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Thoughts on Simplifying the Estimation of HIV Incidence John Hargrove, Alex Welte, Paul Mostert [and...
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Transcript of Thoughts on Simplifying the Estimation of HIV Incidence John Hargrove, Alex Welte, Paul Mostert [and...
Thoughts on Simplifying the Estimation of HIV Incidence
John Hargrove, Alex Welte, Paul Mostert [and others]
Estimates of incident (new) cases are important in the assessment of changes in an epidemic, identifying “hot spots”
and in gauging the effects of interventions
HIV incidence most accurately estimated via longitudinal studies – but these are
lengthy, expensive, logistically challenging.
Do provide a “gold standard” against which to judge other estimates of HIV incidence
An alternative way of estimating incidence, involving none of the
disadvantages of a longitudinal study, would be to use a single chemical test
that can be used to estimate the proportions of recent vs long-
established HIV infections in cross-sectional surveys
Idea: identify HIV test where measured outcome not simply +/- but rather a graded
response increasing steadily over a long period
BED-CEIA AssayCase 23903G
Days since last negative
0 100 200 300 400 500 600 700
Nor
mal
ised
O
D
0.0
0.5
1.0
1.5
2.0
2.5
One such assay is the BED-CEIA developed
by CDC
Graph shows result for a seroconverting client taken from the
ZVITAMBO study carried out in
Zimbabwe
[14,110 post partum women followed up at
6-wk, 3-mo, then every 3-mo to two
years]
Theoretical graph of sqrt(OD-n) vs ln(ti, j)
Log time (ti, j days) since last negative0 1 2 3 4 5 6 7
Sq
ua
re r
oo
t o
f O
D-n
-1.6
-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
1.6
Selected OD cut-off (B)
Negative baseline (A)
Slope = b1,i
Intercept = b0,i
..
..
.
Window (Wi )
The idea is to calibrate the BED assay to estimate the “average” time [or
“window”] taken for a person’s BED optical density [OD] to increase to a given
OD cutoff
In cross-sectional surveys proportion of HIV positive people with BED < cut-off allows
us to calculate the proportion of new infections – and thus the incidence.
Estimation of the window period is thus central to the successful application of the
BED
Data from commercial seroconversion panels withaccurately known times of seroconversion indicate
Problem 1.
Delay (~25 days) between sero-conversion and the onset
of then increase in BED optical
density
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180
Days since BED OD started to increase
BE
D O
Dn
Observed OD
Fitted line
Extrapolated portion
Sero-negative
Baseline OD = 0.0476
Extrapolated time when OD = baseline
Date ofseroconversion
Date ofinfection
2
'
1
Window period ()
Sero-positive
Min < 0.8; max > 0.8; S > 2; t < 90
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000Days since last negative
BED
Opt
ical
Den
sity
Problem 2: Considerable
variability between
clients in a real
population. No prospect of using BED to
identify individual
recent infections. Idea only to
estimate population incidence
Problem 3: Often have limited follow-up: of 353 seroconverters in ZVITAMBO, 167 only
produced a single HIV positive sample,
Samples per client (S)
1 2 3 4 5 6 7 8
Frequency 167 89 35 21
24 8 8 1
Problem 4: The available data for a given client quite often do not span the OD cut-
off. The proportion that fail to do so varies with the chosen cut-off. Failure to
span increases the uncertainty in estimating the time at which the OD cut-
off is crossed
Problem 5: There is a large variation (27 – 656 days) in the time (t0) elapsing
between last negative and first positive HIV tests. The degree of uncertainty in the
timing of seroconversion increases with increasing t0
Min < 0.8; max > 0.8; S > 2; t < 90
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
pti
ca
l De
ns
ityMax < 0.8; S > 2; t < 90
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
pti
ca
l De
ns
ity
Min > 0.8; S > 2; t < 90
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
pti
ca
l De
ns
ity
S = 2; t < 90
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
pti
ca
l De
ns
ity
Max < 0.8; S > 2; 90 <= t < 120
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
ptic
al D
ensi
ty
Min > 0.8; S > 2; 90 <= t < 120
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
ptic
al D
ensi
ty
S = 2; 90 <= t < 120
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
ptic
al D
ensi
ty
Min < 0.8; Max > 0.8; S > 2; 90 <= t<120
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
ptic
al D
ensi
ty
Max < 0.8; S > 2; t >= 120
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
pti
ca
l De
ns
ity
Min > 0.8; S > 2; t >= 120
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
pti
ca
l De
ns
ity
S = 2; 120 < t < 182
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
pti
ca
l De
ns
ity
Min < 0.8; Max > 0.8; S > 2; t >=120
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
pti
ca
l De
ns
ity
S = 2; t >= 183
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Days since last negative
BE
D O
pti
ca
l De
ns
ity
We need to consider how variation in
samples per client, t0 , and failure to span the
cut-off affect our estimate of the window period.
How to approach problem?
Scatter-plot of the data?
