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eLife logoLink to eLife
. 2024 Apr 16;13:e89801. doi: 10.7554/eLife.89801

A retrospective cohort study of Paxlovid efficacy depending on treatment time in hospitalized COVID-19 patients

Zhanwei Du 1,2,, Lin Wang 3,, Yuan Bai 1,2,, Yunhu Liu 1, Eric HY Lau 1,2,4, Alison P Galvani 4, Robert M Krug 5, Benjamin John Cowling 1,2,, Lauren A Meyers 6,7,
Editors: James M McCaw8, Diane M Harper9
PMCID: PMC11078542  PMID: 38622989

Abstract

Paxlovid, a SARS-CoV-2 antiviral, not only prevents severe illness but also curtails viral shedding, lowering transmission risks from treated patients. By fitting a mathematical model of within-host Omicron viral dynamics to electronic health records data from 208 hospitalized patients in Hong Kong, we estimate that Paxlovid can inhibit over 90% of viral replication. However, its effectiveness critically depends on the timing of treatment. If treatment is initiated three days after symptoms first appear, we estimate a 17% chance of a post-treatment viral rebound and a 12% (95% CI: 0–16%) reduction in overall infectiousness for non-rebound cases. Earlier treatment significantly elevates the risk of rebound without further reducing infectiousness, whereas starting beyond five days reduces its efficacy in curbing peak viral shedding. Among the 104 patients who received Paxlovid, 62% began treatment within an optimal three-to-five-day day window after symptoms appeared. Our findings indicate that broader global access to Paxlovid, coupled with appropriately timed treatment, can mitigate the severity and transmission of SARS-Cov-2.

Research organism: Viruses

Introduction

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) first appeared in Wuhan, China in late 2019 and quickly expanded into a global pandemic (Wan, 2020). As of March 2023, the COVID-19 pandemic has caused over 605 million reported infections, 6.8 million deaths, and substantial socioeconomic damage worldwide (Mathieu et al., 2020). Throughout the pandemic, vaccines (Basta et al., 2020) and a variety of non-pharmaceutical interventions have been widely used to mitigate transmission and avert severe clinical outcomes (Lai et al., 2020). However, the premature relaxation of restrictions, contradictory messaging, and erosion of public adherence have undermined these efforts (Han et al., 2020). Numerous variants of interest (VOI) and variants of concern (VOC) (World Health Organization, 2020) have emerged, spreading more quickly than the ancestral strain (CDC, 2021) and evading vaccine-induced and infection-induced immunity (Wang et al., 2021).

The race to develop SARS-CoV-2 antiviral drugs has yielded at least 36 therapeutics (Zimmer et al., 2020). In December of 2021, the US Food and Drug Administration (FDA) issued emergency use authorization for both molnupiravir (a small-molecule ribonucleoside prodrug of N-hydroxycytidine) and Paxlovid (a combination of nirmatrelvir, an inhibitor of the SARS-CoV-2 main protease, and ritonavir, an HIV-1 protease inhibitor and CYP3A inhibitor; Zimmer et al., 2020). Clinical studies suggest that outpatient treatment of high-risk symptomatic adult patients with molnupiravir and Paxlovid within 5 days after symptom onset could reduce the hospitalization risk by 30% (US Food and Drug Administration, 2022) and 88% (US Food and Drug Administration, 2021), respectively. In May of 2022, the US launched a national Test-to-Treat program to facilitate rapid administration of these two oral antivirals through pharmacies, health clinics, and telehealth providers (The White House, 2022). In March 2022, the Hong Kong Hospital Authority (HKHA) began regularly treating COVID-19 inpatients with molnupiravir and Paxlovid (Leung et al., 2022), which substantially reduced their risks of progression to severe disease and death (Wong et al., 2022).

Drugs that suppress viral replication not only improve patient outcomes but may also reduce infectiousness to others. Such antivirals can thus be deployed on a population scale to curb pandemic waves, either as a complement to or a replacement of socioeconomically costly measures such as travel restrictions and stay-home orders. A prior study of Baloxavir, a drug that suppresses influenza replication, demonstrates that administration to 30% of infected cases within 48 hr after symptom onset would typically avert over six thousand deaths and 22 million infections in the US during a typical epidemic season (Du et al., 2020).

Clinical trial data for Paxlovid suggests that it may similarly curtail SARS-CoV-2 viral replication, if administered shortly after symptoms appear (Wong et al., 2022). Here, we estimate the impact of the timing of Paxlovid treatment on viral load, using a within-host mathematical model of Omicron replication fitted to viral titer data for cohorts of COVID-19 inpatients in Hong Kong who either did or did not receive Paxlovid treatment.

We analyzed HKHA electronic health records (EHR) for 208 SARS-CoV-2 positive patients between ages 8 and 103 who were hospitalized for mild to moderate illness between January 6 and May 1, 2022, when the Omicron BA.2 was the dominant variant in Hong Kong. The EHR data includes age, sex, vaccination history, drug prescriptions, symptoms, and daily viral titer measurements starting from the fourth day after symptom onset (Materials and methods). To construct cohorts, we first identified 104 COVID-19 mild-to-moderate patients who received Paxlovid treatment without oxygen therapy. We then used propensity score matching to select 104 patients who were not treated with Paxlovid or molnupiravir.

Results

By fitting a mathematical model of SARS-CoV-2 kinetics within a single patient to the viral load measurements, we estimate the rates at which viral particles infect susceptible host cells (β), infected cells are cleared (δ), and infected cells release viral particles (π), as well as the maximum efficacy of Paxlovid for reducing the replication rate of SARS-CoV-2 viruses (0.91) (National Library of Medicine (U.S.), 2023; Hammond et al., 2022; Supplementary file 1, Supplementary file 2). The fitted model simulates viral load trajectories that mirror the observed data in the treated and untreated cohorts (Figure 1A and B, Figure 1—figure supplement 1).

Figure 1. Estimated efficacy of Paxlovid for suppressing SARS-CoV-2 viral load depending on timing of treatment.

Observed and model estimated viral load kinetics for each day post onset of symptoms (DPOS) for hospitalized COVID-19 patients who (A) received Paxlovid treatment (N=104) or (B) did not receive antiviral treatment (N=104) between 6 January and 1 May 2022 in Hong Kong. Blue points correspond to actual individual patients; red squares and error bars indicate medians and 95% interpercentile ranges across simulated patients. Day zero corresponds to the first day of symptoms. (C) Distribution of treatment initiation times for the 104 patients who received Paxlovid (Supplementary file 4). (D) Estimated patient viral loads for three different Paxlovid treatment initiation times. Points and shading represent the estimated medians and 95% interpercentile ranges across 1000 simulations. (E) Chance of a post-treatment rebound (gray line, right y-axis) and expected reduction in infectiousness across all patients (blue bars, left y-axis) and patients who do not experience a rebound (black bars, left y-axis), depending on the timing of treatment initiation. Rebound probabilities are estimated by the fraction out of 1000 simulations in which the viral titer reached higher values after treatment than before treatment. Reduced infectiousness is estimated by comparing the areas under the estimated infectiousness curves for untreated versus treated patients. Bars and whiskers indicate medians and 95% interpercentile ranges across 1000 pairwise comparisons.

Figure 1.

Figure 1—figure supplement 1. Comparison of individual COVID-19 patient viral titer data to model estimates.

Figure 1—figure supplement 1.

Each graph corresponds to measurements for hospitalized COVID-19 patients who either (A) received Paxlovid treatment (N=104) or (B) did not receive any antiviral drug (N=104) between 6 January and 1 May 2022 in Hong Kong (blue points). Red lines show estimates from the fitted model for each individual. Day zero indicates the first day of infection.

