data will shallow out, but still cannot settle into endemic state

Gamma function fits to Congo data

0

2

4

% H

IV+

What we fit – the Reference Group Model

• Uses a plausible epidemiological model

• Incorporates population change over time

• Fits 4 parameters– r – controlling the rate of growth

– f0 – the proportion of new risk pop entrants

– t0 – the start year of the epidemic

– behavior change parameter

Reference group fit to Congo data

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2

4

% H

IV+

Reference Group model parameters

0

10

20

30

40

50

% H

IV+

t0f0

r

Effect of varying r – rate of growth

0

2

4

6

8

% H

IV+ r

2r

r/2

Effect of varying f0 – new entrants at-risk

0

5

10

15%

HIV

+

f0

2f0

f0/2

Effect of varying t0 – start time of epidemic

0

5

10%

HIV

+

t0 = 2000t0 = 1990

t0 = 1980

Effect of varying phi – recruitment

0

2

4

6

8

% H

IV+

=100

= -100

= 0

The Projection Page in EPP

Building a national epidemic in EPP

• The curvefit– Basic unit of computation– Represents a specific sub-population of

people vulnerable to HIV– EPP collects demographic data and HIV

trends for that sub-population– Then fits a Reference Group model to the

HIV trends in that sub-population

C

Building a national epidemic in EPP

• The sub-epidemic– Is composed of one or more curvefit– Optionally includes other sub-epidemics– Total HIV in a sub-epidemic is formed by

summing HIV in its curvefits and sub-epidemics SE1

CC SE2

C

Building an epidemic in EPP

• The workset (the national epidemic)– Includes all curvefits and sub-epidemics

used to build the national epidemic– Sub-epidemics may optionally be used to

model different geographic areas– Total HIV is the sum of HIV in all curvefits

contained in the workset

The workset tree

SE1

CC SE2

C

Workset

CC

Examples of worksets - Botswana

Botswana

RuralUrban

Examples of worksets - Thailand

North

FSW

Thailand

Northeast Central South BKK

Client IDU Remain

FSW Client IDU Remain

Templates – predefined epidemics

• Default templates– Concentrated– Urban-Rural

• User can create & name own templates– Geographic breakdowns– Specific sub-populations

Demo I

Worksets pageCreating a workset

Creating a workset from a template

Define Epidemic pageAdding and deleting curvefits

Adding and deleting sub-epidemics

Adding a template

The Worksets Page in EPP

Workset panel

Template panel

Epidemic structure

Name & country selection

The Define Epidemic Page in EPP

Epidemic structureUser controls to

add & delete curvefits & sub-

epidemics

Defining your populations in EPP

• Specify base year and give total population in that year– Defaults: UN Pop for 2003

• For base year– Specify number in each sub-population– Reduce unassigned population to zero

Defining your populations in EPP• Choose special pop characteristics

– MSM, IDU, FSW, Clients, STI, or lo-risk

• Set demographic parameters– proportion male– b – birth rate– mu – mortality– l15 – survival to age 15– gr – 15+ pop growth rate

Demo II

Define Pops pageAssigning population and dividing it among

the curvefits in the workset

The Define Pops Page in EPP

National and unassigned population

Special characteristics

Demographics

The Data Entry Page in EPP

User defined site names

Automatic means and medians

Prevalence by site & year

Data adjustments within EPP• Prevalence adjustments

– Annual increases or reductions for a changing mix of high and low prevalence sentinel sites

– 0.8 adjustment for rural sites by default - they overestimate actual prevalence in most places

• Weights– Applied on a per-site basis

• Selective inclusion of sites– Double-click box to include/exclude specific sites

Prevalence adjustmentson the Data Entry Page

• Reduce or increase the prevalence values before using them for fitting– Adjust for lack of representativeness of

available surveillance sites– If sites underestimate prevalence, use

adjustment > 1.0– If overestimate, use adjustment < 1.0– Reference Group recommendation for rural

projections is to use 0.8

Weights and checkboxeson the Data Entry Page

• Weights used in the calculation of means, medians and least squares

• Checkboxes completely exclude sites

ii

iii

w

xwx

22 )ˆ( iii

i xxwLSQ

Demo III

Data Entry pageEffect of prevalence adjustments, weights,

and checkboxes

The Projection Page in EPP

What & how to fit

Initial guess

EPP Projection Page - Features

• Can fit different things– All data – Medians– Means

• All fits are made with adjustments, site selection and weighting applied as chosen by user on Data Entry Page

EPP Projection Page - Features

• Can fit different ways– Fix t0, vary r, f0 and phi (default)– Fit all variable (t0, r, f0 and phi)– Fix r, vary rest– Fix f0, vary rest

• If click “Set to fix phi”, no phi fitting done

• User can change initial guesses

The Projection Page in EPP

Best fit &user changes

EPP Projection Page - Features

• Can change parameters manually after fitting and save results

• Can reset to the best fit if you really mess things up

EPP Results Page

• Allows you to examine any combination of curvefits & sub-epidemics

• Can plot original data

• Can see trends in prevalence, number HIV+, and sub-population size

• Allows numerical results to be viewed

• Can generate Spectrum file

EPP Results PageWhich curvefits and

sub-epidemics to show

Get the numbers, export to Spectrum

Graph of results

What todisplay

Audit Check Page

• Need to check your concentrated epidemics against:– Plausible sizes for sub-populations– Maximum prevalences observed– Lo-risk to high-risk infection ratio

Audit Check Page

Sub-pop sizechecks

Lo-risk/hi-risk check

Prevalencechecks

Demo IV

Projections pageFitting the epidemic

Results PageLooking at the results

Audit CheckValidating your concentrated epidemic

And if you have a question on any page…..

• Just hit the “Help” button!– Page specific help– More detailed explanations

When do we use EPP?

• Reference Group recommendation:– When we have 5 years of trend data for at-

risk populations

How should we use EPP?

• For 5 year projection into future– By default end year is 2008

• User can change this on Worksets page, but not recommended

• Examine influence of sub-epidemic components and timing – Look at impact of different sub-populations– Explore different fits for sub-populations

• Timing of peak, height of peak, endemic level

Technical issues in applying EPP

• Concentrated epidemics– Size of at-risk populations– Inclusion of “low-risk” partner populations– Use of “remaining population”

• Consider validity of generalizing from limited studies of at-risk populations

Technical issues in applying EPP

• Always– Review impact of data outliers on fits– Run Audit Check to validate against

international experience

Issues to consider

• When to use EPP and when to use spreadsheets in concentrated epidemics– Data availability

• Trends needed for EPP

– Certainty of key sub-population size estimates

Closing remarks• The tools cannot substitute for the absence of

data• The tools cannot improve bad data

– GIGO (garbage in, garbage out)

• Thus, the tools must be seen as part of a process of both improving surveillance systems and preparing more accurate estimates

• The process will play out over years

Formal Model Description

Z = at-risk populationX = not at-risk populationY = infectedN = X + Y + Z 

ZNrYENXfdt

dZt )/()/(

XENXfdt

dXt ))/(1(

t

xxxx xtgZNrYZNrYdt

dY

0

dx)(/)/(

11

))1((exp

))1((exp)/(

00

0

ff

NX

fNX

NXf

For those with strong stomachs (do not show after lunch):