The HIV viral load set point has long been used as a predictor of disease progression1–4 and more recently as a parameter of HIV vaccine efficacy.5 The definition of viral load set point, however, is more variable. During the early phase of primary HIV-1 infection, the plasma viral load increases sharply by several orders of magnitude to a peak in the first few weeks postinfection, then drops rapidly within months to a relatively stable level, which has been called the viral load set point.3 The HIV-infected individuals who have a higher viral load set point have a faster progression to AIDS and death.3,6–8 However, most data on the timing and clinical relevance of HIV-1 viral load set points have come from studies in North America, Europe, and Africa.9–15 To date, no longitudinal studies have been performed to examine the viral load set point in acute HIV-1 infected Chinese, who have a different genetic background from those of other races. In addition, there is no consensus on the time at which the set point is reached due to modest numbers of subjects with well-defined dates of acquisition of infection or seroconversion, limited frequency of sampling in most acute infection cohorts, and more recently the use of early antiretroviral therapy after infection acquisition, which precludes the determination of the natural evolution to set point. In one study, plasma viral load set point was loosely defined as the viral load measured between 4 and 24 months after HIV-1 infection.1,3,16 Alternatively, it was estimated using a method that calculates the average of all measurements taken after 4 months since the onset of infection and with the assumption that all these observations were in the steady state.3,17 However, neither of the 2 methods can estimate the exact time at which the viral load set point is attained.
In this study, we collected longitudinal clinical and laboratory data from patients with acute HIV-1 infection and then used regression models to estimate the viral load set point values and the exact time at which set point was attained. Our data showed that time to viral load set point after the onset of infection was variable but earlier than reported in other studies. This study also provides unique information for therapeutic and vaccine clinical trials to be conducted in Chinese patients.
This study used subjects from an ongoing prospective clinical cohort study of primary HIV-1-infected individuals in Beijing (Wu et al, unpublished data). Starting in October 2006, men who have sex with men were enrolled into a longitudinal prospective cohort study if they were at least 18 years old and HIV-negative at baseline. After enrollment, these HIV-negative men were monitored every 2 months for plasma HIV antibodies, HIV RNA levels, and clinical signs of acute infection. The subjects for whom the HIV antibody status was negative or indeterminate but positive by nucleic acid amplification testing were defined as having acute HIV-1 infection.12 Whole-blood specimens were collected at weeks 1, 2, 4, 8, and 12, and then every 3 months thereafter from detection of seroconversion and used to separate plasma, serum, and peripheral blood mononuclear cells. None of the subjects were treated by antiretroviral therapy during acute HIV infection. The study was approved by the Beijing YouAn Hospital Research Ethics Committee, and written informed consent was obtained from each subject.
The subjects with <4 available samples within the first 4 months after the estimated date of HIV-1 infection were excluded. No HIV-1 RNA viral load determination after the initiation of therapy was included in the analysis. Overall, 87 individuals were diagnosed with Primary HIV Infection, who were estimated to have been infected in the midpoint between the last seronegative and the first seropositive. According to the estimated date of acquisition of HIV infection, they were divided into 3 groups: (1) 17 with an enzyme-linked immunosorbent assay, which was negative but HIV RNA positive, and who were estimated with HIV-1 infection that occurred 17 days before the first sample was found to be positive for HIV RNA in these patients based on a published algorithm9; (2) 25 with an indeterminate western blot, who were estimated to have been infected 30 days before the index or enrollment specimen; and (3) 45 with a negative finding for HIV-1 antibody and also negative result for HIV-1 RNA followed by a seropositive and RNA positive with a time between tests <2 months. The study population had an average age of 33.2 (SD: 9.5) years at enrollment, a median of 7 (range, 4–14) sequential viral load measurements, and a median follow-up length of 283 days (range, 80–698 days).
Standard HIV type 1 (HIV-1) enzyme-linked immunosorbent assay (Abbott recombinant HIV-1/2 third generation, Vironostika HIV Uni-Form II plus O; Abbott, Chicago, IL) and western blot analysis (Genelabs, Redwood City, CA; HIV Blot2.2, AE2029) kits were used for antibody tests. Plasma HIV-1 RNA copies were measured by a quantitative reverse transcriptase–polymerase chain reaction HIV-1 RNA test (Roche Cobas Amplicor HIV-1 monitor test). Samples that tested RNA-positive with HIV-1 copy numbers below the limit of quantitation (400 copies per milliliter) were assigned a value of 200 copies per milliliter for statistical purposes.
