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New method for estimating HIV incidence and time from infection to diagnosis using HIV surveillance data

results for France

Ndawinz, Jacques D.A.a,b; Costagliola, Dominiquea,b,c; Supervie, Virginiea,b

Author Information
doi: 10.1097/QAD.0b013e32834af619



Findings from several studies suggest that early antiretroviral treatment of HIV-infected people may have both individual and public health benefits [1–4]. Providing treatment early in the course of the HIV infection has been associated with reduced HIV-related morbidity and mortality [2]. Furthermore, HIV-infected persons on effective HIV treatment are less likely to transmit HIV to others [1,4]. On the basis of these evidences, new international treatment recommendations – urging clinicians to treat patients earlier – were recently released [5]. Knowledge of HIV status is the first necessary condition for accessing early treatment. However, as HIV infection can remain asymptomatic for a long period of time, many HIV-infected people remain undiagnosed until late in the course of infection. The estimated proportion of HIV-infected people who remain undiagnosed varies from 90% in sub-Saharan Africa [6] to 20–30% in Europe [7] and in the United States [8]. Undiagnosed HIV is thus a major challenge for the implementation of new treatment guidelines in all countries.

To reduce undiagnosed HIV infection, many western countries plan to revise, or have recently revised, their HIV screening guidelines [9]. New guidelines recommend to routinely offer HIV tests to the whole sexually active population. This is a major shift in policy since currently most HIV screening is done at the patient's request [10,11]. It is too early to measure the impact of the new screening guidelines since they still have to be implemented in most countries. However, explicit metrics, and methods to measure them, need to be defined to monitor progress of the process and future outcomes of the new guidelines [9].

The objective of the new guidelines is earlier detection of HIV-infected patients to allow earlier access to care and treatment, and improved control of HIV transmission. Two metrics reflecting these objectives are time between infection and diagnosis and HIV incidence [9,12]. To the best of our knowledge, no method has ever been published that provides estimates of the length of time between infection and diagnosis over time. In comparison, statistical approaches for measuring HIV incidence have evolved as the underlying data sources have grown and become more sophisticated [13]. Recently, the US Centers of Disease Control and prevention used a new statistical method, the biomarker approach [13,14], to obtain nationwide estimates of HIV incidence [15]. The biomarker approach requires data on HIV biomarkers that distinguish between recent and long-standing infection [14,15] in addition to HIV surveillance data. HIV biomarker data are not available in most countries [16], impeding the application of the biomarker approach in these countries. Furthermore, as currently implemented, the biomarker approach makes one major assumption: test-seeking behaviors remain stable over time [14,15]. HIV test-seeking practices will inevitably change with the implementation of the new screening guidelines, making thus estimates of HIV incidence, derived using the biomarker approach, vulnerable to bias.

Back-calculation models [13] using incidence of AIDS and the AIDS incubation period have been widely used in the past to reconstruct the HIV incidence [13,17,18]. However, the advent of antiretroviral therapy has significantly slowed progression to AIDS, and trends in AIDS incidence no longer reliably reflect recent trends in HIV incidence. Mandatory reporting of new HIV diagnosis has provided new opportunities for estimating the HIV incidence using the back-calculation method [19,20]. Indeed, HIV infection is generally diagnosed before AIDS, thus HIV diagnosis counts can provide valuable information on recent trends in HIV incidence. The difficulty of back-calculating HIV incidence from HIV diagnosis counts is that the length of time between infection and HIV diagnosis (i.e. HIV testing rates) is not known and can change over time. In principle it is possible to estimate HIV incidence as well as HIV testing rates on the basis of HIV diagnosis counts, as the data contain information on both components [20]. However, identifiability problems may occur in distinguishing changes in testing rates from changes in incidence [20]. Sweeting et al.[20] have resolved the lack of identifiability through the use of additional information on HIV diagnoses: CD4 cell counts around HIV diagnosis. However, all countries do not record CD4 cell counts at initial HIV diagnosis (<50% of European countries) [16,21] and when they do, data are often incomplete [16,21]. Consequently, there is a need for developing new statistical methods for estimating HIV incidence involving the use of data that are easy to collect at the national level.