Makes no use of the information of the trend for individual clients and ignores the fact that the sequential points for that
client are not independent.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 100 200 300 400 500 600 700 800 900 1000
Time since seroconversion
BE
D O
ptic
al d
ensi
ty
A.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
loge days since last negative test
Sq
ua
re r
oo
t o
f O
D v
alu
es
Alternative which uses trend in BED OD
is suggested by an approximately linear relationship between square root of OD and
time-since-last-negative HIV test (t).
Allows a regression approach taking out
variance due to t and to difference between
clients
110
130
150
170
190
210
230
250
270
290
0.65 0.75 0.85 0.95 1.05 1.15
OD Cut-off
Win
do
w (
da
ys)
Minimum 3
Minimum 4
Minimum 5
130
140
150
160
170
180
190
200
210
40 60 80 100 120 140 160 180 200Maximum days last negative to first positive
Win
do
w (
da
ys)
13
2149 53
55 60
68
Gives consistent results; in that results independent of whether we insist on minimum of 3, 4 or 5
samples per client; and on value of t0 between 75 and 180 days
0.0
0.4
0.8
1.2
1.6
2.0
2.4
0 100 200 300 400 500 600 700 800
Days since last negative
Opt
ical
den
sity
Are we even using the right transformation?And should we be using the time of last
negative HIV test as the origin
Try instead to do a preliminary
estimate of the time when OD
starts to increase by fitting a quadratic
polynomial to the data. Then use this estimate as
the origin.
A.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
loge days since last negative test
Squa
re ro
ot o
f OD
val
ues
C.
-7
-6
-5
-4
-3
-2
-1
0
1
0 1 2 3 4 5 6 7
loge estimated days since seroconversion
log
e O
D v
alue
s
11445X
14557A
15513K
15801X
16715D
16853F
17926A
18101N
20606K
20674F
21556F
23903G
23983A
B.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 1 2 3 4 5 6 7
loge estimated days since seroconversion
Squa
re ro
ot o
f OD
val
ues
Seems to suggest that the true relationship may actually be a power function.
What it really were? What would we see if we plotted OD vs time since-last negative
Our problem is that we do not know when seroconversion occurred.We only know the time of the last HIV negative test.
And the greater the delay between last negative and first positive tests the greater the
uncertainty
True window173 days
0.0
0.2
0.4
0.6
0.8
1.0
-160 -80 0 80 160 240Days since function intersects baseline level
Opt
ical
den
sity
Examples of times when HIV -ve tests might have been taken
Offset = 0 days
y = 0.334x - 0.768
R2 = 0.976Window = 126 d
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
3 4 5 6 7log e (days since last negative)
squa
re r
oot (
OD
)Offset = 100 days
y = 0.53x - 2.08
R2 = 1.00Window = 196 d
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
3 4 5 6 7log e (days since last negative)
squa
re r
oot (
OD
)
For zero offset the window is UNDER-estimated; for 100-day offset it is OVER-
estimated
True window period
120
140
160
180
200
220
0 40 80 120 160Offset (days)
Est
ima
ted
win
do
w
This approach to window estimation is clearly not optimal since the window estimate changes with the timing of the last HIV-
negative testBut can we do any better?
If OD increases as a power function fit:
or equivalently
where a and b are constants, t is the time since the last negative and t0 is
the estimated time of seroconversion.
bttaOD )( 0
)ln()ln()ln( 0ttbaOD
We use the data to estimate a, b and t0 by non-linear regression
For the generated data [without noise] this approach gives the correct window –
regardless of the time of the last negative test
But for real data in 40% of 61 cases the time of seroconversion was estimated to be before the time of the last negative test or after the
time of the first positive.[Work in progress]
Turnbull survival analysis different approach suggested by Paul Mostert (Stellenbosch Statistics
Department).
This is a slightly more sophisticated variant of the Kaplan Meier survival analysis. Works on the basis
that the (unknown) times of: i) seroconversion
ii) OD cut-off
each lie between two known times
The times of the two events are quantified using interval censoring
Estimation of HIV window period since SC using Turnbull's algorithm
window period (days)
estim
ated
exc
eedi
ng p
roba
bility
0 100 200 300 400
0.0
0.2
0.4
0.6
0.8
1.0 Turnbull window estimates RunsAll data (red; 183 d)2: Excluding max OD < 0.8 (purple; 141 d)3: Excluding min OD > 0.8 (green; 210 d)4: Excluding 2 and 3 (blue; 163 d)
The window length is estimated using a non-parametric survival technique which makes no assumptions about any parametric models and
underlying distributions. .
No interpolation is used to obtain the cut-off time where the BED OD reaches 0.8 or the
seroconversion time point. Only time points that will define the interval boundaries were used,
which means that time points more than four for a specific women were not fully utilised. However, time points as few as two per women could be
used in this estimation of window length.
Conclusion
There is still no general agreement on how best to estimate the window for methods like the BED. Fortunately most of those described seem to give fairly similar answers – though
it’s not clear to what extent this is happening by chance.