Regression Models for Estimating the Viral Set Point
Suppose there are m untreated HIV-infected patients, each with n i viral load measurements with i = 1, …, m. Let V ij and t ij denote the logarithm (base 10) of the viral load and the days since infection for the jth examination of the ith patient (i = 1, …, m and j = 1 ,…, n i), respectively.
be the estimated time to steady state postinfection for the ith patient and the estimated viral load at that time, namely, the viral set point, respectively. Let
be the estimated peak value of the viral load and the time to viral load peak for the ith patient, respectively. Let
be the estimated lowest viral load (i.e. the viral load nadir) before day
postinfection and the time to the viral load nadir for the ith patient, respectively.
Viral Load Kinetic Patterns
A linear segmented regression of viral load from the time since infection was fitted for each individual, to obtain estimates of the parameters (
), and (
) described above for the ith patient.
We modeled the dynamic changes of viral load using a mathematical equation that has as many as 4 terms. The first term describes a linear increase to the viral load peak. The second term describes a linear decline of viral load from the peak to a nadir concentration. The third term describes a subsequent slight linear increase of viral load to the set point. The last term corresponds to the steady phase of the change of viral load, during which the viral load approaches a stable value. For this last term, a constant viral load was used. In clinical practice, however, ≥1 parts of this idealized viral load pattern may not be observed in some patients. Thus, we eliminated terms corresponding to missing parts of the pattern. All the possible viral load kinetic patterns in our observations are illustrated in Figure 1.
Using the above terms, assumptions, and notations, we obtained the following 6 equations:
where β1 < 0 and β2 and β0 > 0 in these models were the rates of the decline and the increment of viral load, respectively. The β3 was the change in the rate of the viral load in the steady period. In general, individuals with viral load decline or increment of <0.5 log10 copies per milliliter in 6 months were defined as having achieved a steady state. Thus, if the absolute value of β3 was <0.0027 log10 copies per milliliter per day (i.e. 1 log10 copies per milliliter per year), the viral loads were defined as achieving the steady state and the viral set point could then be obtained. Otherwise, the individual was defined as having experienced failure to reach a steady state, and no viral set point could be estimated.
Models (1)–(6) represent the kinetic patterns 1–6 shown in Figures 1A–F, respectively. After we obtained estimates of all the parameters that appeared in 1 of the 6 models by fitting the model to the data for the ith patient using least squares regression, estimates of the viral load peak
could be obtained by substituting
for t ij in the corresponding model, respectively. To estimate the parameter
was calculated as the average of all the observed viral loads after time
. In model (6), the time to steady state, that is,
, could not be estimated due to the lack of significant change of all the observed viral loads.
Empirical Method of Viral Set Point Calculation
Another goal of this study was to compare mathematical regression models with the empirical method to measure the value of the viral load set point. We also calculated the set point as the average of all measurements taken at 4 months after infection according to the empirical model.4
All values were given as mean ± SD in log10 units. The paired samples t-test was used to test for the difference in viral set points estimated by the 2 methods. P < 0.05 (2-sided) was considered statistically significant.
To examine the absolute agreement between the viral load estimated by using the proposed viral load kinetic models and those estimated by the empirical method, the Lin concordance correlation coefficient (CCC)18 was calculated and the location shift and scale shift of the CCC. Visual assessment of agreement was obtained by the use of Bland–Altman plots.19,20
Statistical analyses were performed with SPSS for Windows version 15.0 (SPSS, Chicago, IL) and GraphPad Prism version 5.01 for Windows (GraphPad Software, San Diego, CA). The fitness of the viral load kinetic models and the estimation of parameters were done with MATLAB version 7.6 (MathWorks, Natick, MA).