Here we devised a new model for estimating, over time, HIV incidence and time between infection and diagnosis of HIV infection based on HIV surveillance data. Our approach takes into account temporal changes in HIV test-seeking behaviors and requires few data on individuals newly diagnosed with HIV: date of diagnosis, clinical status at diagnosis [primary HIV infection (PHI), AIDS, neither PHI nor AIDS] and HIV exposure category. In this study, we illustrate our approach by applying the model to French surveillance data.


In France, mandatory nationwide reporting of new HIV diagnoses was implemented in March 2003. Data on new HIV diagnoses, including date of diagnosis, demographic information (sex, nationality, and HIV exposure category), and clinical status at diagnosis (PHI, asymptomatic, symptomatic without AIDS or AIDS) have since been recorded in a national database [22]. Between April 2003 and December 2008, a total of 28 175 new HIV diagnoses were recorded in the database. Missing data were estimated by using multiple imputation techniques [23]. Ten imputed datasets were generated by using the missing-at-random assumption. Numbers were then adjusted for under-reporting and reporting delay, based on previous studies [22] (see appendix for full details). Corrected data are shown in Fig. 1. We distinguished six HIV exposure categories, as follows: men who have sex with men (MSM), injecting drug users (IDUs), French-national heterosexual women, French-national heterosexual men, non-French-national heterosexual women and non-French-national heterosexual men. Most non-French-national heterosexuals originated from sub-Saharan Africa.

Fig. 1
Fig. 1:
French HIV surveillance data.(a) Annual number of newly diagnosed cases of HIV infection. (b) Proportion of individuals initially diagnosed during the primary stage of HIV infection (PHI). (c) Proportion of individuals initially diagnosed with AIDS. Data, collected by the French National Institute for Public Health Surveillance (InVS), were corrected for missing entries, under-reporting, and the reporting delay. Ten datasets were generated to account for missing entries. Values are means of the 10 datasets. aAll nationalities; ball nationalities, both sexes.

During the period 2003–2008, MSM accounted for most new diagnoses, followed by non-French-national heterosexual women, non-French-national heterosexual men, French-national heterosexual men, French-national heterosexual women and IDUs (Fig. 1a). The proportions of individuals at the different stages of HIV infection at diagnosis varied over time and across exposure categories (Fig. 1b and c). In 2008, the proportion of individuals diagnosed with PHI was highest among MSM (18%) and lowest among non-French-national heterosexual women (5%) (Fig. 1b). The proportion of individuals initially diagnosed with AIDS was highest among French-national heterosexual men (20%) and lowest among MSM (9%) (Fig. 1c). These data clearly showed that HIV testing practices in France varied within and across HIV exposure categories.

To estimate our two metrics (i.e. HIV incidence and time between infection and diagnosis) from data on new HIV diagnoses, we devised a novel back-calculation model based on the one designed by Becker et al.[19]. Our approach can be summarized as follows (see appendix for full details). The first step consisted of assigning specific test-seeking behaviors to newly diagnosed individuals according to their clinical status at initial diagnosis. Newly diagnosed individuals had one of the three clinical statuses at initial diagnosis: PHI, AIDS or neither AIDS nor symptoms of PHI (individuals classified without AIDS nor symptoms of PHI at initial diagnosis could be asymptomatic or symptomatic patients without AIDS). By definition, individuals with symptoms of PHI were diagnosed very early in the course of HIV infection. We thus assumed that these individuals decided to be tested because they experienced, and recognized, symptoms of PHI, or because they had recently been exposed to HIV. Other individuals were more likely to be diagnosed later in the course of the disease. We thus assumed that individuals initially diagnosed without AIDS nor symptoms of PHI decided to be tested for other reasons than those of individuals with symptoms of PHI (e.g. routine medical examination or onset of HIV symptoms that occur towards the end of the incubation period), whereas individuals with AIDS at initial diagnosis were not tested for HIV before being diagnosed with AIDS. It is important to note that our approach does not require that all HIV-infected individuals diagnosed during PHI be notified as such, allowing the notification of PHI symptoms to vary over time and between transmission categories.