Of the 104 patients who received Paxlovid, 63% initiated treatment within five days post the onset of symptoms (DPOS) (Figure 1C). As we vary the treatment initiation time from one to nine DPOS, the model projects precipitous drops in viral load within the first 24 hr of receiving Paxlovid (Figure 1D). If treatment is initiated the day after symptoms appear, we estimate a 74% chance that viral growth will rebound substantially post treatment (Figure 1E, Supplementary file 3), peaking around 10 DPOS. For more delayed treatment schedules, the probability and magnitude of rebounds are lower. Patients who initiate treatment three or five DPOS have an estimated 17% or 1% chance of a rebound, respectively. The estimated overall reduction in infectiousness for patients who do not experience rebounds declines from 12% (95% CI: 0%, 16%) for patients who start treatment three DPOS to 0% (95% CI: 0%, 9%) for patients starting treatment 10 DPOS (Figure 1E, Supplementary file 3).

Discussion

Using a within-host model of viral kinetics, we estimated the efficacy of Paxlovid for reducing SARS-CoV-2 viral load for mild-to-moderate COVID-19 patients during the early 2022 Omicron wave in Hong Kong. Rapid reductions in viral load may not only benefit the patient, but also indirectly protect household members and others who come in contact with them. Recent studies suggest a logit-linear relationship between viral load and infectiousness (Marc et al., 2021). Thus broad and rapid administration of Paxlovid, to even mild and moderate cases, may be a logistically and economically viable strategy for slowing transmission on a community scale in comparison with socioeconomically burdensome social distancing measures. To this end, the U.S. Test-to-Treat program is designed so that 90% of Americans can access antivirals within five miles of their residence (The White House, 2022). However, uptake in the US has been relatively low, with only 11% COVID-19 cases receiving antiviral prescriptions between May and early July of 2022 (Kulke, 2024). The low uptake may stem from slow rollouts in some areas, complex eligibility requirements, testing, and potential drug interactions (Erman, 2022), as well as concerns about viral rebounds following Paxlovid treatment (Callaway, 2022), which our model reproduces when we assume that antiviral efficacy declines after the 5-day course of treatment (Figure 1D).

Access to Paxlovid may be even more vital in Hong Kong, which suffered the world’s highest death rate during the March and April 2022 Omicron wave. At the time, only 51% of individuals over age 80 and 76% older of individuals between 70 and 80 years had received at least one dose of vaccine (Mathieu et al., 2020). Although Paxlovid is known to be life-saving, under 40% of infected COVID-19 cases in Hong Kong over age 60 have received the drug by late July 2022 (Liu, 2022). Low rates of antiviral uptake may stem from misinformation, lack of access, and the rising proportion of cases that opt for at-home rapid tests and do not seek healthcare (Cheung et al., 2022; Kasakove, 2021). Telemedicine and online healthcare services can accelerate and expand access to antivirals (Centers for Disease Control and Prevention, 2024), but may not reach some of the older populations in Hong Kong.

Our parameter estimates for the Omicron variant are generally comparable to prior estimates based on viral titers measured in patients infected with the ancestor strain in 2020 (Ke et al., 2021). However, our estimate for the effect of innate immunity at suppressing viral replication rate is significantly lower than the prior estimate, which is consistent with a recent study suggesting that Omicron variants may be more immune evasive than ancestral variants (Willett et al., 2022). As further validation of our estimates, we compare projections of the fitted model with observed viral titers from 208 patients (Figure 1—figure supplement 1) and demonstrate that model can reproduce the rebounds experienced by some COVID-19 patients following Paxlovid treatment, under the assumption that Paxlovid efficacy begins to decline after the fifth day of treatment (Figure 1D). Our model of SARS-CoV-2 viral load dynamics following Paxlovid treatment allows us to estimate the potential benefits of early treatment for reducing infectiousness, while accounting for variation across patients and potential rebounds in viral growth. The model projections corroborate prior estimates for the impact of treatment initiation time on the duration of viral shedding (Wang et al., 2023).

Our analysis is limited by several model assumptions. First, we do not consider possible variation in viral measurements by specimen types (e.g., the deep throat saliva, sputum, throat swab, nasal swab, combined nasal and throat swab, nasopharyngeal swab Centre for Health Protection, 2021), which are not provided in the data analyzed. Second, we do not stratify our estimates by patient age group, risk group, or vaccination status, which could impact both intrinsic viral kinetics and drug efficacy (Puhach et al., 2022). Third, we do not consider the possible emergence of Paxlovid-resistant viruses, which could significantly reduce drug efficacy. Laboratory studies have identified amino acid substitutions (Jochmans et al., 2022; Zhou et al., 2022) that could confer resistance. Although such variants have not yet been found in clinical trials, broad use of Paxlovid could spur the emergence of drug-resistance, as has been documented for the SARS-CoV-2 antiviral Remdesivir (Gandhi et al., 2022).

In conclusion, fast-acting antiviral drugs like Paxlovid have the potential to reduce SARS-CoV-2 transmission while improving patient outcomes. The development of global distribution programs that provide rapid and equitable access could enhance our ability to combat COVID-19 as the virus and the landscape of immunity continue to evolve.

Materials and methods

Data

We analyzed electronic health records of hospitalized Hong Kong Hospital Authority patients between 8 and 103 years of age who were COVID-19 positive but did not receive oxygen therapy, between January 6, 2022 and May 1, 2022 (Figure 2). COVID-19 status was determined by a transcription-polymerase chain reaction (RT-qPCR) test or a rapid antigen test. Each patient record includes demographic information, drug administration data, symptoms, laboratory test results, and daily viral titer measurements (i.e. RT-qPCR cycle threshold (Ct) values) between 8 and 15 days post symptom onset. We convert Ct values to viral load as given by log10(Viral load [copies/mL])=–0.32 Ct+14.11 (Jeong et al., 2021; Peiris et al., 2003).

Figure 2. Demographic and virologic characteristics of the 208 hospitalized COVID-19 patients in the study.

Figure 2.

The distribution of (A) ages and (B) daily viral titers across the 104 hospitalized COVID-19 patients who received Paxlovid treatment (red) and the 104 patients who did not receive any antiviral drug (red) between January 6 and May 1, 2022 in Hong Kong. The box plots in panel B indicate the median, interquartile range, and range of the observed viral titers across patients for each day after symptom onset (DPOS). Day zero corresponds to the first day that symptoms occur.

To select cohorts of patients with mild-to-moderate illness, we classify patients according to their daily reported clinical conditions as follows: (1) critical: in intensive care unit, intubated, in shock, or require extracorporeal membrane oxygenation; (2) serious: require oxygen supplement of 3 L or more per minute; (3) stable: mild influenza-like illness symptoms; (4) satisfactory: progressing well and likely to be discharged soon. We select only patients who maintain stable or satisfactory levels throughout their hospital stay.

Cohort selection

After identifying 104 patients who received Paxlovid but not oxygen therapy in the data set, we used propensity score matching to create a cohort of 104 other patients who received neither an antiviral drug (Paxlovid or molnupiravir) nor oxygen therapy. We matched based on age group (5~17, 18~50, 51~65, >65), gender, and vaccination status (i.e. fully vaccinated or not).

Within-host model of SARS-CoV-2 viral kinetics and antiviral treatment

Within a given host i, susceptible cells (Ui) can be infected by active viruses Vi at a rate β and thereby transition to cells in the eclipse phase (Ei) and infected cells (Ii), according to the following system of equations by including a prototypical innate response (e.g. type-I interferon) (Ke et al., 2021) that makes cells refractory to viral infection (Ri):

dUidt=βUiViϕIiUi+ρRi
dRidt=ϕIiUiρRi
dEidt=βUiVikEi
dIidt=kEiδIi
dVidt=(1ϵt)πIicVi

where the death rate and the replication rates of infected cells are δ and π, respectively, and the viral death rate is c. The interferon-induced conversion of target cells to refractory cells has the rate Φ. And the rate at which refractory cells become target cells again is ρ. The antiviral efficacy is ϵ, which is the rate at which the drug inhibits the replication of infected cells. The initial number of infected cells (E0),the initial number of target cells (U0), the virus clearance rate c, and the rate of the eclipse phase are fixed as 1 cell, 8×107 cells, 10 per day, and 4 per day, respectively (Ke et al., 2021). We incorporate a gradual decline in Paxlovid efficacy following a five-day course of treatment, using a pharmacokinetic model introduced in a recent study of Paxlovid rebound dynamics. Our model assumes that Paxlovid efficacy (ϵt) is 0 prior to the first dose and then given by:

ϵt=ϵmaxCtCt+EC50
Ct=C^kakekaeketekaId1[1e(keka)t(1eNd,tkaId)+(ekeIdekaId)(e(Nt1)keId1ekeId1)e((Nd,t1)ke+ka)Id]

where t is the time elapsed since receiving the first dose and ϵmax is the maximum antiviral effectiveness, which we estimate by fitting the model to clinical trial data. EC50 is the concentration at which the drug effectiveness is half-maximal (62 nM) (US Food and Drug Administration, 2021); C^ is the product of the bioavailability of the drug and the mass of the drug administered in a dose per volume (6.25×103 nM) (US Food and Drug Administration, 2021; National Center for Biotechnology Information, 2024); Nd,t is the number of doses administered in the period up to time t; ke is the elimination rate (2.8 /day) (US Food and Drug Administration, 2021); ka is the absorption rate (17.5 /day) (Dixit and Perelson, 2004; Perelson et al., 2023); Id is the dosing interval (1/2 day) (Dixit and Perelson, 2004; Perelson et al., 2023).