Application of the Proposed Models
One of the 6 models discussed in the Materials and Methods section was used to estimate viral loads in all 87 enrolled patients (Fig. 1). Eighteen patients had either an increase or a decrease in viral load for >0.0027 log10 copies per milliliter per day, meaning that their viral load failed to reach a steady state. Another example of failure to reach a steady state was that viral load fluctuated beyond ±0.5 log10 copies per milliliter around the estimated levels of the steady state of viral loads for at least 3 times in a period of at least 3 months. Nine patients experienced this type of fluctuation, and their viral load set points were not estimated. All these 27 patients failed to reach the steady state, resulting in being unable to estimate their viral load set points (2 representative longitudinal viral load measurements in patients who failed to reach the steady state are shown in Fig. 2).
Among the 60 remaining patients, 22 patients, grouped into group 1, had already reached the steady state at the first measurement postinfection (as shown in Fig. 1F). Therefore, the time to steady state could not be estimated due to a lack of significant changes of all the observed viral loads for these patients. Then, the rest of the 38 patients whose viral load set point could be estimated were grouped into group 2.
The results of the 3 kinds of outcome, that is, being able to estimate both the viral load set point and the time to reach the set point, being able to estimate only the viral load set point, and failing to reach the steady state, are listed in Table 1.
Estimate of Viral Load Set Points and the Time to Reach Them
For the 60 patients who had achieved steady state, viral load set points were estimated as 4.28 ± 0.86 log10 copies per milliliter (range, 2.16–5.72 log10 copies per milliliter) by using our kinetic models. Viral load set points were estimated in the range of 2.73–5.55 log10 copies per milliliter (mean ± SD: 4.42 ± 0.80 log10 copies per milliliter) and 2.16–5.72 log10 copies per milliliter (mean ± SD: 4.19 ± 0.89 log10 copies per milliliter) for patients in group 1 (n = 22) and group 2 (n = 38), respectively. Sixty individuals were divided into 3 classes with differential progression by using our kinetic models. They are 18(30%), 29(48%), and 13(22%) who have a viral load set point of <10,000; 10,000–100,000; and >100,000 copies per milliliter, respectively. Times to achieve the viral load set point for group 1 patients were not calculated because their viral load had already reached the steady state at the first measurement postinfection. Times to viral load set point after infection for the 38 patients in group 2 were estimated in the range of 21–119 days (mean ± SD: 63.8 ± 27.1 days; Fig. 3). For the 38 patients in group 2 whose time to viral load set point could be estimated, 7.9% [3/38, 95% confidence interval (CI): 2.7% to 20.8%], 50.0% (19/38, 95% CI: 34.9% to 65.1%), 18.4% (7/38, 95% CI: 9.2% to 33.4%), and 23.7% (9/38, 95% CI: 13.0% to 39.2%) of them reached viral load steady state within 30, 31–60, 61–90, and after 90 days, respectively. In other words, a patient had a 50% probability of reaching viral load set point between 31 and 60 days and had a 76.3% probability of reaching viral load set point within 90 days.
Agreement Between Viral Load Set Points Estimated by Two Different Methods
To validate our new method, we compared its estimates with those of a published method.4 For the 60 patients who had achieved the steady state, their viral load set points were estimated as 4.28 ± 0.86 log10 copies per milliliter (range, 2.16–5.72 log10 copies per milliliter) by using our kinetic models, compared with 4.25 ± 0.87 log10 copies per milliliter (range, 2.16–5.82 log10 copies per milliliter) by the empirical method published by others.4 Table 2 presents the absolute agreement assessment between our new model and the empirical method by addressing means and scale and location components of the CCC for each group. The bias correction factors for groups 1 and 2 and total were all very close to 1, meaning that the best-fit lines deviated very little from the perfect fit 45 degree line (measurement of accuracy; Fig. 4A).
The Bland–Altman plots that assess agreement between our new model and the empirical method are shown in Figure 4B. About 90.9% (20/22), 92.1% (35/38), and 93.3% (56/60) of the differences between each pair of estimated viral load set points lay within the 95% limits of agreement for group 1, group 2, and total, respectively. No significant systematic bias was observed, that is, the average differences between paired viral load set points were all close to zero.