The next step consisted of linking the observed incidence of newly diagnosed cases to the unobserved incidence of HIV infection by specifying the distribution of the time between infection and diagnosis in each group of individuals. Individuals diagnosed with PHI were assigned a short time between infection and initial diagnosis (3 months in median) [24]. Individuals diagnosed with AIDS at initial diagnosis were assigned values derived from published estimates of the natural AIDS incubation time (10 years in median) [25]. Thus, the only remaining unknown was the distribution of the time between infection and initial diagnosis among individuals diagnosed before AIDS onset and without PHI symptoms. Following Becker et al.[19], we assumed that this distribution was dependent on two unknown parameters that represent uptake of routine testing and onset of HIV symptoms that occur towards the end of the incubation period.

The last step of our approach consisted in obtaining estimates, as well as their precision, of the unknown parameters of the model, namely the two unknown parameters of the pre-AIDS HIV testing distribution and the unobserved number of new infections. This was achieved using maximum-likelihood techniques. Using the group-specific estimates of the number of new HIV infections and the group-specific distribution of the time between infection and diagnosis, we were able to calculate the overall distribution of the time between infection and diagnosis. Finally, we calculated incidence rates as the number of new HIV infections divided by the number of individuals at risk of HIV infection. We obtained the number of individuals at risk of HIV infection by subtracting the number of HIV-infected persons from the population size (see Table S1,

To validate our results, we used estimates of the two metrics to calculate the percentage of late diagnosis among newly diagnosed individuals, and compared our calculations with observed data. We defined late diagnosis as a diagnosis made more than 8 years after infection, which is the average period required for the CD4 cell count to fall below the critical threshold of 200 cells/μl [26].


We applied our new back-calculation model to French data on the reported number of newly diagnosed cases of HIV infection between April 2003 and December 2008 in order to estimate both the annual number of new HIV infections and the time between infection and diagnosis in six exposure categories (MSM, IDUs, French-national heterosexual women and men, non-French-national heterosexual women and men). We restricted our estimation period to 2004–2007 for two reasons. First, data on the clinical status of new HIV diagnoses were not available before April 2003. Second, recent trends in estimates of HIV incidence are highly dependent on the quality of surveillance data, and the data for 2008 are very sensitive to assumptions made about the reporting delays.

Our estimates show that the annual number of new infections tended to increase slightly among MSM and heterosexuals between 2004 and 2007, whereas it tended to fall slightly among IDUs (Fig. 2). These trends were not statistically significant, however. With 2969 new infections occurring in 2007 [95% confidence interval (CI) 2529–3310] MSM accounted for the largest number of new infections (38.0% in 2007), followed by non-French-national heterosexuals (31.5%), French-national heterosexuals (29.0%), and IDUs (1.5%) (Table 1). Among non-French-national heterosexuals, the incidence was higher among women than men, with, respectively, 1454 (95% CI 1029–1765) and 1015 (95% CI 559–1437) new infections in 2007. The reverse was true among French-national heterosexuals, with 1399 new infections among men (95% CI 817–1970) and 892 among women (95% CI 445–1213) in 2007. IDUs accounted for 123 (95% CI 21–224) new infections in 2007. This number may seem small compared to the other exposure categories, but the estimated incidence rate per 100 000 person-years was second highest among IDUs, after MSM (Table 1).

Fig. 2
Fig. 2:
Estimated annual number of new HIV infections and 95% bootstrap confidence intervals per exposure category (—) in France.aAll nationalities; ball nationalities, both sexes.
Table 1
Table 1:
Estimated numbers of new HIV infections and HIV incidence rates for France in 2007, by exposure category.

To calculate the total number of new infections that occurred in France, cases of exposure occurring outside France had to be excluded. Whereas it is reasonable to assume that the vast majority of infected IDUs, MSM and French-national heterosexuals contracted the virus in France, it is difficult to determine where non-French nationals were infected [27,28]. However, a lower (respectively upper) bound for the overall incidence in France can be obtained by adding together the numbers of new infections among MSM, IDUs and French-national heterosexuals (respectively, among all exposure categories). We thus estimated that between 5382 (95% CI 3812–6717) and 7851 (95% CI 5400–9919) new HIV infections occurred in France in 2007 (Table 1). These numbers are slightly but not significantly higher than those estimated for 2004 (Fig. S1,

We estimated the time between infection and diagnosis according to the year of infection in each exposure category. Means, medians and interquartile ranges (IQRs) for individuals infected in 2007 are shown in Fig. 3. The mean time between infection and diagnosis was 37.0 months for MSM infected in 2007, 41.2 months for non-French-national heterosexual women, 44.6 months for IDUs, 50.5 months for French-national heterosexual women, 53.0 months for French-national heterosexual men and 53.5 months for non-French-national heterosexual men. Note that IQRs were narrower for women than for men (Fig. 3), suggesting that HIV testing behaviors were less heterogeneous among women. Our results also show that HIV testing practices changed very slightly during the period 2004–2007: the mean time between infection and diagnosis shortened among MSM, remained stable among non-French-national heterosexual men, and lengthened in all the other exposure categories (Table 2).

