Episodes of transient viremia, or “viral blips”—their nature, their causes, and their clinical consequences—have been a topic of concern for clinicians and HIV patients alike. A number of hypotheses have been proposed to explain such phenomena: assay variations,1 random statistical and biological variations around mean viral loads,2 opportunistic infections,3 activation of target cells with different drug sensitivities,4 activation of latently infected cells,4,5 therapy change or noncompliance,6–8 drug resistance,9,10 and transient release of virus from tissue reservoirs.
Mathematical models have contributed much to our understanding of HIV persistence and viral blips (for a review, see Rong and Perelson11). Using a model described in a recent article,12 we previously addressed the hypothesis that superinfection with heterologous HIV strains might be one of the many possible reasons for viral blips, and we found that superinfection of a heterologous strain is unlikely to be considered as a reason for viral blips among patients under combinational antiretroviral therapy (cART).
We believe that one contributing factor to the diverse outcomes of the various studies on viral blips is that there has been no consensus on the definition of viral blips and the choice of sampling frame to detect them (Table 1). This has made comparison across studies difficult as we may not be comparing like with like.
Viral Blip Definitions in Different Studies
Table 1 lists a number of articles that have studied viral blips (for more details, see Table A1, Supplemental Digital Content 1, https://links.lww.com/QAI/A262). A definition of viral blips is influenced by the following:
- the lower limit of HIV RNA detection offered by the assay above which a viral blip is detected: most studies used 50 copies per milliliter as the cutoff point, but there were other values used;
- whether there was an upper viral load limit: some studies considered any measurements above a certain threshold (eg, 500 or 1000 copies/mL) as an indication of treatment failure and therefore a “blip” must be something below that threshold, whereas other studies might not have any upper viral load limit for a blip;
- any requirement for preceding and/or subsequent measurements that were below the detectable level: some studies made explicit such a requirement, for example, preceded by 2 consecutive measurements that were <50 copies per milliliter and followed by the one that was <50 copies per milliliter;
- whether consecutive measurements above the detection threshold count as blips or treatment failure, for example, Podsadecki et al8 defined 2 consecutive measurements that were ≥50 copies per milliliter as “treatment failure.”
The variety of definitions of viral blips makes comparison of their prevalence or incidence across studies difficult. Later, we will discuss how definitions affect the number of viral blips identified in a study.
Choices of Sampling Frame in Different Studies
Table 1 also lists the frequency of measurement used in these studies. Most studies, especially those among routine clinical cohorts, had a sampling frame of around every 3 months (or 12 weeks). Some studies using data from clinical trials had a sampling frame of unevenly spaced measurements over a matter of weeks. The only exception is Nettles et al,2 in which measurements were taken every 2 or 3 days. We argue that what is detected in Nettles et al2 needs to be treated as a separate category (random statistical and biological variations around mean viral loads) and the viral blips in Nettles et al2 should not be compared with those of other studies (that might be the results of other factors).
The difficulty in defining a “true” viral blip coincides with the problem of the choice of sampling frame. As will be demonstrated later in this article, both the definition of viral blips and the measurement sampling frame are of great importance in determining the number and frequency of viral blips observed in a cohort of patients. In a clinical setting, where a clinic visit is usually scheduled every 3 or 4 months, consecutive viral load measurements above the detection threshold, after achieving viral suppression, is often considered as an indication of treatment failure. However, as has been demonstrated,24 a transient episode of viremia usually lasts for 3 weeks and 2 consecutive detectable viral load measurements could well be 2 viral blips. Nevertheless, as will be shown, our simulation results are consistent with the hypothesis that poor drug compliance correlates with a high number of positive detectable viral load measurements, regardless of whether they were “true” blips or not.
In this mathematical modeling study, we shall address how nonadherence to therapy can lead to viral blips and how our definition of viral blips and our sampling frame affect our findings.