Our study described a novel model to estimate viral load set point in patients with acute HIV infection. It is generally acknowledged that the viral load set point is one of the key predictors for disease progression and prognosis of HIV-1 infection.12,21–23 The concept has more recently been applied to gauge the efficacy of preventative HIV vaccine by comparing early postinfection set points in cases of breakthrough infections in vaccines with set points in infected persons in the control arm of the studies.24 Therefore, the precise determination of the set point is important for the field. The current approach for estimating the viral load set point is to measure a series of viral loads at 4 months and later after the initial detection of infection, and then calculate their average level, which is defined as the set point. This is acceptable because frequently the set point is reached after 4 months of HIV infection.3,5,17,25 However, this method can only be used to obtain the viral load set point level after the acute phase of HIV infection, which is an important window for viral reservoir formation and rapidity of HIV transmission. To date, there is no model available to estimate time to development of set points or predict distributions of VLs within the acute phase of HIV infection.
In this study, we presented a novel set of mathematical models to predict viral load set point early during the acute phase of HIV infection. There are a number of strengths of our data and models. First, to generate this model, we used a large series of viral load measurements that were collected as early as week 1 after acute infection when patients were still HIV antibody negative, but RNA positive. For each subject, all the viral load measurements were put into ≥1 mathematic models to estimate the viral load set point and the time to reach that set point. Second, for the subjects who were already in the steady state at the time of the first test, the average of all the viral load measurements was considered as the set point, but the time to set point could not be estimated due to the lack of significant change of all the observed viral loads. Third, for those who had not reached the steady state at the first measurement but finally reached that state, viral load kinetics was used to estimate the set point and the time to reach it, and the peak and nadir of the viral load if present. Another advantage of our method is that the set point was estimated based on all observed viral loads. Thus, our approach is more systematic than the currently used empirical method that only uses the viral loads at 4 months and later after the onset of infection to estimate the viral load set point.3,5,17
To evaluate the validity of our new method, we compared results derived from our models and those that were obtained using the empirical method in our patient cohort. By using our method and that of Fellay et al,4 viral load set points were calculated to be 4.28 ± 0.86 and 4.25 ± 0.87 log10 copies per milliliter (P = 0.08), respectively. Consistency between the 2 methods was further tested by CCC measurement, which showed >95% in agreement. Additional tests with CCC on means, scales, and location components of each group showed a bias correction factor very close to 1, which also indicates an excellent agreement between the 2 methods. Moreover, we used Bland–Altman plots to compare these 2 sets of viral load set points further, and again the results showed no significant systematic bias. Finally, viral load set points were estimated to be at 4.42 ± 0.80 and 4.19 ± 0.89 log10 copies per milliliter for subjects who were already in a steady state in the first test (group 1), and who had not reached a steady state during the first test (group 2), respectively. Both numbers are comparable with the results by using different methods reported in previous studies.19,22,26 These results demonstrate that our novel method is as accurate and reliable as the existing methods.
Our new method has an additional advantage of being able to estimate the time to reach viral load set point after infection in each individual, whereas empirical methods3,5,17 can only analyze a group of individuals. Furthermore, our method eliminates the influence of patient’s failure to adhere to the scheduled follow-up visits during which critical viral load measurements are obtained to estimate the viral load set point. Lastly, the time to reach viral load set point was estimated to be between 21 and 119 days (63.8 ± 27.1 days) in this study, which was earlier than the commonly accepted 120 days in primarily white patient cohort.6,27–29 However, whether these results are attributable to different modeling methods or a reflection of different patient populations remains to be studied.
There are limitations to this study. The results were obtained from a relatively limited number of cases. Therefore, our models could benefit from additional verification in a larger prospective study of acute HIV-1 infection. Despite a lack of perfection, it would be interesting to apply our newly developed models to HIV vaccine study or therapeutic clinical trials.
In summary, we have demonstrated a novel approach to estimate viral load set point at the very early stage of HIV infection. Application of this method may help physicians to gain an insight into early intervention strategies that prevent viral reservoir formation and viral transmission in acutely HIV-infected patients. Its application may also help scientists to more rationally design end-point measures for HIV vaccine trials.
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Keywords:© 2012 Lippincott Williams & Wilkins, Inc.
HIV-1; viral load; set point; acute infection; seroconversion