The incubation period of the SARS-CoV-2 Omicron variant is estimated to be 3.6 days (Du et al., 2022). We calibrate parameters in the model using a nonlinear mixed-effect model with both the fixed effect (population scale) and random effect (individual scale) in software MONOLIX 2021R1 (Traynard et al., 2020). Fixed effects are population parameters that govern all patients and random effects are variable across individuals. To estimate the six model parameters governing the viral load dynamics, we fitted the within-host model to the observed SARS-Cov-2 RNA titer (log10 copies/mL) measured across 208 patients adults treated with or without Paxlovid between January 6, 2022 and May 1, 2022. We used the Stochastic Approximation Expectation-Maximization (SAEM) algorithm to estimate these parameters (Miao et al., 2011; Traynard et al., 2020) assuming fixed values for the initial numbers of infecting virions and susceptible target cells following Ke et al., 2021 and confirmed the convergence of the estimates via trace plots. The SAEM algorithm is an established method in population pharmacology modeling with clear convergence indicators (Delyon et al., 1999; Population parameter using SAEM algorithm, 2016).

Incorporating uncertainty into viral load projections

We use the within-host model to simulate the viral load trajectories of patients under various treatment scenarios. For each simulation, we randomly select parameter values from triangular distributions with modes and ranges set to the medians and 95% CI estimated from the clinical data (Supplementary file 1).

To estimate the impact of treatment time on viral load dynamics (Figure 1D) and infectiousness (Figure 1E), we compare pairs of model simulations (with versus without Paxlovid treatment). Each pair shares the same randomly-generated parameter values, including an incubation period randomly selected from a previously-estimated distribution (Triangular(2.3,3.6,4.9) days) (Du et al., 2022).

In order to translate differences in the simulated viral titers into differences in infectiousness, we used the following published model relating household transmission risk to viral load (Marc et al., 2021).

logit(Pi(t))={αiflog10(Vi(t))6α+β(log10(Vi(t))6)iflog10(Vi(t))>6

where Pi(t) denotes the probability that individual i infects a susceptible household member at time, t,α =–2.94, which corresponds to a baseline probability of transmission of 5% (Marc et al., 2021), and β = 0.49 (Marc et al., 2021). We assume that the relative infectiousness of a patient throughout their infection can be approximated by the area under the household infectivity curve from the time of infection (tr) until 15 days post the onset of symptoms (tΓ), as given by

Ωi=tγtΓPi(t)dt.

For a given pair of simulations (i), we then compare the projected infectiousness of the treated patient ip to that of the untreated patient iu, as given by

Δi=1ΩipΩiu.

For each treatment initiation time considered, we report the median and 95% confidence intervals of the reduction in infectiousness (Δ) based on 1000 pairs of simulations.

Acknowledgements

Individual patient-informed consent was not required in this study using anonymized data. Financial support was provided by the AIR@InnoHK Programme from Innovation and Technology Commission of the Government of the Hong Kong Special Administrative Region, Health and Medical Research Fund Research Fellowship Scheme, Food and Health Bureau, Government of the Hong Kong Special Administrative Region (grant no. 07210147), National Natural Science Foundation of China (grant no. 82304204), the US National Institutes of Health (grant no. R01 AI151176), the Centers for Disease Control and Prevention COVID (grant no. U01IP001136).

Funding Statement

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Contributor Information

Benjamin John Cowling, Email: bcowling@hku.hk.

Lauren A Meyers, Email: laurenmeyers@austin.utexas.edu.

James M McCaw, University of Melbourne, Australia.

Diane M Harper, University of Michigan-Ann Arbor, United States.

Funding Information

This paper was supported by the following grants:

  • Innovation and Technology Commission - Hong Kong AIR@InnoHK to Zhanwei Du.

  • Health and Medical Research Fund 07210147 to Zhanwei Du.

  • National Natural Science Foundation of China 82304204 to Yuan Bai.

  • National Institutes of Health AI151176 to Lauren A Meyers.

  • Centers for Disease Control and Prevention U01IP001136 to Lauren A Meyers.

Additional information

Competing interests

employee of Laboratory of Data Discovery for Health Limited.

No competing interests declared.

reports honoraria from AstraZeneca, Fosun Pharma, GlaxoSmithKline, Moderna, Pfizer,Sanofi Pasteur, and Roche; employee of Laboratory of Data Discovery for Health Limited; the authors report no other potential conflicts of interest.

Author contributions

Conceptualization, Formal analysis, Visualization, Writing – original draft, Methodology, Writing – review and editing.

Conceptualization, Formal analysis, Writing – original draft.

Conceptualization, Writing – original draft.

Software.

Writing – original draft.

Writing – original draft.

Writing – original draft.

Resources, Funding acquisition, Writing – original draft.

Conceptualization, Formal analysis, Funding acquisition, Writing – original draft, Writing – review and editing.

Ethics

Human subjects: Individual patient-informed consent was not required in this study using anonymized data.

Additional files

Supplementary file 1. Within-host model parameter estimates.

We used a nonlinear mixed-effects method to fit a within-host model of viral kinetics to the viral titer measurements from 208 patients, 104 were treated with Paxlovid and 104 did not receive any antiviral drugs (Traynard et al., 2020). The reported medians and variation across individuals (95% interpercentile ranges) integrate both fixed and random effects estimates for each parameter.

elife-89801-supp1.docx (7.7KB, docx)
Supplementary file 2. Population-wide parameter estimates for the within-host model.

The table provides population-wide fixed and random effects estimates for the viral dynamic parameters, whereas Supplementary file 1 provides the estimated median and variation across individuals for each parameter. The values assume that antiviral efficacy follows a logit-normal distribution and all other parameters follow log normal distributions*. Values in parentheses are relative standard errors (RSE) as a percent.

elife-89801-supp2.docx (8.3KB, docx)
Supplementary file 3. Estimated reduction in overall infectiousness and likelihood of a post-treatment rebound, depending on the timing of Paxlovid initiation in days post onset of symptoms (DPOS).

To estimate the probability of a rebound, we computed the fraction out of 1000 simulations in which the viral titer rebounded to higher values following treatment than observed prior to treatment. To estimate reduction in infectiousness, we run 1000 pairs of treatment versus no treatment simulations. Following each simulation, we calculate the total infectiousness from the time of infection until 15 DPOS using estimates relating viral titer to infectiousness provided in Marc et al., 2021. For each pair, we then compute the percent difference in total infectiousness of the treatment simulation relative to the no treatment simulation. The table reports medians and 95% CIs across all treated patients, patients who do not experience a post-treatment rebound, and patients who do.

elife-89801-supp3.docx (8.6KB, docx)
Supplementary file 4. The distribution of treatment initiation times for the 104 patients who received Paxlovid.

Day zero corresponds to the first day of symptoms.

elife-89801-supp4.docx (7.2KB, docx)
MDAR checklist

Data availability

All data used in this study can be accessed through Github: https://github.com/ZhanweiDU/PaxHK/.

