Appendix: Inferring HIV incidence from case surveillance with CD4 counts

Section 1: Parameter tableAppendix Table A1: Parameters used in the simulation of CD4 count with time during HIV infection.

Parameter Value ReferenceDistribution of CD4 count of HIV-uninfected individuals

891 (median, interquartile range (IQR) 709-1121) cells/µL

[1-18]

Median CD4 count nadir during primary infection

418 cells/µL [19]

Days until primary HIV CD4 nadir

17 days [19]

Distribution of CD4 count peak just following primary infection

636 (95% CI: 586 - 686) cells/µL Appendix Section 3

Days until primary HIV CD4 peak

40 days [19]

Estimate of median square root CD4 count decline following primary infection

1.6 (95% CI: 1.4 to 1.8) Appendix Section 4

Estimate of individual variability for a given median square root CD4 decline (SD about the above parameter)

0.6958 Appendix Section 5

Section 2: Deduplication of multiple diagnosisMultiple reporting of the same diagnosis is accounted for by using a method proposed by Larsen et

al. [35], in which the number of unique birthdates are used to estimate the expected number of

diagnoses of people born in that year. This method requires a birthdate for every entry in the

database. There were 190 records with no date of birth recorded. A date of birth was chosen at

random for these individuals by sampling the year of birth of individuals in that year, and assigning a

random date in that year to those individuals.

Number of distinct cases= n ln (n/(n-b))

Where n= available birth dates (365 or 366), and b= number of distinct birth dates filled. We

estimated that 3,113 of the local diagnoses were duplicates, leaving 30947 diagnoses for the

calculation of incidence in Australia. The results of the deduplication are summarised in Appendix

Figure A3.

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Appendix Figure A1: The proportion of suspected duplicates by year of diagnosis.

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Section 3: Primary infection dynamicsIn the model, CD4 declines rapidly during primary infection and then rebounds. Kauffmann et al. [19]

followed the CD4 decline during primary infection, and found that the lowest CD4 count during

primary infection occurred 17 days after presentation of symptoms (with a median of 418 cells/µL)

followed by a rebound to a peak of 756 cells/µL at 40 days. The figure of 418 cells/µL and the times

measured in that study were used in the model; however, the rebound level was selected as

described below.

Section 4: Choice of median rebound peak CD4 level

During primary infection, the CD4 count of a person with HIV tends to rebound after a rapid decline.

The choice of median rebound CD4 count is important in this model, as the rebound CD4 is a strong

determinant of the time required to reach lower CD4 levels.

Lang et al.[20] closely followed the trajectories of people living with HIV (PLHIV) in the early stages of

infection, and reported a median CD4 at a fixed time (12 months). This study provides direct

measurements of CD4 count and hence can be considered reliable for the purposes of modelling. In

this study, CD4 is 636 at 12 months in seroconverters (of 37 seroconverters), which is when CD4

counts stabilise and resemble CD4 count decline of the seroprevalent population. This figure agrees

with seroconverter CD4 intercepts in Lodi 2010 (CD4=624.1 cells/µL) [21] and the CD4 intercepts for

MSM younger than 40 years (621 [609-634] or 631 [619-643] cells/µL) in CASCADE (2003)[22].

In contrast, the study by Kaufmann et al. [19] closely followed the CD4 counts of seroconverters,

finding that the mean of the highest reading of CD4 counts following infection is 756 cells/µL. We

suggest that this result is an inappropriate measure for our model, as CD4 counts within an

individual can vary greatly[23] and choosing the highest reading for an individual over a period will

be greater than the expected mean at a set time (e.g. measuring at 3 months exactly). This

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interpretation is supported by the result for median CD4 count at 12 months in this study, which is

reported as being 470 cells/µL, implying a very large decline of 286 cells/µL following primary

infection rebound in the first year.

The 2013 surveillance data of Australian recent infections (0-12 months) had a mean CD4 of 533

cells/µL, which is somewhat lower than the result from Lang et al. [20]. This figure includes people

with acute infection, some of whom will be experiencing their CD4 low following infection. It also

includes people who would be up to 12 months past their infection date who we may expect to have

about 60-80 cells/µL lower than those at their CD4 rebound following primary infection. Assuming a

square root decline over 12 months of 1.6 (see Appendix Section 4), and an equal distribution of

testing over those 12 months, at 6 months the mean CD4 will be 576 cells/µL (square root

CD4=24.0), meaning the starting square root CD4 is approximately 24.0+1.6/2=24.8 (CD4 count =

615 cells/µL). Lodi (2011) [24] reported a CD4 intercept (553 cells/µL intercept for men over 30

years) that was somewhat lower than the figure in Lodi (2010) (624.1 cells/µL intercept) [21] .

We chose the mean intercept to be 636 (in agreement with Lang et al.) with wide uncertainty

bounds (95%UB: 586-686). The mean intercept determined the proportional decline of the

uninfected CD4 count to the primary infection CD4 rebound peak. In doing so, the distribution of

CD4 counts around the median is preserved by applying the proportional decline to each individual

as each individual has a different CD4 count as determined by the distribution of HIV-uninfected CD4

counts. The median HIV-uninfected CD4 count used was 891 cells/µL, determined by finding a

weighted average of a collection of studies investigating CD4 counts of uninfected individuals[1-18].

A decline to 636 cells/µL represents a 28.6% decline in CD4 counts. Hence, in a simulation with an

average decline to 636 cells/µL, a person with a CD4 count starting at 1000 cells/µL will have their

CD4 count decline to 714 cells/µL. In other simulations, the average decline may be to more or less

than 636 (to accommodate for the uncertainty in the in CD4 count rebound peak).

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Section 5: CD4 declineIn the model, we assumed that CD4 decline occurred on the square root scale, with faster declines in

the early stages than in the later stages of infection. To inform the selection of this parameter, we

investigated multiple studies. To select the correct decline for the Australian population, studies

were included that primarily report on people infected with HIV from developed countries with

predominantly Caucasian (as racial background can affect decline[25]). Study populations were also

excluded if they focused on particular conditions (e.g. haemophilia).

The simulated CD4 progression follows a square root decline until CD4 counts reach an average of 61

cells/µL, from which point declines progress linearly. A collection of studies that report the decline of

CD4 counts on the linear scale are shown in Appendix Table A2, which we used to inform the choice

of CD4 decline parameter.

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Appendix Table A2: Studies reporting CD4 decline on the linear scale.

Study N CD4 decline per year(cells/µL)

Lee (1989) [26] 112 68

Veugelers (1997) [27]

Vancouver 129 59.87

Sydney 79 36.42

Amsterdam 140 54.1

San Francisco General Hospital 19 43.45

San Francisco Men's Health 46 55.42

Prins (1999) [28] 664 60

Deeks (2004) [29] 68 96

Mellors (2007) [30] 1640 64

Drylewicz (2008) [31] 418 49

Muller (2009) [25] 463 52.5

Wolbers (2010) [32] 2820 61

Lewden (2010) [33] 373 63

The weighted mean of the decline from these studies is 61 cells per year. If the mean CD4 count is

400 cells/µL, and a loss of 61 cells/µL occurs in the year following, this results in a CD4 count of 339

cells/µL, the square roots of these values are 20.00 and 18.41 respectively. This represents an annual

decline in square root CD4 counts of 1.588 per year.

This result is in alignment with the result from CASCADE collaboration (2003) [22] which showed a

square root decline between 1.22 and 1.67 depending on age and whether the result was adjusted

for right censoring. Note that the result above is not exactly in alignment with two studies by Lodi et

al. Firstly, Lodi 2010 found that in the seroconverter group, CD4 square root decline was 1.758 per

year in the baseline group (<30 years, MSM) and up to 1.908 in men older than 30 years[21]. In a

later study, Lodi 2011 found square root decline to be 1.159 per year[24], a highly divergent result to

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the 2010 results. Both of these results are from multi-parameter models, which used CD4 count

intercept and CD4 decline in the model. Lodi 2010 had a high starting CD4 and a fast CD4 decline,

while Lodi 2011 had a low starting CD4 and a slow CD4 decline, implying that the fitting function was

converging to similar times and more observations in the centre of observations (after the second

and third year). Hence, these results have a high degree of variability for CD4 count immediately

following infection.

Pillay et al. investigated transmitted drug resistance (TDR) CD4 decline rates, also using CASCADE

data. In their analysis, non-TDR individuals had a square root decline of 1.7 (95% CI, 0.8–2.6). Keller

et al. [34] also investigated the CD4 decline in Canada, finding square root CD4 declines of between

1.6 and 1.67 prior to ART initiation.

Given the above results and the variability between the studies, we selected a median square root

decline of 1.6 with an uncertainty bound of 1.4 to 1.8 to inform the uncertainty analysis.

Section 6: Individual variability in CD4 declineIndividuals in the simulation have unique CD4 declines with time. To give an estimate of that

variability, we used the results from Wolbers et al.[32]. In this study, the estimated pre-cART CD4

slope was 61 (IQR: 46-81) cells/µL with a median CD4 cell count at cART initiation of 289 cells/µL.

Converting the declines to square root declines using 289 cells/µL as the end point, the square root

decline was 1.7083 (IQR 1.3030-2.2354). The mean distance between the interquartile ranges and

the median was 0.4662, which gave a standard deviation in the square root decline of 0.6958. Given

the stochasticity in within-individual CD4 measurements with time, the variability in CD4 count

decline is possibly overestimating the variability of decline. Since we do not know the true variability

between people, we chose to use the upper bound of variability as calculated above.

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Appendix Figure A2: Modelled stochasticity associated with repeated measurements of CD4 count. The x-axis is the median CD4 count for an individual after repeated measurements. The y-axis is the CD4 count at a single measurement of CD4 count.