We used a coupled ordinary differential equation model of the human immune system infected with HIV, which has been described in detail elsewhere.12 The state variables of the model are the population of CD4 cells (quiescent, active, latently infected, activated infected, and virally productive), CD8 cells (quiescent and active), and cytotoxic lymphocytes (resting or active). The parameter values we used were as previously detailed,12 unless otherwise stated. In our earlier analysis, more than 1 strain of HIV was represented, here we limited the analysis to a homogeneous viral population. The level of drug affecting the viral dynamics was also varied to represent specific drug adherence patterns. A single simulation represented a patient who becomes infected and then progresses to receive treatment. To stabilize the representation of the immune system dynamics, patients were simulated for 2 years before the introduction of virus compartments at the time of infection. Then, after 8 years after infection, treatment was represented with a further 2 years before the simulations were terminated. To represent each level of adherence of a particular pattern, 100 simulations were performed. To allow for model solution, a flexible time step was used.
Drug Adherence Pattern
Three parameters were identified as important for a model of drug adherence: (1) proportion of doses taken (p), (2) SD of the random dose-timing error, and (3) any systematic dose-timing bias.25 We incorporated the first 2 of these. At the beginning of each day, a random number was drawn from a binomial distribution with a proportion of average doses taken (p) and possible outcomes of 0, 1, or 2, that is, Bin (2, p). If a number 1 or 2 was drawn, then a random number would be drawn from a normal distribution with a mean of 0.5 day and an SD of 2.5 hours (0.1042 day). The exact timing of the dose was then the random number minus 0.25 day. If the number 2 was drawn from the binomial distribution (ie, 2 doses on that day), a second random number would be drawn from the normal distribution, again N (0.5, (0.1042)2). The exact timing of the second dose was that of the first dose plus the second random number. In other words, if we follow the example of Ferguson et al25 and take 3 AM as the boundary between each 24-hour period (a day), then the timing of the 2 doses would be N (9 AM, (2½ hours)2) and N (9 PM, (2½ hours)2). One hundred simulations were performed for each proportion of average doses taken (p), which spans at an interval of 0.05, from 0 to 1 (inclusive).
We used 3 sampling frames for counting the number of events of transient viremia (for details, see Supplemental Digital Content 1,https://links.lww.com/QAI/A262): (1) Less than 1 week; (2) Monthly; (3) Quarterly (3-monthly).
Definition of Viral Blips
As shown in “Viral Blip Definitions in Different Studies,” different definitions of viral blips were used in different articles. Here we use 3 sets of definitions to investigate the impact of different definitions upon the study results.
Definition Set 1A
Less Than 1-Week Sampling Frame
An episode of transient viremia or a viral blip was defined as a continuous series of viral load measurements ≥50 copies per milliliter after suppression of viral load below detectable level and before the next measurement of undetectable viral load as observed in the time series for the patient (a definition used in Nettles et al2).
Definition Set 2A
Monthly and Quarterly Sampling Frame
Each viral load measurement of ≥50 copies per milliliter is considered to be an independent event of transient viremia (ie, an individual blip).
Definition set 2B
Monthly and Quarterly Sampling Frame
A viral load measurement of ≥50 copies per milliliter, preceded and followed by viral load measurement of <50 copies per milliliter, is defined as an independent event of transient viremia (ie, a “single” blip). If it is consecutively preceded or followed by a viral load measurement of ≥50 copies per milliliter, it is defined as a “treatment failure.”
Sampling Frame and Viral Blip Definition
We analyzed the sampling frame data of the more realistic adherence pattern to determine the effect of viral blip definition on the quantity of blips observed. As an example, Figure 1 shows that at low drug adherence levels (p), a large number of blips identified under definition set 2A will be classified as “treatment failure” in definition set 2B because they were “consecutive” measurements of ≥50 copies per milliliter. This highlights that different viral blip definitions give different results.
Although the number of blips observed in a given period of time would be different if different sampling frames are used, the proportion of observations that are blips are similar in both monthly and quarterly sampling frames, as seen in Supplemental Digital Content 1 (see Figure S2,https://links.lww.com/QAI/A262). The percentage of measurements of ≥50 copies per milliliter with a given sampling frame in a given period of time is a better indication of the extent of viral blips than incidence rate (the number of blips observed in a given period of time) without taking account of sampling frame (see Supplemental Digital Content 1,https://links.lww.com/QAI/A262).