Fig. 3
Fig. 3:
Estimated time between HIV infection and diagnosis of HIV infection (for individuals infected in 2007) per exposure category in France.The intervals are presented in increasing order of the mean values. Q1 and Q3 are first and third quartiles, respectively. aAll nationalities; ball nationalities, both sexes.
Table 2
Table 2:
Estimated changes in the length of time between HIV infection and diagnosis of HIV infection (in months) between 2004 and 2007 by exposure category.

We used our estimates to calculate the percentage of late diagnosis among individuals diagnosed in 2008, and compared our calculations with observed data. The percentage of late diagnosis in 2008 was calculated to be 32% overall, 17% among MSM, 31% among French-national heterosexual women, 36% among non-French-national heterosexual women, 46% among non-French-national heterosexual men, 50% among IDUs, and 52% among French-national heterosexual men. The French National Institute for Public Health Surveillance (InVS) recently reported that, in 2008, the CD4 cell count at initial HIV diagnosis was below 200 cells/μl in 29% of cases overall, 18% among MSM, 34% among heterosexuals, and 48% among IDUs [29]. Among heterosexuals, late diagnosis was more frequent in men than in women, whereas the percentage did not differ between French nationals and non-French nationals. Our estimates are thus in excellent agreement with those reported by the InVS.


We have developed a new model for estimating two key metrics: HIV incidence and time between infection and diagnosis. Our model accounts for temporal changes in HIV test-seeking behaviors. Our approach can be applied to any country collecting the date of HIV diagnosis as well as the clinical status at diagnosis (PHI, AIDS, neither PHI nor AIDS), which includes most western countries [16,21]. Country-specific values of these two metrics will be very useful for monitoring the impact of new guidelines promoting early HIV diagnosis in western countries [10,11,30]. We illustrated our method by applying it to French surveillance data. To the best of our knowledge, this is the first time that incidence of HIV infection (accounting for temporal changes in HIV test-seeking behaviors) and the length of time between infection and diagnosis are estimated for France.

Not surprisingly, we found that the time between infection and diagnosis varied markedly according to the exposure category, from 37.0 months among MSM to 53.5 months among non-French-national heterosexual men. To validate our estimates, we examined the main reasons for testing, as stated by newly diagnosed HIV-infected individuals. In 2009, the main reason was ‘recent exposure to HIV’ among MSM (35% of MSM), ‘a routine medical check-up’ (e.g. during pregnancy) among non-French-national heterosexual women (39%) and ‘clinical symptoms’ among French-national heterosexual women (33%; medical check-ups came second at 28%), non-French-national heterosexual men (43%) and French-national heterosexual men (46%) [29]. No data were available for IDUs. These data thus suggest that the time between infection and diagnosis should be shortest among MSM, longest among heterosexual men, and intermediate for heterosexual women, in keeping with our estimates. We also found that the length of time increased or decreased very slightly (by less than 1.2 months) during the period 2004–2007, depending on the exposure category. Absence of significant decrease in the length of time between infection and diagnosis during the period 2004–2007 was expected since French screening policies have not changed since the 1990s.

