3.1.1 Before creating datasets

Creating the datasets that are required by the two methods may be a considerable amount of work. To avoid unnecessary preparation of datasets there are two main issues to consider:

• Are there data available on CD4 counts at the time of HIV diagnosis?
• Are surveillance data available for multiple calendar years?

Depending on the answers to these questions, one or both methods may be applicable according to the scheme below.

The Incidence Method requires surveillance data over multiple years, ideally covering the duration of the HIV epidemic in a country. This method will work with or without CD4 counts at the time of HIV diagnosis, although the first option is preferred. The Incidence Method will also work if data on CD4 counts are only available for several years.

The London Method requires at least one year of data, including CD4 counts at the time of HIV diagnosis. This method will also work with multiple years of data.

Both the Incidence Method and the London Method are based on CD4 cell decline in adult HIV-1-positive individuals. Therefore, HIV-2-positive individuals and HIV-positive children below 16 years of age should be excluded from the datasets.

3.1.2 Populations

Before using the tool, the user may define populations in which the total national or regional HIV population can be divided. Distinguishing one or more populations may be appropriate if the user expects major differences in time between infection and diagnosis between the populations. Differences in time to diagnosis may be indicated by differences in the mean or median CD4 count at the time of diagnosis. Still, the tool will also work when all HIV-positive individuals in a country are considered as one single population. In that case, however, estimates of time to diagnosis in the Incidence Method will be an average over the total population.

Populations can be based, for instance, on route of transmission: men who have sex with men, heterosexual men and women, injecting drug users. Other examples of populations include native HIV-positive individuals and migrants, or people living HIV in a specific city. The choice of populations will depend on the nature of the HIV epidemic in a given country.

When defining populations, the user should also consider the population size. The outcomes of the ECDC HIV Modelling Tool are harder to interpret for smaller populations with only a few new HIV diagnoses per year. A good approach may therefore be to first consider all HIV-positive individuals as a single population and then as a next step disaggregate this single population into smaller populations.

3.1.3 Preparation of datasets

The Incidence Method and the London Method each require their own datasets. There is no overlap between these datasets, although these data will most likely be extracted from the same surveillance system.

3.2.1 Header row

Each data set needs a header row. In a CSV file, the header row is simply a list of variable names and may look like this with comma (“,”) as list separator:

• in Notepad

  Year,population_1,population_2,population_3

• in Excel

  Year  population_1  population_2  population_3

In this case the CSV file contains information on 3 groups. The names of these groups are arbitrary but should be same in all data sets that are necessary for the tool.

3.2.2 Data row

The header row is followed by rows containing epidemiological data, one row for each calendar year. Each data row contains a calendar year followed by one or more numbers, for instance the number of AIDS diagnoses. Numbers do not necessarily have to be integers, which could be the case, for instance, when a correction for reporting delay is made.

• in Notepad

  1982,0,0,0
  1983,0,0,0
  1984,2,1,3
  1985,17,15,20
  1987,20,23,20
  ..,..,..,..
  2013,51.5,30,25

• in Excel

  1982     0   0   0
  1983     0   0   0
  1984     2   1   3
  1985    17  15  20
  1987    20  23  20
  ..      ..  ..  ..
  2013  51.5  30  25

In the example above, for the first population there are zero diagnoses in 1982 and 1983, 2 in 1984, 17 in 1985, and so on. For 2013, there are 50 observed diagnoses, but corrected for a reporting delay of 5% assuming for instance that 5% of the diagnoses has not yet been reported the expected number would be 51.5.

For calendar years in which the surveillance system captured a specific data item but no data (diagnoses) were observed, there should be a corresponding row with 0 diagnoses in the CSV file (as in the example above for 1982 and 1982). In contrast, for calendar years in which the surveillance system did not yet capture a specific data item, there should be no corresponding row (as in the example above for 1981 and earlier years). Putting a 0 in this case may lead to wrong results, because the tool will treat a number of 0 diagnoses the same was a any other number.

Note that the tool will assume 0 observations or diagnoses for intermediate years that are missing in the input datasets (as in the example above for 1986).

3.2.3 Excel and regional settings

As mentioned already the tool automatically detects both field and decimal separators used in the data sets and can properly interpret values. Output data sets are in CSV format as well and the tool will use the field and decimal separators from the operating systems’ regional settings.

However, we would like to comment here about the behaviour of Excel when it comes to dealing with CSV files. Many users will most likely use that software to prepare input data sets and examine results.