The following dataset was generated:

Du Z. 2024. PaxHK. GitHub. PaxHK

References

  1. Basta NE, Moodie EMM, VIPER Group COVID19 Vaccine Tracker Team COVID-19 Vaccine Development and Approvals Tracker. 2020. [January 20, 2023]. https://covid19.trackvaccines.org/
  2. Callaway E. COVID rebound is surprisingly common - even without Paxlovid. Nature. 2022 doi: 10.1038/d41586-022-02121-z. [DOI] [PubMed] [Google Scholar]
  3. CDC SARS-CoV-2 Variant Classifications and Definitions. 2021. [May 18, 2021]. https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/variant-surveillance/variant-info.html
  4. Centers for Disease Control and Prevention New COVID-19 Test to Treat Initiative and Locator Tool. 2024. [April 6, 2022]. https://emergency.cdc.gov/newsletters/coca/040422.htm
  5. Centre for Health Protection Infection Control Advice on Specimen Collection to Test for COVID-19. 2021. [June 13, 2022]. https://www.chp.gov.hk/en/resources/346/index.html
  6. Cheung PHH, Chan CP, Jin DY. Lessons learned from the fifth wave of COVID-19 in Hong Kong in early 2022. Emerging Microbes & Infections. 2022;11:1072–1078. doi: 10.1080/22221751.2022.2060137. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Delyon B, Lavielle M, Moulines E. Convergence of a stochastic approximation version of the EM algorithm. The Annals of Statistics. 1999;27:94–128. doi: 10.1214/aos/1018031103. [DOI] [Google Scholar]
  8. Dixit NM, Perelson AS. Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracellular delay. Journal of Theoretical Biology. 2004;226:95–109. doi: 10.1016/j.jtbi.2003.09.002. [DOI] [PubMed] [Google Scholar]
  9. Du Z, Nugent C, Galvani AP, Krug RM, Meyers LA. Modeling mitigation of influenza epidemics by baloxavir. Nature Communications. 2020;11:2750. doi: 10.1038/s41467-020-16585-y. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Du Z, Liu C, Wang L, Bai Y, Lau EHY, Wu P, Cowling BJ. Shorter serial intervals and incubation periods in SARS-CoV-2 variants than the SARS-CoV-2 ancestral strain. Journal of Travel Medicine. 2022;29:taac052. doi: 10.1093/jtm/taac052. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Erman M. Analysis: Demand for Pfizer’s COVID pills lags around the world. Reuters; 2022. [Google Scholar]
  12. Gandhi S, Klein J, Robertson AJ, Peña-Hernández MA, Lin MJ, Roychoudhury P, Lu P, Fournier J, Ferguson D, Mohamed Bakhash SAK, Catherine Muenker M, Srivathsan A, Wunder EA, Kerantzas N, Wang W, Lindenbach B, Pyle A, Wilen CB, Ogbuagu O, Greninger AL, Iwasaki A, Schulz WL, Ko AI. De novo emergence of a remdesivir resistance mutation during treatment of persistent SARS-CoV-2 infection in an immunocompromised patient: a case report. Nature Communications. 2022;13:1547. doi: 10.1038/s41467-022-29104-y. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Hammond J, Leister-Tebbe H, Gardner A, Abreu P, Bao W, Wisemandle W, Baniecki M, Hendrick VM, Damle B, Simón-Campos A, Pypstra R, Rusnak JM, EPIC-HR Investigators Oral Nirmatrelvir for high-risk, nonhospitalized adults with Covid-19. The New England Journal of Medicine. 2022;386:1397–1408. doi: 10.1056/NEJMoa2118542. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Han E, Tan MMJ, Turk E, Sridhar D, Leung GM, Shibuya K, Asgari N, Oh J, García-Basteiro AL, Hanefeld J, Cook AR, Hsu LY, Teo YY, Heymann D, Clark H, McKee M, Legido-Quigley H. Lessons learnt from easing COVID-19 restrictions: an analysis of countries and regions in Asia Pacific and Europe. Lancet. 2020;396:1525–1534. doi: 10.1016/S0140-6736(20)32007-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Jeong YD, Ejima K, Kim KS, Iwanami S, Bento AI, Fujita Y, Jung IH, Aihara K, Watashi K, Miyazaki T, Wakita T, Iwami S, Ajelli M. Revisiting the guidelines for ending isolation for COVID-19 patients. eLife. 2021;10:e69340. doi: 10.7554/eLife.69340. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Jochmans D, Liu C, Donckers K, Stoycheva A, Boland S, Stevens SK, De Vita C, Vanmechelen B, Maes P, Trüeb B, Ebert N, Thiel V, De Jonghe S, Vangeel L, Bardiot D, Jekle A, Blatt LM, Beigelman L, Symons JA, Raboisson P, Chaltin P, Marchand A, Neyts J, Deval J, Vandyck K. The Substitutions L50F, E166A and L167F in SARS-CoV-2 3CLpro Are Selected by a Protease Inhibitor in Vitro and Confer Resistance to Nirmatrelvir. bioRxiv. 2022 doi: 10.1101/2022.06.07.495116. [DOI] [PMC free article] [PubMed]
  17. Kasakove S. As At-Home Tests Surge, Doubts Rise About Accuracy of Public Covid Counts – The New York Times. 2021. [January 21, 2023]. https://www.nytimes.com/2021/12/30/us/at-home-rapid-covid-tests-cases.html
  18. Ke R, Zitzmann C, Ho DD, Ribeiro RM, Perelson AS. In vivo kinetics of SARS-CoV-2 infection and its relationship with a person’s infectiousness. PNAS. 2021;118:e2111477118. doi: 10.1073/pnas.2111477118. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Kulke S. Paxlovid is vastly underused despite being widely available, study finds. 2024. [January 20, 2023]. https://news.northwestern.edu/stories/2022/08/study-finds-paxlovid-is-vastly-underused-despite-being-widely-available/
  20. Lai S, Ruktanonchai NW, Zhou L, Prosper O, Luo W, Floyd JR, Wesolowski A, Santillana M, Zhang C, Du X, Yu H, Tatem AJ. Effect of non-pharmaceutical interventions to contain COVID-19 in China. Nature. 2020;585:410–413. doi: 10.1038/s41586-020-2293-x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Leung K, Jit M, Leung GM, Wu JT. The allocation of COVID-19 vaccines and antivirals against emerging SARS-CoV-2 variants of concern in East Asia and Pacific region: A modelling study. The Lancet Regional Health. Western Pacific. 2022;21:100389. doi: 10.1016/j.lanwpc.2022.100389. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Liu O. Coronavirus: Hong Kong health experts call for doubling of antiviral distribution rate for elderly as city logs 4,276 cases. 2022. [September 5, 2022]. https://www.scmp.com/news/hong-kong/health-environment/article/3186633/coronavirus-hong-kong-health-experts-call
  23. Marc A, Kerioui M, Blanquart F, Bertrand J, Mitjà O, Corbacho-Monné M, Marks M, Guedj J. Quantifying the relationship between SARS-CoV-2 viral load and infectiousness. eLife. 2021;10:e69302. doi: 10.7554/eLife.69302. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Mathieu E, Ritchie H, Rodés-Guirao, L, Appel C, Giattino C, Hasell J, Macdonald B, Dattani S, Beltekian D, Ortiz-Ospina E, Roser M. Coronavirus Pandemic (COVID-19) – Our World in Data. 2020. [January 17, 2024]. https://ourworldindata.org/coronavirus
  25. Miao H, Xia X, Perelson AS, Wu H. On identifiability of nonlinear ode models and applications in viral dynamics. SIAM Review. Society for Industrial and Applied Mathematics. 2011;53:3–39. doi: 10.1137/090757009. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. National Center for Biotechnology Information PubChem Compound Summary for CID 155903259, Nirmatrelvir. 2024. [October 18, 2023]. https://pubchem.ncbi.nlm.nih.gov/compound/155903259
  27. National Library of Medicine (U.S.) EPIC-HR: Study of Oral PF-07321332/Ritonavir Compared With Placebo in Nonhospitalized High Risk Adults With COVID-19. 2023. [February 10, 2023]. https://clinicaltrials.gov/study/NCT04960202
  28. Peiris JSM, Chu CM, Cheng VCC, Chan KS, Hung IFN, Poon LLM, Law KI, Tang BSF, Hon TYW, Chan CS, Chan KH, Ng JSC, Zheng BJ, Ng WL, Lai RWM, Guan Y, Yuen KY, HKU/UCH SARS Study Group Clinical progression and viral load in a community outbreak of coronavirus-associated SARS pneumonia: a prospective study. Lancet. 2003;361:1767–1772. doi: 10.1016/s0140-6736(03)13412-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Perelson AS, Ribeiro RM, Phan T. An Explanation for SARS-CoV-2 Rebound after Paxlovid Treatment. medRxiv. 2023 doi: 10.1101/2023.05.30.23290747. [DOI]
  30. Population parameter using SAEM algorithm Monolix. 2016. [September 9, 2023]. https://monolix.lixoft.com/tasks/population-parameter-estimation-using-saem/
  31. Puhach O, Adea K, Hulo N, Sattonnet P, Genecand C, Iten A, Jacquérioz F, Kaiser L, Vetter P, Eckerle I, Meyer B. Infectious viral load in unvaccinated and vaccinated individuals infected with ancestral, Delta or Omicron SARS-CoV-2. Nature Medicine. 2022;28:1491–1500. doi: 10.1038/s41591-022-01816-0. [DOI] [PubMed] [Google Scholar]
  32. The White House FACT SHEET: Biden administration announces launch of first federally-supported test to treat site. The White House. 2022. [January 20, 2023]. https://www.whitehouse.gov/briefing-room/statements-releases/2022/05/26/fact-sheet-biden-administration-announces-launch-of-first-federally-supported-test-to-treat-site/
  33. Traynard P, Ayral G, Twarogowska M, Chauvin J. Efficient pharmacokinetic modeling workflow with the MonolixSuite: A case study of Remifentanil. CPT. 2020;9:198–210. doi: 10.1002/psp4.12500. [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. US Food and Drug Administration Fact sheet for healthcare providers: emergency use authorization for Paxlovid. 2021. [August 27, 2022]. https://www.fda.gov/media/155050/download
  35. US Food and Drug Administration Fact sheet for healthcare providers: emergency use authorization for Lagevrio (molnupiravir) capsules. 2022. [August 27, 2022]. https://www.fda.gov/media/155054/download
  36. Wan W. WHO declares a pandemic of coronavirus disease covid-19 – The Washington Post. 2020. [March 12, 2020]. https://www.washingtonpost.com/health/2020/03/11/who-declares-pandemic-coronavirus-disease-covid-19/
  37. Wang Z, Schmidt F, Weisblum Y, Muecksch F, Barnes CO, Finkin S, Schaefer-Babajew D, Cipolla M, Gaebler C, Lieberman JA, Oliveira TY, Yang Z, Abernathy ME, Huey-Tubman KE, Hurley A, Turroja M, West KA, Gordon K, Millard KG, Ramos V, Da Silva J, Xu J, Colbert RA, Patel R, Dizon J, Unson-O’Brien C, Shimeliovich I, Gazumyan A, Caskey M, Bjorkman PJ, Casellas R, Hatziioannou T, Bieniasz PD, Nussenzweig MC. mRNA vaccine-elicited antibodies to SARS-CoV-2 and circulating variants. Nature. 2021;592:616–622. doi: 10.1038/s41586-021-03324-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Wang Y, Zhao D, Liu X, Chen X, Xiao W, Feng L. Early administration of Paxlovid reduces the viral elimination time in patients infected with SARS-CoV-2 Omicron variants. Journal of Medical Virology. 2023;95:e28443. doi: 10.1002/jmv.28443. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. Willett BJ, Grove J, MacLean OA, Wilkie C, De Lorenzo G, Furnon W, Cantoni D, Scott S, Logan N, Ashraf S, Manali M, Szemiel A, Cowton V, Vink E, Harvey WT, Davis C, Asamaphan P, Smollett K, Tong L, Orton R, Hughes J, Holland P, Silva V, Pascall DJ, Puxty K, da Silva Filipe A, Yebra G, Shaaban S, Holden MTG, Pinto RM, Gunson R, Templeton K, Murcia PR, Patel AH, Klenerman P, Dunachie S, Haughney J, Robertson DL, Palmarini M, Ray S, Thomson EC, PITCH Consortium. COVID-19 Genomics UK (COG-UK) Consortium SARS-CoV-2 Omicron is an immune escape variant with an altered cell entry pathway. Nature Microbiology. 2022;7:1161–1179. doi: 10.1038/s41564-022-01143-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. Wong CKH, Au ICH, Lau KTK, Lau EHY, Cowling BJ, Leung GM. Real-world effectiveness of early molnupiravir or nirmatrelvir-ritonavir in hospitalised patients with COVID-19 without supplemental oxygen requirement on admission during Hong Kong’s omicron BA.2 wave: a retrospective cohort study. The Lancet. Infectious Diseases. 2022;22:1681–1693. doi: 10.1016/S1473-3099(22)00507-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  41. World Health Organization Tracking SARS-CoV-2 variants. 2020. [April 15, 2024]. https://www.who.int/en/activities/tracking-SARS-CoV-2-variants/
  42. Zhou Y, Gammeltoft KA, Ryberg LA, Pham LV, Fahnøe U, Binderup A, Hernandez CRD, Offersgaard A, Fernandez-Antunez C, Peters GHJ, Ramirez S, Bukh J, Gottwein JM. Nirmatrelvir Resistant SARS-CoV-2 Variants with High Fitness in Vitro. bioRxiv. 2022 doi: 10.1101/2022.06.06.494921. [DOI] [PMC free article] [PubMed]
  43. Zimmer C, Corum J, Kristoffersen M. Coronavirus Drug and Treatment Tracker — The New York Times. 2020. [January 21, 2023]. https://www.nytimes.com/interactive/2020/science/coronavirus-drugs-treatments.html