Apart from the annual number of new infections, our model provides estimates of the HIV incidence. With almost 3000 new infections in 2007, and 38.0% of all new infections, we found that MSM were the hardest hit by HIV in France, followed by non-French-national heterosexuals (31.5%), French-national heterosexuals (29.0%), and IDUs (1.5%). We also found that the number of new infections increased slightly, but not significantly, among MSM and heterosexuals between 2004 and 2007. Our results thus confirm recent behavioral studies suggesting an increase in at-risk behaviors among MSM [31], and surveillance data showing an increase in the number of sexually transmitted infections (gonorrhea, chlamydia and syphilis), not only among MSM but also among heterosexuals [32]. In contrast, the annual number of new infections among IDUs remained below 150 during the period 2004–2007. Nevertheless, the incidence rate (i.e. the number of newly infected persons as a percentage of all persons at risk) was second highest among IDUs, after MSM. By adding together the numbers of cases in each exposure category, we estimated that the number of new infections increased, but not significantly, between 2004 and 2007, reaching 7851 (95% CI 5400–9919) in 2007. This latter figure certainly overestimates the number of new infections that occurred in France in 2007, as a certain proportion of individuals, which no doubt differs across the exposure categories, were infected outside France [27,28]. However, it is not possible to single out individuals infected abroad from available data.

The InVS recently published estimates of the HIV incidence in France [33], based on the biomarker approach [14,15]. Our estimates broadly concur with those from the InVS for the period 2004–2007, with the exception of non-French-national heterosexuals. Indeed, we estimated that the number of new infections among non-French-national heterosexuals increased slightly between 2004 and 2007, whereas the InVS estimated that the number of new infections fell by 45% among non-French-national heterosexual men and by 25% among non-French-national heterosexual women [33]. For such a marked drop to have occurred, at least one of the following events must have taken place: a change in the immigration pattern, a decrease in the HIV prevalence in sub-Saharan Africa, and reduced at-risk sexual behaviors among non-French nationals living in France. None of these explanations is supported by available data [32,34,35]. These differences between the two studies may rather be due to two factors: the use of different methodologies and the fact that the method used by the InVS required data obtained with the French biomarker assay that has low sensitivity in identifying recent HIV infections in sub-Saharan Africans [36,37]. The second factor may have led the InVS to underestimate the incidence among non-French nationals. Further studies are now required to understand the reasons behind such differences and determine whether there are systematic differences in results from the two estimation approaches.

Several factors may affect the accuracy of our estimates. As the data were incomplete, they were adjusted for missing entries, under-reporting, and the reporting delay. Inaccurate adjustment of the reporting delay can have a considerable impact on very recent estimates of incidence. Therefore we did not attempt to estimate the incidence beyond 2007. The method further depends on accurate specification of the distribution of the time between infection and diagnosis, which is unknown. We succeeded in estimating the unknown parameters of this distribution as part of the back-calculation by integrating in our model individual data on the clinical status at initial diagnosis. It would not have been possible to estimate these parameters by using dates of initial diagnosis alone. In our model, times from infection to an AIDS diagnosis and from infection to an HIV diagnosis (i.e. non-AIDS diagnosis) were assumed to be independent. This assumption may be a simplification of reality; however, it has been made in previous studies [19]. Furthermore, we validated our model by comparing model predictions with observed data and found an excellent agreement. This suggests that the assumptions of our model are reasonable.


In this study, we have shown that our novel back-calculation model can be used to obtain estimates of the HIV incidence and of the time between infection and diagnosis in different exposure categories, based on HIV surveillance data that are available in most western countries. When we applied our model to French surveillance data, we found that the HIV incidence in France did not fall between 2004 and 2007, and that the time between infection and diagnosis remains excessively long. New policies to expand the offer and acceptance of voluntary HIV testing are thus urgently needed. Monitoring and evaluation of new testing policies can be performed through the use of our method.


N.J.D.A., D.C. and V.S. designed the research; N.J.D.A. and V.S. performed the research; N.J.D.A., D.C. and V.S. analyzed the data and wrote the paper. This study was done within the framework of ANRS Coordinated Action 23. The authors thank the French National Institute for Public Health Surveillance (InVS), and especially Françoise Cazein, for providing data on newly diagnosed cases of HIV infection in France. V.S. thanks Romulus Breban for very fruitful discussions. V.S. is grateful for the financial support of the Sidaction, in the form of a postdoctoral research fellowship. N.J.D.A. is grateful for financial support from the French Ministry of Education, Research and Technology, in the form of a MENRT PhD fellowship. The authors thank both reviewers for their constructive comments and suggestions.

Conflicts of interest

There are no conflicts of interest.


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AIDS; epidemiology; France; incidence of HIV; mathematical model; surveillance; testing policy; time between HIV infection and diagnosis

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