Prediction of Drug Adherence from Observed Viral Blips
We next ask the question: Can we infer a patient's drug adherence level from the number of observed viral blips? Figure 2 shows the relationship between the percentage of observations with ≥50 copies per milliliter against drug adherence, from the results of 2100 simulated patients (100 simulations per drug adherence level, p = 0, 0.05, 0.1 … 1) in the presence of cART (reverse transcriptase inhibitors and protease inhibitors) for 2 years. Variations are not very big as shown by the interquartile ranges. It shows that if >10% of observations made are of ≥50 copies per milliliter, it is likely that the drug adherence of the patient is <0.5; if the percentage of observations ≥50 copies per milliliter is very low (<5%), possible drug adherence ranges from 0.4 to 0.9.
Sensitivity Analysis and Comparison With the ATHENA Cohort
We found that the relationship between viral blips and drug adherence in the simulations was most sensitive to changes in the average infection rate of an activated CD4 T cell per virion (β) and parameters that influence the CD4 cell activation process. Figure 3 shows that with an increase in β, the same percentage of viral load observations being ≥50 copies per milliliter indicates a higher drug adherence level, whereas with a decrease in β, it indicates a lower drug adherence level. As seen in the Supplemental Digital Content (https://links.lww.com/QAI/A262), the model is insensitive to a change in value of the majority of parameter values within a biological plausible range. Of all the 36,940 RNA measurements among patients with suppression of viral load after commencement of cART in the AIDS Therapy Evaluation in the Netherlands (ATHENA) cohort of the Netherlands, 8% were >50 copies per milliliter.23 This roughly corresponds to what we found in our simulations at drug adherence around 0.4 (Fig. 1). The inference that the “average adherence” in the ATHENA cohort could be around 40% should be interpreted with great caution (as discussed below). The full results of the sensitivity analysis of the model parameters and a comparison with the ATHENA cohort can be found in the Supplemental Digital Content (https://links.lww.com/QAI/A262).
In this article, we investigated the impact of different sampling frames and definitions of viral blips in the detection of these blips because of the nonadherence to cART through a mathematical model. We highlighted the problem of the use of a variety of definitions of viral blips and choices of sampling frame rendering comparison across published studies difficult.
The model showed that by using different sampling frames, a different number of blips will be observed. We chose 3 sampling frames: <1 week, monthly, and quarterly. Our model records results every 100 time steps (ie, once every 2–7 days). Therefore, data from this sampling frame are the most detailed data for each patient that we were able to generate and they formed the standard against which we understood the outputs of the other 2 sampling frames. The <1 week sampling frame is similar to that used in Nettles et al.2
Ten patients were analyzed intensively in Nettles et al,2 which is the only study with a very frequent sampling frame (every 2–3 days). In their study, 78% of 18 blips observed in 10 patients in less than 8 months occurred when drug levels were above the trough concentrations provided by drug manufacturers and therefore there was no association between low drug concentrations and blips (P = 0.22, χ2 test). Our model specifically tested the situation with the hypothesis that nonadherence to antiretroviral treatment leads to viral blips. It does not exclude other potential causes of viral blips. Nettles et al2 argued that viral blips were just random variations around an undetectable mean viral load. Given its small sample size (713 measurements in 359 observations in 10 patients), it is possible that the blips they observed were of a different category to those of other studies that argued for the clinical significance of blips.24,26–28 As our simulations incorporated both the element of stochasticity and various levels of drug adherence, it is possible to exclude random variation as an explanation for the different outcomes observed in simulations of different levels of drug adherence.