Editor's evaluation

James M McCaw 1

This study presents a valuable model-based analysis of how time to treatment post-symptom onset may influence Paxlovid efficacy in hospitalised COVID-19 patients. The analysis, based on a large data set, provides information on the action of the drug and supports clinical decision-making. Furthermore, it provides solid evidence for the role of the drug in reducing infectiousness in those receiving treatment.

Decision letter

Editor: James M McCaw1
Reviewed by: Qingpeng Zhang2

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Decision letter after peer review:

Thank you for submitting your article "A retrospective cohort study of Paxlovid efficacy depending on treatment time in hospitalized COVID-19 patients" for consideration by eLife. Your article has been reviewed by 2 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Miles Davenport as the Senior Editor.

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Essential revisions (for the authors):

1) Both reviewers have queried the model fitting process and as a consequence, the reliability and/or interpretability of the results. Given the absence of data from the growth phase of infection for the patients, it is unclear how parameters that determine growth can be fitted, nor how the values of the population-level parameters that have been determined through the use of MONOLIX can be reliably interpreted. One reviewer has suggested a Bayesian hierarchical approach which would certainly have merit, allowing for prior knowledge on these parameters (from other studies of within-host SARS-CoV-2 dynamics) to be incorporated. At least one (and perhaps both) of the reviewers, and me as the editor, are familiar with MONOLIX and understand its strengths and limitations for undertaking mixed-effects analyses.

In revising the manuscript, these statistical concerns must be addressed. While an alternative Bayesian analysis has been suggested (and I would feel has great merit), it is not required and I will of course consider any suitably justified approach.

Whatever approach is taken, a clear explanation of why the parameter estimates (existing or recomputed) may be considered reliable and how uncertainty on them may influence the conclusions must be provided.

Furthermore, individual patient fits should also be provided (in supplementary material presumably given the hundreds of patients' time-series data being analysed). Also, individual time-series data for each patient should be made available to support alternative analyses.

Reviewer #1 (Recommendations for the authors):

Du et al. investigated the impact of the timing of Paxlovid treatment on SARS-CoV-2 viral load using a within-host mathematical model. They observed that even though the viral load could drop within the first 24 hours of receiving Paxlovid, it reduced more if patients were treated earlier after symptom onset. Their findings suggest that fast-acting antiviral drugs like Paxlovid have the potential to slow SARS-CoV-2 transmission while improving patient outcomes.