Sharing CSV files for opening in Excel where different regional settings are applied can be troublesome. Excel reads the list and decimal separators from the operating system’s regional settings and expects the opened CSV file to follow the exact same convention with respect to the separators. Very often Windows sets comma (“,”) as the list separator and a period (“.”) as the decimal separator. It follows this convention for many Western European countries, including United Kingdom. However, for other countries, for instance Germany, it applies a different convention - semi-colon (“;”) as the list separator and comma (“,”) as the decimal separator. Therefore the same data set will be saved by Excel in different formats depending on the regional settings applied:

• in the UK

  1982,0,0,0
  1983,0,0,0
  1984,2,1,3
  1985,17,15,20
  1987,20,23,20
  ..,..,..,..
  2013,51.5,30,25

• in Germany

  1982;0;0;0
  1983;0;0;0
  1984;2;1;3
  1985;17;15;20
  1987;20;23;20
  ..;..;..,..
  2013;51,5;30;25

It can be easily checked which setting is currently applied in Excel by opening one of the CSV files in the examples distributed with the tool. The examples include data sets using a comma (“,”) as commas separator. If Excel does not put each value in to a separate cell, then it means that it did not recognize the list separator. Most likely the data sets that use semi-colon (“;”) as the list separator will be displayed correctly.

If it is intended to share data between operating systems with different regional settings, then we advise to use Excel file format (file extensions “.xls” or “.xlsx”), rather than CSV (file extension “.csv”).

4.1.1 Interface

4.1.2 Model

This section specifies several default settings for the Incidence Method and London Method.

6.2.1 Diagnosis probability

Apart from estimating the annual number of new HIV infections, the Incidence Method also estimates the probability that HIV-positive individuals are diagnosed with HIV when their (unobserved) CD4 count is in one of the four CD4 intervals. This probability is usually unknown and needs to be estimated from the observed input data. The tool uses the diagnosis probabilities to calculate the expected time between infection and diagnosis by year of infection.

Before using the Incidence Method, the user needs to specify:

• Time intervals: indicate when the probability of being diagnosed may change.

• Presumed shape: indicate how the probability of being diagnosed may change.

6.2.2 Specifying time intervals

Time intervals in which the diagnosis probabilities may change are given in the left part of the table.

6.2.3 Specifying presumed shape

In the right part of the table you can specify how the diagnosis probability may change in a time interval.

6.2.4 Examples

The examples below show a few possible shapes of the diagnosis probability curve and how these shapes are specified in the tool.

Example I

Presumed shape

The diagnosis probability is zero in 1980 and then gradually increases with calendar time at a rate r₁.

Time intervals and diagnosis probabilities

Example II

Presumed shape

The diagnosis probability is zero from 1980 until 1984. In 1984, the diagnosis probability is o₂ and afterwards increases linearly.

Time intervals and diagnosis probabilities

Example III

Presumed shape

This is the presumed shape used in¹. The diagnosis probability is zero from 1980 until 1984. Between 1984 and 1996, the diagnosis probability is at a constant value o₂. From 1996 onwards, the probability increases linearly, but the rate at which the probability increases with calendar time changes in 2000 from r₃ to r₄ and in 2005 from r₄ to r₅. Diagnosis rates can be different for each of the four CD4 count categories.

Time intervals and diagnosis probabilities

Example IV

Presumed shape

The diagnosis probability is zero from 1980 until 1984, o₂ from 1984 until 1996, o₃ from 1996 until 2000. In 2000, the diagnosis probability is o₄ and then changes linearly. The rate at which the probability increases with calendar changes in 2005 from r₄ to r₅.

Time intervals and diagnosis probabilities

Example V

Presumed shape

Same as in Example III. The diagnosis probability is zero from 1980 until 1984. Between 1984 and 1995, the diagnosis probability is a constant value o₂. After 1996, the probability increases linearly, but the rate at which the probability increase with calendar changes in 2000 from r₃ to r₄ and in 2005 from r₄ to r₅. Diagnosis rates are the same for all CD4 count intervals.

Time intervals and diagnosis probabilities

Example VI

Presumed shape

This is the presumed shape used in Van Sighem et al.⁴ where the diagnosis probability is o₁ between 1980 and 2003. After 2003, the probability increases linearly at a rate that changes in 2005 and 2010. Diagnosis rates can be different for each of the four CD4 count categories.

Time intervals and diagnosis probabilities

6.3.1 Calculation based on

A green tick mark indicates whether the London Method will be based on HIV/AIDS diagnoses only and/or on HIV/AIDS diagnoses plus HIV diagnoses with HIV-related symptoms.