The other 2 sampling frames—monthly and quarterly—were used by most other studies, although studies using clinical trial data usually had more frequent sampling at the beginning of the trial and less frequent as the trial went on (Table 1). In both cases, but especially so in the case of a monthly sampling frame, the a priori definition of blips determines whether consecutive measurements ≥50 copies per milliliter are considered as independent viral blips, treatment failure8 or “bumps,”14 and therefore would significantly affect the incidence of blips that a study reports. As seen in Supplemental Digital Content 1 (Figure S2, https://links.lww.com/QAI/A262), the proportion of observations that are blips are similar in both sampling frames. Therefore, this measure removes the bias introduced by the choice of sampling frame.
By analyzing the results of our “more realistic” model, incorporating variations in the timing of dose taking, we suggested that a relationship possibly existed between drug adherence and viral blips. On the one hand, if very few viral blips are observed (eg, <5% of measurements ≥50 copies/mL in Fig. 2), it does not imply that a good drug adherence is being achieved. On the other hand, if a certain number of viral blips are observed over a period of time (eg, >10% of measurements in 2 years are ≥50 copies/mL in Fig. 2), then it is likely that the patient's compliance to antiretroviral treatment is poor, provided that other reasons of viral blips have been excluded. The alarming observation is that by observing 1 blip in 2 years in a quarterly sampling frame (akin to normal clinical practice), a median adherence level of 0.4 (reverse transcriptase inhibitors and protease inhibitors; Fig. 2) is indicated. Even if the association between viral blips and virological failure is still under debate, viral blips are very likely one of those indicators of poor adherence that signal clinicians to provide more counseling with respect to drug compliance.
The comparison between our simulation results and the ATHENA cohort data suggests a low drug adherence level among patients in the cohort. However, this has to be interpreted with caution. Given the nonlinear relationship between drug adherence and percentage of observations with more than 50 copies per milliliter, it is shown that for a given number of blips observed under a given sampling frame in a given period of time, this can be the result of a range of drug adherence levels (see Supplemental Digital Content 1,https://links.lww.com/QAI/A262). Furthermore, within-host viral evolution has not been incorporated into the model. Taking into account the likely emergence of resistant strains among patients with low drug adherence, the number of viral load measurements that are ≥50 copies per milliliter among patients with drug adherence around 0.5 is likely to be higher in reality than what was found in our simulations (Fig. 1), and the curves in Fig. 2 may shift upwards.
Limitations to this study include the fact that we did not model other potential causes for viral blips, for example, opportunistic infections,3 target cell pools of heterogeneous drug penetration,3 activation of latently infected cells,4 and asymmetric division of activated latently infected cells.29 The drug adherence patterns that we simulated might not be able to capture the variety of more complicated patterns that exist in the real world. The shift in the curve of the relationship between the percentage of viral load measurements being ≥50 copies per milliliter and drug adherence (Fig. 3) demonstrates the inherent uncertainty of the relationship between observed percentage of viral load measurements being detectable and drug adherence level because of variation in fitness between different viral strains. Given that the average infection rate of an activated CD4 T cell per virion (β) for a given strain is hard to ascertain in a clinical setting, there is still more research to be done before we can apply this relationship to determine the average drug adherence level of a patient in a given period of time. Our article does not capture the many clinical decisions that clinicians would make once a viral blip is detected. It also does not investigate the impact of a change of viral load assay upon blip detection. Furthermore, variations in pharmacokinetic profiles within a particular drug class were not simulated. Nevertheless, we believe that our model captured the essence of the phenomenon of drug adherence variation and its relationship with the emergence of viral blips.
By using a mathematical model that generates viral blips with low drug adherence patterns, we highlighted the importance of the definition of viral blips and sampling frame in the existing literature on viral blip incidence and prevalence. Given such a variety of definitions and sampling frames used across the studies, it is not surprising that little consensuses have arisen regarding the nature and incidence of viral blips across HIV patient populations. We therefore suggest that we should standardize the definitions of viral blips and the choice of sampling frame, and to report the proportion of observations of a given sampling frame in a given period of time that are ≥50 copies per milliliter, so that comparable data can be generated across different populations.
The authors thank Tom Connor, Dr James Griffin, Dr T. Deirdre Hollingsworth, and Dr James Truscott for their advice on computer programming and mathematical modeling.
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