Section 7: Fitting of the modelThe model uses the CD4 count at diagnosis data for each year, and attempts to replicate the

distribution of CD4 counts at diagnosis by varying the assumed testing rate and minimising the error

between the histogram of the diagnosis data and the histogram of the simulated CD4 counts at

diagnosis. A lower testing rate implies that the CD4 count at diagnosis will be lower, and a higher

testing rate implies a higher CD4 count at diagnosis, on average. An optimisation for the testing rate

is performed for every parameter selection of parameters within the uncertainty bounds specified.

An example of the result of the optimisation is shown in Appendix Figure A1 for the 2009 to 2013

data.8

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Appendix Figure A3: Diagnosis data from 2009 to 2013 and the simulated sample population

diagnosis data. The simulated sample population data is optimised by minimising the difference

between the histogram of the observed CD4 counts at diagnosis and the simulated CD4 count at

diagnosis.

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Section 8: Forward projection of currently undiagnosed cases

Many of the infections that occur in the final years of the back-projection simulation are yet to be diagnosed. Hence, an estimate of the currently undiagnosed population needs to be made. We assume the diagnoses rates do not change greatly with time. As such, we can use the distribution of time between infection and diagnosis of recently diagnosed individuals to make an estimate of the undiagnosed.

The distribution of time between infection and diagnosis for people in the past 5 years is shown in Appendix Figure A4.

Appendix Figure A4: distribution of time between infection and diagnosis for people diagnosed between 2009 and 2013.

The algorithm treats the distribution as continuous, the choice of bar width in the histogram is to make interpretation of the distribution easier.

To describe how the methodology works we will consider a fictional example. Consider that the above distribution represents the distribution of times between infection and diagnosis for the last five years of back projected cases. The back projection calculation places 150 cases in the year 2013. However, there should be many cases that are as yet undiagnosed. We need to try to match the distribution of time between infection and diagnosis to the number of currently diagnosed cases to

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determine the undiagnosed in the distribution. To do so, we simulate an infection occurring at a random time during that year and when that case is expected to be diagnosed. Consider a case that occurs a quarter of the way through the year 2013 (2013.25 in decimal time). If the case is diagnosed before 2014, it appears in the observations of real diagnoses. For this to happen, the simulated time between infection and diagnosis needs to be less than 0.75 years. If the case is diagnosed before after 2014 (i.e. the time between infection and diagnosis >0.75 years), it is a currently undiagnosed case. We select time from the distribution and if it and undiagnosed case, we add 1 to the number of simulated undiagnosed cases. If it is a diagnosed case, we add one to the number of diagnosed cases.

Appendix figure A5: In this example, if the time selected is to the left of the red line, it counts as a diagnosed case, and as an undiagnosed case if it is to the right.

This process is repeated until the total number of diagnosed cases reach 150 (for this example). The number of cases that are undiagnosed may reach, say, 312. This process is repeated for each of the 20 years prior to the final year of observations. In this way, an estimate can be found for the number of infections that have occurred in each of these years that are yet to be diagnosed. The estimated number of undiagnosed cases are added to the number of cases back projected to have been incident in that year to estimate the total incidence in that year.

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Section 9: Further analysis of uncertainty in time between infection and diagnosis Appendix Figure A6: Comparison of the mean and median time between infection and the associated uncertainty of each estimate in each year.

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Appendix Figure A7: Population median CD4 count and uncertainty of the median (based on variation in CD4 decline parameters) of individuals undergoing no ART.

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Section 10: Evidence of late reportingThere appears to be very low levels of late reporting in the Australian HIV surveillance registry.

Appendix Table A3: Adjustment to reported HIV diagnoses by mid-2014.

Year Reported diagnoses in report in year immediately following

Reported Diagnoses in 2014 report

Percent change

2008 995 1015 +2.01%2009 1050 1069 +1.81%2010 1043 1057 +1.34%2011 1137 1142 +0.44%2012 1253 1253 +0.00%

Section 11: Comparison of MSM and non-MSM resultsThere are substantial differences between the results for MSM and non-MSM individuals. We have provided supplementary figures to provide further insight into the differences between these groups.

Appendix Figure A8: Median CD4 count (interquartile range) of MSM and non-MSM individuals diagnosed with HIV in Australia.

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Appendix Figure A9: Median estimated time between infection and diagnosis (interquartile range) of MSM and non-MSM individuals diagnosed with HIV in Australia.

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Section 12: Sensitivity of selected parameters We have selected some input parameters to analyse the impact on a limited number of results.

The model has a parameter that determines a cut-off date at which point there are assumed to be zero new infections of HIV prior to that date. This parameter has an impact on the peak of the modelled infections. Appendix Figure A10: Assumed date of first possible infection vs peak yearly incidence

Appendix Figure A11: Sensitivity of median time until diagnosis to changes in assumed CD4 following primary infection.

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Appendix Figure A12: Sensitivity of incidence in final year of simulation to changes in assumed CD4 following primary infection.

Appendix Figure A13: Sensitivity of median time until diagnosis to changes in assumed CD4 square root decline.

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Appendix Figure A14: Sensitivity of incidence in final year of simulation to changes in assumed CD4 square root decline.

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