Data mostly support the conclusions of this paper, but some aspects of data analysis need to be clarified and extended.

1) The authors claimed that demographic information, drug administration data, symptoms, laboratory test results, and daily viral titer measurements of patients are available in EHR data, so it is necessary to describe important characteristics of patients (e.g., distribution of age and daily viral load) for better understanding of the study cohort.

2) Using the within-host model to estimate viral load trajectories is solid mathematically. However, the authors should discuss whether the parameters estimated by the model are reasonable biologically.

3) There have already been several papers using epidemiological methods (e.g., https://onlinelibrary.wiley.com/doi/abs/10.1002/jmv.28443) to investigate the impact of treatment initiation time on the efficacy of Paxlovid. The authors need to compare their findings with relevant literature, which might demonstrate the clinical significance of the results.

5) There are some errors in Figure 1D and Figure 1E. First, the two sub-figures do not share the legend. Therefore, please move the current legend in Figure 1E to Figure 1D. As described in the results [The overall reduction in viral load post symptom onset (relative to untreated cases) declines from 34% (95% CrI: 26%, 42%) for patients treated on the first day of symptom onset to 30% (95% CrI: 23%, 39%) for patients treated six days after symptom onset (Figure 1E, Methods)], the X-axis title of Figure 1E should be "Treatment initiation day after post symptom onset" not "Days post symptom onset".

6) The legend of Figure 2 seems to be incomplete.

7) I recommend that the authors include a schematic diagram to depict the process represented by the within-host model visually.

Reviewer #2 (Recommendations for the authors):

Du et al. estimated the efficacy of Paxlovid in reducing viral growth in SARS-CoV-2 infection by fitting a viral dynamics model to viral load data from 208 hospitalised patients in Hong Kong. They found that Paxlovid could reduce viral replication by more than 90% and treatment with Paxlovid on the first day of symptom onset may marginally be better than treatment six days later.

My major concern is parameter identifiability. As shown in Figure 1, the viral load data was only collected from day 4 post-symptom onset and has little information about viral growth phase. With the proposed viral dynamics model, the data is insufficient to estimate any model parameter that determines the viral growth rate, such as β, pi, δ, and more importantly epsilon. Even with a simpler model that excludes the refractory cell compartment, I don't believe those parameters are identifiable based on the clinical data presented in Figure 1. Therefore, I would be concerned unless the authors can demonstrate the identifiability of those parameters reported as main results.

I agree the model chosen is a typical model to use for studying viral dynamics and I have no problem with the model structure and construction. But the data doesn't cover the viral growth phase such that some parameters that determine the viral growth rate cannot be identified by the data. I would suggest using a Bayesian method to fit the model to data to check parameter identifiability.

eLife. 2024 Apr 16;13:e89801. doi: 10.7554/eLife.89801.sa2

Author response


Essential revisions (for the authors):

1) Both reviewers have queried the model fitting process and as a consequence, the reliability and/or interpretability of the results. Given the absence of data from the growth phase of infection for the patients, it is unclear how parameters that determine growth can be fitted, nor how the values of the population-level parameters that have been determined through the use of MONOLIX can be reliably interpreted. One reviewer has suggested a Bayesian hierarchical approach which would certainly have merit, allowing for prior knowledge on these parameters (from other studies of within-host SARS-CoV-2 dynamics) to be incorporated. At least one (and perhaps both) of the reviewers, and me as the editor, are familiar with MONOLIX and understand its strengths and limitations for undertaking mixed-effects analyses.

In revising the manuscript, these statistical concerns must be addressed. While an alternative Bayesian analysis has been suggested (and I would feel has great merit), it is not required and I will of course consider any suitably justified approach.

Whatever approach is taken, a clear explanation of why the parameter estimates (existing or recomputed) may be considered reliable and how uncertainty on them may influence the conclusions must be provided.

Thank you for this constructive feedback. It is true that the clinical trial data were collected from day 4 post-symptom onset and thus did not include much information about viral growth phase. However, our model is able to fit the early viral growth phase using estimates for the initial number of infected cells [E0] (1 cell) and the initial number of uninfected target cells [U0] (8×107 cells), as in ref.(Ke et al., 2021). When we fit the model to the clinical data assuming these starting values, we are able to estimate model parameters that govern both the early (unobserved) growth phase and the post symptom-onset (observed) decline phase. We now clarify this aspect of the estimation procedure as well as our use of the Stochastic Approximation Expectation-Maximization (SAEM) algorithm to estimate these parameters (MONOLIX 2021R1)(Miao et al., 2011; Traynard et al., 2020), as follows:

“To estimate the six model parameters governing the viral load dynamics, we fitted the within-host model to the observed SARS-Cov-2 RNA titer (log10 copies/mL) measured across 208 patients adults treated with or without Paxlovid between January 6, 2022 and May 1, 2022. We used the Stochastic Approximation Expectation-Maximization (SAEM) algorithm to estimate these parameters (Miao et al., 2011; Traynard et al., 2020) assuming fixed values for the initial numbers of infecting virions and susceptible target cells following ref. (Ke et al., 2021) and confirmed the convergence of the estimates via trace plots. The SAEM algorithm is an established method in population pharmacology modeling with clear convergence indicators (Delyon et al., 1999; “Population parameter using SAEM algorithm,” 2016).”

Furthermore, individual patient fits should also be provided (in supplementary material presumably given the hundreds of patients' time-series data being analysed). Also, individual time-series data for each patient should be made available to support alternative analyses.

As requested, we have added a new figure (Figure 1—figure supplement 1) depicting the observed and model-estimated viral titer time series for each of the 208 patients in the study.

We also indicate that the primary data are available upon request in Acknowledgments, as follows:

“All data used in this study can be accessed through Github: https://github.com/ZhanweiDU/PaxHK/.”

Additional Updates

In addressing the reviewers’ concerns, we made two significant modifications to improve the fidelity of our model.

1. We extended our within-host model to incorporate a gradual decline in Paxlovid efficacy following a five-day course of treatment, as analyzed in ref. (Perelson et al., 2023a). This is now described in the Methods section as follows:

“We incorporate a gradual decline in Paxlovid efficacy following a five-day course of treatment, using a pharmacokinetic model introduced in a recent study of Paxlovid rebound dynamics (Perelson et al., 2023a). Our model assumes that Paxlovid efficacy (ϵt) is 0 prior to the first dose and then given by:

ϵt=ϵmaxCtCt+EC50
Ct=C^kakekaeketekaId1[1e(keka)t(1eNd,tkaId)+(ekeIdekaId)(e(Nt1)keId1ekeId1)e((Nd,t1)ke+ka)Id]

where t is the time elapsed since receiving the first dose and ϵmax is the maximum antiviral effectiveness, which we estimate by fitting the model to clinical trial data. EC50 is the concentration at which the drug effectiveness is half-maximal (62 nM) (Food et al., 2021); C^ is the product of the bioavailability of the drug and the mass of the drug administered in a dose per volume (6.25×103 nM) (Food et al., 2021; Perelson et al., 2023b; PubChem, n.d.); Nd,t is the number of doses administered in the period up to time t; ke is the elimination rate (2.8/day) (Food et al., 2021; Perelson et al., 2023b); ka is the absorption rate (17.5/day) (Dixit and Perelson, 2004; Perelson et al., 2023b); Id is the dosing interval (1/2 day) (Dixit and Perelson, 2004; Perelson et al., 2023b).

2. We modified our method for estimating the reduction in infectiousness due to Paxlovid, based on estimates relating viral titer to household transmission that were recently published in eLife(Marc et al., 2021). Rather than comparing the areas under simulated viral titer curves, we compare the areas under the corresponding infectivity curves, now described in the Methods section as follows:

“To estimate the impact of treatment time on viral load dynamics (Figure 1D) and infectiousness (Figure 1E), we compare pairs of model simulations (with versus without Paxlovid treatment). Each pair shares the same randomly-generated parameter values, including an incubation period randomly selected from a previously-estimated distribution (<inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image1.png" /> days) (Du et al., 2022).

In order to translate differences in the simulated viral titers into differences in infectiousness, we used the following published model relating household transmission risk to viral load (Marc et al., 2021).

<inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image2.png" />

where <inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image3.png" /> denotes the probability that individual <inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image4.png" /> infects a susceptible household member at time <inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image5.png" />, <inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image6.png" /> = -2.94, which corresponds to a baseline probability of transmission of 5% (Marc et al., 2021), and <inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image7.png" /> = 0.49 (Marc et al., 2021). We assume that the relative infectiousness of a patient throughout their infection can be approximated by the area under the household infectivity curve from the time of infection (<inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image8.png" />) until 15 days post the onset of symptoms (<inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image9.png" />), as given by

<inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image10.png" />

For a given pair of simulations (<inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image4.png" />), we then compare the projected infectiousness of the treated patient <inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image11.png" /> to that of the untreated patient <inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image12.png" />, as given by

<inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image13.png" />

For each treatment initiation time considered, we report the median and 95% confidence intervals of the reduction in infectiousness (<inline-graphic mimetype="image" mime-subtype="png" xlink:href="media/image14.png" />) based on 1000 pairs of simulations.”

The revised version of Figure 1, the new Figure 1—figure supplement 1, new Supplementary File 3, and new Supplementary File 4, reflect these updates.

Reviewer #1 (Recommendations for the authors):

Du et al. investigated the impact of the timing of Paxlovid treatment on SARS-CoV-2 viral load using a within-host mathematical model. They observed that even though the viral load could drop within the first 24 hours of receiving Paxlovid, it reduced more if patients were treated earlier after symptom onset. Their findings suggest that fast-acting antiviral drugs like Paxlovid have the potential to slow SARS-CoV-2 transmission while improving patient outcomes.

Data mostly support the conclusions of this paper, but some aspects of data analysis need to be clarified and extended.

1) The authors claimed that demographic information, drug administration data, symptoms, laboratory test results, and daily viral titer measurements of patients are available in EHR data, so it is necessary to describe important characteristics of patients (e.g., distribution of age and daily viral load) for better understanding of the study cohort.

In addition to the new Figure 1—figure supplement 1 comparing viral titer data for each patient to model projections (above), we have added a new figure (Figure 2) summarizing the demographic characteristics of patients, including ages and daily viral load.

2) Using the within-host model to estimate viral load trajectories is solid mathematically. However, the authors should discuss whether the parameters estimated by the model are reasonable biologically.

Ref. (Ke et al., 2021) uses a similar within-host model to estimate key viral dynamic parameters from a data set that includes viral titers measured in 17 patients in 2020. We compare our estimates to theirs in the following table.

Author response table 1. Comparison of population estimates of parameters in our study and ref.

(Ke et al., 2021). The means and 95% confidence intervals (CI) are derived assuming that individual parameters follow log-normal distributions

Parameter Estimated value Estimate from ref. (Ke et al., 2021)
Cell infection rate in 10-9 mL/Copies in days-1 (β) 17 [7, 45] 32 [12, 85]
Rate in log10 for the interferon-induced conversion of target cells to refractory cells (Φ) -9.37 [-14.81, -3.93] 3.11 [-0.52, 4.77]
Rate in 10-3 at which refractory cells become target cells again (ρ) 5.2 [2.1, 12.8] 4.4 [3.0, 6.5]
Infected cell clearance rate in days-1 (δ) 0.5 [0.2, 1.6] 1.7 [1.1, 2.7]
Virus production rate in Copies/ mL in days-1 (π) 68.6 [32.7, 145.0] 45.3 [28.3, 72.5]

Thus, our new estimates are fairly consistent with this prior study. The differences may be attributable to the fact that the earlier study analyzed data from patients infected with an ancestral strain from 2020 and our considers infection with a later (Omicron) variant. The largest discrepancy is in the estimated effect of innate immunity at suppressing viral replication (Φ). Our lower estimate is consistent with a recent study suggesting that the Omicron variant may be more immune evasive than ancestral variants (Willett et al., 2022).

As suggested, we have updated the text to discuss the reasonability of our parameter estimates:

“Our parameter estimates for the Omicron variant are generally comparable to prior estimates based on viral titers measured in patients infected with the ancestor strain in 2020 (Ke et al., 2021). However, our estimate for the effect of innate immunity at suppressing viral replication rate is significantly lower than the prior estimate, which is consistent with a recent study suggesting that Omicron variants may be more immune evasive than ancestral variants (Willett et al., 2022). As further validation of our estimates, we compare projections of the fitted model with observed viral titers from 208 patients (Figure 1—figure supplement 1) and demonstrate that model can reproduce the rebounds experienced by some COVID-19 patients following Paxlovid treatment, under the assumption that Paxlovid efficacy begins to decline after the fifth day of treatment (Figure 1D).”

3) There have already been several papers using epidemiological methods (e.g., https://onlinelibrary.wiley.com/doi/abs/10.1002/jmv.28443) to investigate the impact of treatment initiation time on the efficacy of Paxlovid. The authors need to compare their findings with relevant literature, which might demonstrate the clinical significance of the results.

Thank you for highlighting this relevant work. We believe that our study is significant and makes the following contributions to our understanding of Paxlovid impacts on viral dynamics and infectiousness. (i) by estimating key within-host viral dynamic and Paxlovid efficacy parameters from a larger data set of individual viral load measurement we are able to corroborate some prior estimates and improve on other estimates, (ii) by analyzing data from more recent Omicron infections, our estimates of Paxlovid efficacy may be more appropriate for recently circulating variants and highlight potential differences stemming from evolutionary changes in immune evasiveness, (iii) whereas prior studies either characterized viral titer dynamics in the absence of treatment (Ke et al., 2021) or the impact of treatment on viral elimination time (Wang et al., 2023), our study characterizes the full time series of viral titer dynamics and implications for infectiousness, depending on whether a patient receives Paxlovid and the timing of treatment initiation following symptom onset. In addition to the new text comparing our estimates to prior estimates (see just above), we have added the following sentence to the Discussion.

“Our model of SARS-CoV-2 viral load dynamics following Paxlovid treatment allows us to estimate the potential benefits of early treatment for reducing infectiousness, while accounting for variation across patients and potential rebounds in viral growth. The model projections corroborate prior estimates for the impact of treatment initiation time on the duration of viral shedding (Wang et al., 2023).”

Reviewer #2 (Recommendations for the authors):

Du et al. estimated the efficacy of Paxlovid in reducing viral growth in SARS-CoV-2 infection by fitting a viral dynamics model to viral load data from 208 hospitalised patients in Hong Kong. They found that Paxlovid could reduce viral replication by more than 90% and treatment with Paxlovid on the first day of symptom onset may marginally be better than treatment six days later.

My major concern is parameter identifiability. As shown in Figure 1, the viral load data was only collected from day 4 post-symptom onset and has little information about viral growth phase. With the proposed viral dynamics model, the data is insufficient to estimate any model parameter that determines the viral growth rate, such as β, pi, δ, and more importantly epsilon. Even with a simpler model that excludes the refractory cell compartment, I don't believe those parameters are identifiable based on the clinical data presented in Figure 1. Therefore, I would be concerned unless the authors can demonstrate the identifiability of those parameters reported as main results.

I agree the model chosen is a typical model to use for studying viral dynamics and I have no problem with the model structure and construction. But the data doesn't cover the viral growth phase such that some parameters that determine the viral growth rate cannot be identified by the data. I would suggest using a Bayesian method to fit the model to data to check parameter identifiability.

Thank you for this constructive feedback. It is true that the clinical trial data were collected from day 4 post-symptom onset and did not include much information about viral growth phase. However, our model is able to fit the early viral growth phase using estimates for the initial number of infected cells [E0] (1 virion) and the initial number of uninfected target cells [U0] (8×107 cells), as in ref.(Ke et al., 2021). When we fit the model to the clinical data assuming these starting values, we are able to estimate model parameters that govern both the early (unobserved) growth phase and the post symptom-onset (observed) decline phase. We now clarify this aspect of the estimation procedure as well as our use of the Stochastic Approximation Expectation-Maximization (SAEM) algorithm to estimate these parameters (MONOLIX 2021R1) (Miao et al., 2011; Traynard et al., 2020). The SAEM algorithm is faster than classical MCMC algorithms and is now widely used for population pharmacology modeling(“Population parameter using SAEM algorithm,” 2016). Its convergence has been demonstrated rigorously (Delyon et al., 1999) and its implementation in Monolix is particularly efficient. The updated methods read as follows:

“To estimate the six model parameters governing the viral load dynamics, we fitted the within-host model to the observed SARS-Cov-2 RNA titer (log10 copies/mL) measured across 208 patients adults treated with or without Paxlovid between January 6, 2022 and May 1, 2022. We used the Stochastic Approximation Expectation-Maximization (SAEM) algorithm to estimate these parameters (MONOLIX 2021R1) (Miao et al., 2011; Traynard et al., 2020)assuming fixed values for the initial numbers of infecting virions and susceptible target cells following ref.(Ke et al., 2021) and confirmed the convergence of the estimates via trace plots. The SAEM algorithm is an established method in population pharmacology modeling with clear convergence indicators (Delyon et al., 1999; “Population parameter using SAEM algorithm,” 2016).”

The following trace plots show the convergence of our parameter estimates, with the red lines indicating a switch from the exploratory phase to the smoothing phase.

Author response image 1.

Author response image 1.

Our new estimates are qualitatively consistent with prior studies, as we now describe in the Discussion section:“Our parameter estimates for the Omicron variant are generally comparable to prior estimates based on viral titers measured in patients infected with the ancestor strain in 2020 (Ke et al., 2021). However, our estimate for the effect of innate immunity at suppressing viral replication rate is significantly lower than the prior estimate, which is consistent with a recent study suggesting that Omicron variants may be more immune evasive than ancestral variants (Willett et al., 2022). As further validation of our estimates, we compare projections of the fitted model with observed viral titers from 208 patients (Figure 1—figure supplement 1) and demonstrate that model can reproduce the rebounds experienced by some COVID-19 patients following Paxlovid treatment, under the assumption that Paxlovid efficacy begins to decline after the fifth day of treatment (Figure 1D).”

References

Delyon B, Lavielle M, Moulines E. 1999. Convergence of a Stochastic Approximation Version of the EM Algorithm. Ann Stat 27:94–128.

Dixit NM, Perelson AS. 2004. Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracellular delay. J Theor Biol 226:95–109.

Du Z, Liu C, Wang L, Bai Y, Lau EHY, Wu P, Cowling BJ. 2022. Shorter serial intervals and incubation periods in SARS-CoV-2 variants than the SARS-CoV-2 ancestral strain. J Travel Med 29. doi:10.1093/jtm/taac052

Food US, Administration D, Others. 2021. Fact sheet for healthcare providers: emergency use authorization for Paxlovid. Recuperada de https://www fda gov/media/155050/download el 17:2021.

Ke R, Zitzmann C, Ho DD, Ribeiro RM, Perelson AS. 2021. in vivo kinetics of SARS-CoV-2 infection and its relationship with a person’s infectiousness. Proceedings of the National Academy of Sciences 118:e2111477118.

Marc A, Kerioui M, Blanquart F, Bertrand J, Mitjà O, Corbacho-Monné M, Marks M, Guedj J. 2021. Quantifying the relationship between SARS-CoV-2 viral load and infectiousness. ELife 10. doi:10.7554/eLife.69302

Miao H, Xia X, Perelson AS, Wu H. 2011. ON IDENTIFIABILITY OF NONLINEAR ODE MODELS AND APPLICATIONS IN VIRAL DYNAMICS. SIAM Rev Soc Ind Appl Math 53:3–39.

Perelson AS, Ribeiro RM, Phan T. 2023a. An explanation for SARS-CoV-2 rebound after Paxlovid treatment. medRxiv. doi:10.1101/2023.05.30.23290747

Perelson AS, Ribeiro RM, Phan T. 2023b. An explanation for SARS-CoV-2 rebound after Paxlovid treatment. medRxiv. doi:10.1101/2023.05.30.23290747

Population parameter using SAEM algorithm. 2016.. Monolix. https://monolix.lixoft.com/tasks/population-parameter-estimation-using-saem/

PubChem. n.d. Nirmatrelvir. https://pubchem.ncbi.nlm.nih.gov/compound/155903259

Traynard P, Ayral G, Twarogowska M, Chauvin J. 2020. Efficient Pharmacokinetic Modeling Workflow With the MonolixSuite: A Case Study of Remifentanil. CPT Pharmacometrics Syst Pharmacol 9:198–210.

Wang Y, Zhao D, Liu X, Chen X, Xiao W, Feng L. 2023. Early administration of Paxlovid reduces the viral elimination time in patients infected with SARS-CoV-2 Omicron variants. J Med Virol 95:e28443.

Willett BJ, Grove J, MacLean OA, Wilkie C, De Lorenzo G, Furnon W, Cantoni D, Scott S, Logan N, Ashraf S, Manali M, Szemiel A, Cowton V, Vink E, Harvey WT, Davis C, Asamaphan P, Smollett K, Tong L, Orton R, Hughes J, Holland P, Silva V, Pascall DJ, Puxty K, da Silva Filipe A, Yebra G, Shaaban S, Holden MTG, Pinto RM, Gunson R, Templeton K, Murcia PR, Patel AH, Klenerman P, Dunachie S, PITCH Consortium, COVID-19 Genomics UK (COG-UK) Consortium, Haughney J, Robertson DL, Palmarini M, Ray S, Thomson EC. 2022. SARS-CoV-2 Omicron is an immune escape variant with an altered cell entry pathway. Nat Microbiol 7:1161–1179.

Associated Data

    This section collects any data citations, data availability statements, or supplementary materials included in this article.

    Data Citations

    1. Du Z. 2024. PaxHK. GitHub. PaxHK

    Supplementary Materials

    Supplementary file 1. Within-host model parameter estimates.

    We used a nonlinear mixed-effects method to fit a within-host model of viral kinetics to the viral titer measurements from 208 patients, 104 were treated with Paxlovid and 104 did not receive any antiviral drugs (Traynard et al., 2020). The reported medians and variation across individuals (95% interpercentile ranges) integrate both fixed and random effects estimates for each parameter.

    elife-89801-supp1.docx (7.7KB, docx)
    Supplementary file 2. Population-wide parameter estimates for the within-host model.

    The table provides population-wide fixed and random effects estimates for the viral dynamic parameters, whereas Supplementary file 1 provides the estimated median and variation across individuals for each parameter. The values assume that antiviral efficacy follows a logit-normal distribution and all other parameters follow log normal distributions*. Values in parentheses are relative standard errors (RSE) as a percent.

    elife-89801-supp2.docx (8.3KB, docx)
    Supplementary file 3. Estimated reduction in overall infectiousness and likelihood of a post-treatment rebound, depending on the timing of Paxlovid initiation in days post onset of symptoms (DPOS).

    To estimate the probability of a rebound, we computed the fraction out of 1000 simulations in which the viral titer rebounded to higher values following treatment than observed prior to treatment. To estimate reduction in infectiousness, we run 1000 pairs of treatment versus no treatment simulations. Following each simulation, we calculate the total infectiousness from the time of infection until 15 DPOS using estimates relating viral titer to infectiousness provided in Marc et al., 2021. For each pair, we then compute the percent difference in total infectiousness of the treatment simulation relative to the no treatment simulation. The table reports medians and 95% CIs across all treated patients, patients who do not experience a post-treatment rebound, and patients who do.

    elife-89801-supp3.docx (8.6KB, docx)
    Supplementary file 4. The distribution of treatment initiation times for the 104 patients who received Paxlovid.

    Day zero corresponds to the first day of symptoms.

    elife-89801-supp4.docx (7.2KB, docx)
    MDAR checklist

    Data Availability Statement

    All data used in this study can be accessed through Github: https://github.com/ZhanweiDU/PaxHK/.

    The following dataset was generated:

    Du Z. 2024. PaxHK. GitHub. PaxHK


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