When calculations are based on HIV/AIDS diagnoses plus HIV diagnoses with HIV-related symptoms, the London Method requires knowledge of the CD4 count-specific rate of HIV-related symptoms. While the CD4 count-specific rate of occurrence of AIDS is known, the CD4 count-specific rate of occurrence of such HIV-related symptoms is less well described. There is evidence to suggest that the rate of developing HIV-related symptoms is approximately two- to four-fold higher compared to the rate of AIDS². By default, the CD4 count-specific rates of HIV-related symptoms are assumed to be two-fold the CD4 count-specific rates of AIDS, but this can be changed by the user.

6.4.1 Calendar year ranges

The five slider bars show the range of calendar years used in the calculations of the Incidence Method. These ranges are specified by the wizard and are based on the minimum and maximum calendar year in the input datasets.

Ranges can be made wider or narrower by dragging the rectangles at either end of the green bar. Alternatively, the lower boundary (Start year) and upper boundary (End year) of each calendar year range can be selected by clicking the up or down button in the white boxes above the slider bars.

6.4.2 Full/partial data

If (complete) HIV surveillance data are not available from the start of the HIV epidemic but only from a certain year Y onwards, no should be selected here. In this case it is still possible to estimate the number of newly acquired HIV infections and the undiagnosed population. However, these estimates will only be reliable for the most recent calendar years, i.e., for years where the undiagnosed proportion of people who acquired their HIV infection before year Y is small. Since data before year Y are not available, the tool cannot estimate the total population living with HIV.

Please note that model outcomes for recent calendar years may be similar if yes is selected despite data not being available from the start of the HIV epidemic. However, the estimation process will be less efficient, especially if a large number of parameters needs to be estimated or if confidence intervals are calculated.

The following settings are recommended if data are only available from year Y onwards:

• Start year of Range of calculations is the approximate year in which the HIV epidemic started in a country (default value 1980). Stop year is the most recent year for which data are available.

• The slider bars for the data items should start in the year from which surveillance data are available. In the figure below, data on HIV diagnoses, stratified by the presence of a concurrent AIDS event or CD4 cell count, are available from 2003 onwards.

  

• In the diagnosis matrix, make sure Start Year for the first time interval equals the start year of the range of calculations and End Year equals Y. For this first time interval, select Start from new baseline and, if data on CD4 counts are available in year Y, also Different by CD4 count categories, but do not select Changing during time interval. Since there are no data before year Y, it is not possible to estimate diagnosis probabilities in more than one time interval. An example of a diagnosis matrix can be found in Example VI.

• Do not specify too many knots for the incidence curve. The default value of 4 is likely to be enough.

6.4.3 Confidence intervals

The tool has the option to determine confidence intervals on estimated parameters and model outcomes via a so-called bootstrap analysis (see below Intermezzo: bootstrap analysis).

A bootstrap analysis can be time-consuming because it involves running the Incidence Method multiple times on bootstrap replicates of the data. Confidence intervals should, therefore, only be determined when the main model gives a satisfactory description of the observed data.

6.4.4 Incidence curve

For each calendar year, the Incidence Method determines the annual number of HIV infections from the estimated HIV incidence curve. In the tool, this incidence curve is fully described by a limited number of parameters that is determined by the number of so-called knots. A higher number of knots will result in more flexibility for the incidence curve, but also involves estimating a higher number of parameters.

6.4.5 Maximum likelihood

Maximum likelihood methods are used to find the set of parameters that best fit the observed data. To define the likelihood, it is assumed that all data items are distributed according to a certain probability density function around a mean defined by the model. For convenience, instead of maximising the likelihood, the tool minimises the equivalent deviance measure.

6.4.6 Diagnosis rate

6.4.7 Country-specific settings

The tool has the possibility to incorporate county-specific settings.

Currently, this option is only implemented for the Netherlands where a correction needs to be done for truncation of HIV diagnoses before 1996. National surveillance of HIV diagnoses only started in 1996 and patients diagnosed before that time were recorded if they survived up to 1996.

6.5.1 Calendar year ranges

The slider bar shows the range of calendar years used in the calculations of the London Method.

The range can be made wider or narrower by dragging the rectangles at either end of the green bar. Alternatively, the lower boundary (Start year) and upper boundary (End year) of each calendar year range can be selected by clicking the up or down button in the white boxes above the slider bars.

6.5.2 95% confidence intervals

The tool has the option to determine 95% confidence intervals using a simple simulation method². These confidence intervals include two sources of uncertainty for the estimated number of people living with undiagnosed HIV: the stochastic uncertainty concerning the CD4 count-specific rate of symptoms and the stochastic uncertainty associated with the possibility that the observed number of HIV diagnoses with HIV-related symptoms may not correspond to the expected number based on the CD4 count-specific rate of symptoms.

7.3.1 Incidence Method

The following graphs are available for the Incidence Method:

7.3.2 London Method

The following graphs are available for the London Method: