The unmitigated profile of COVID-19 infectiousness

  1. Ron Sender
  2. Yinon Bar-On
  3. Sang Woo Park
  4. Elad Noor
  5. Jonathan Dushoff
  6. Ron Milo

  • Curated by eLife

    eLife logo

    Evaluation Summary:

    A pathogen's generation interval directly affects estimates of its transmissibility (R), and the period of self-isolation or quarantine needed to prevent transmission. This study shows that the unmitigated generation interval of the original variant of SARS-CoV-2 is several days longer than previously estimated and that interventions have substantially decreased the effective generation interval. These findings improve our ability to model counterfactual intervention-free scenarios. Overall technically sound analyses support the conclusions, and extensive sensitivity analyses show that the findings are robust. However, sampling or ascertainment bias in this relatively small pre-intervention dataset or biased inputs could affect the accuracy of the reported estimates.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)

Reviewed by

Read the full article See related articles

Listed in

Log in to save this article

Abstract

Quantifying the temporal dynamics of infectiousness of individuals infected with SARS-CoV-2 is crucial for understanding the spread of COVID-19 and for evaluating the effectiveness of mitigation strategies. Many studies have estimated the infectiousness profile using observed serial intervals. However, statistical and epidemiological biases could lead to underestimation of the duration of infectiousness. We correct for these biases by curating data from the initial outbreak of the pandemic in China (when mitigation was minimal), and find that the infectiousness profile of the original strain is longer than previously thought. Sensitivity analysis shows our results are robust to model structure, assumed growth rate and potential observational biases. Although unmitigated transmission data is lacking for variants of concern (VOCs), previous analyses suggest that the alpha and delta variants have faster within-host kinetics, which we extrapolate to crude estimates of variant-specific unmitigated generation intervals. Knowing the unmitigated infectiousness profile of infected individuals can inform estimates of the effectiveness of isolation and quarantine measures. The framework presented here can help design better quarantine policies in early stages of future epidemics.

Article activity feed

  1. Version published to 10.7554/elife.79134 on eLife
  2. eLife

    Author Response:

    Reviewer #1 (Public Review):

    The authors show that the unmitigated generation interval of the original variant of SARS-CoV-2 is longer than originally thought. They argue that in the absence of interventions that limit transmission late in the course of infection, the fraction of transmission events that occur before symptom onset would be considerably lower, and the fraction of transmission events occurring 10 days or more after infection of the index case would be substantially higher.

    These findings improve our ability to accurately estimate the basic reproductive number (R0), to evaluate quarantine and isolation policies, and to model counterfactual intervention-free scenarios. Many applied analyses rely on accurate generation interval estimates. To head off confusion, it would be helpful if the authors could provide more comprehensive guidance about which applied analyses should be informed by the unmitigated generation interval, or the observed generation interval. (E.g. the unmitigated interval is useful for quarantine and isolation policies, but would we ever want to use the unmitigated interval to estimate R?).

    The unmitigated generation-interval should be used for estimation of the R0 of the initial epidemic phase, but not for the R(t) of the current epidemics. Estimation of R(t) must account for changes in generation-interval distributions caused by the invasion of new variants and changes in behavior. When analyzing policies of quarantine, isolation or contact tracing, the unmitigated interval should also be adopted to account for late transmissions.

    We added few sentences at the end of our introduction to clarify this point:

    “The estimated unmitigated generation-interval distribution could be adopted for answering questions about quarantine and isolation policy, as well as for estimating the original R0 at the initial spread in China. However, estimation of instantaneous R(t) should account for changes in generation-interval distributions, reflecting mitigation effects and the current variant.”

    The analysis estimates a longer generation interval after accounting for three main sources of bias or error that are common in other analyses:

    1. Recently infected individuals are intrinsically overrepresented in data on a growing epidemic. Thus, shorter incubation periods and forward serial intervals are more likely to be observed, even in the absence of interventions. This analysis adjusts for these dynamical biases.
    2. Interventions or behavioral changes can prevent transmission late in the course of infection. This can shorten the generation and serial intervals over the course of an epidemic. This analysis focuses specifically on transmission pairs observed very early, before the adoption of interventions.
    3. The incubation period and generation interval should be correlated - infectors that progress relatively quickly to symptoms should also become infectious sooner (symptom onset occurs near the peak of viral titers). Most existing analyses assume these intervals are uncorrelated, but this analysis accounts for their correlation.

    Overall, the conclusions seem reasonable and well-supported. The observation that the generation interval decreases over the course of an epidemic is also consistent with existing studies that show the serial interval has similarly decreased over time. But given the implications of the findings, I hope the authors can address a few questions about potential additional sources of bias:

    1. It is somewhat reassuring that the generation interval decreases relatively smoothly as the cutoff date increases (Fig. S6), but it would be helpful if the authors address the potential impact of ascertainment biases. One of the main reasons that the authors estimate a shorter generation interval is that they define January 17th, early in the outbreak before interventions and behavioral changes had taken place, as the cutoff point for the infector's date of symptom onset. This cutoff eliminates biases from interventions, but it also severely limits the size of the transmission-pair dataset (Fig. S3), and focusing on this very early subset of cases may increase the influence of ascertainment bias. Prior to January 17th, should we expect observed transmission pairs to involve more severe cases on average? And is the unmitigated generation interval correlated with case severity?

    We thank the reviewer for identifying a source of possible bias that we overlooked. Following the comment we performed a new sensitivity analysis for the inclusion of the severe cases, summarized in Appendix 1—figure 11.

    Severity of the cases was reported only in Ali et al.’s data, for some of the individuals. In these cases, individuals are divided into one of three conditions: mild, severe (non-fatal) and death. As non-mild cases represent a small fraction of the dataset, we combine them into one category, which we denote as severe.

    Severe cases (including deaths) were overrepresented in the period prior to January 17, with 8 out of 77 cases, compared to 18 out of 745 in the period of January 18-31. The effect of inclusion of severe cases was analyzed by comparing the means of the estimated generation-interval distribution, separately for the two periods in question, using the inference framework with 30 bootstrapping runs. For the earlier period, the estimated means were compared between the dataset with or without the severe cases. For the later period, we also consider the “enriched” dataset, in which severe cases are oversampled for each bootstrap such that the proportion of severe cases matches that during the earlier period (10%). In both cases we see that the effect on the estimated mean generation interval is small.

    1. The analysis assumes the incubation period follows a fixed distribution, whose parameterization comes from a meta-analysis of previously estimated incubation periods. But p.5 discusses the idea that observed incubation periods are affected by the same dynamical biases as forward serial intervals, "For example, when the incidence of infection is increasing exponentially, individuals are more likely to have been infected recently. Therefore, a cohort of infectors that developed symptoms at the same time will have shorter incubation periods than their infectees on average, which will, in turn, affect the shape of the forward serial-interval distribution." Has the incubation period been adjusted for these dynamical biases, or should it be?

    In our analysis we use the incubation period distribution from Xin et al. 2021 which already considers the backward bias caused by the expanding epidemic with the corrected growth rate of 0.1/d. Xin et al. showed in their meta-analysis that the mean incubation period reported by the various sources changed according to the dates used by the source. Incubation periods prior to the peak of the epidemic in China were lower than ones from after the peak, in a manner that coincided with the backward correction they performed (using a similar derivation to that suggested by Park et al. 2021). Accordingly, the distribution of incubation period they report is the intrinsic incubation period, after correction for the growth rate of the initial spread in China. We added two sentences in our methods section to clarify this point:

    “In their meta-analysis, Xin et al. found an increase of the incubation period following the introduction of interventions in China, matching the theoretical framework shown above. Their inferred incubation period distribution includes a correction for the growth rate of the early spread, accordingly.”

    Furthermore, we perform a sensitivity analysis for the shape of the incubation period distribution, and show that it has a minor effect on our conclusions (Appendix 1—figure 10).

    1. It appears that correlation parameter estimates co-vary with estimates of the mean generation interval (Fig. S6; S13b). Are the authors confident that the correlation parameter is identifiable? How much would the median generation interval estimate in the main analysis change if the correlation parameter had been fixed to 0 (which isn't realistic) or to 0.5 (which might be plausible)?

    As the reviewer pointed out, the correlation parameter estimates co-vary with estimates of the mean generation interval. We further analyzed this relation following the comment. The analysis is summarized in supplemental figures S19-20.

    We first examine the relation between the mean generation interval and the correlation parameter based on the uncertainty estimates, consisting of 1000 bootstrap runs. Appendix 1—figure 12 shows a joint bivariate scatter plot of the parameters, together with contours of equal probability. As can be seen there is a connection between the parameters. The estimates centered around the maximum likelihood estimate with correlation parameter of 0.75 and mean generation interval of 9.7 days. The confidence interval for the correlation parameter of 0.45-0.95 corresponds to mean generation intervals in the range of 8-11 days, supporting the conclusion of this study.

    Next, we reanalyzed the dataset while fixing the correlation parameter, as suggested by the reviewer. Appendix 1—figure 13 shows the estimated mean generation interval for fixed correlation parameters with values of 0, 0.25, 0.5, 0.75, 0.9. For each fixed correlation parameter 100 bootstrapping runs. As can be seen, the results reflect the same connection that can be seen in Appendix 1—figure 12, with probable values in the range of 8-11 days, for correlation parameters in the range of 0.5-0.9. Assuming no correlation would cause underestimation of the mean generation interval match previous literature (Hart, Maini, and Thompson 2021; Park et al. 2022).

    Reviewer #2 (Public Review):

    There have been several estimates of the generation time and serial interval published for SARS-CoV-2, but as the authors note, estimates can be subject to biases including shifted event timing depending on the phase of the epidemic, correlation in characteristics between infector and infectee, and impact of control measures on truncating potential infectiousness. This study, therefore, has several strengths. It first collates data on transmission events from the earliest phase of the COVID-19 pandemic, then makes adjustments for these potential biases to estimate the generation time in absence of control measures, and finally discusses implications for transmission.

    Given many subsequent aspects of the COVID-19 pandemic have been defined relative to earlier phases (e.g. relative transmissibility of variants, relative duration of infectiousness), understanding the baseline characteristics of the infection is crucial. I thought this paper makes a useful contribution to this understanding, generating adjusted estimates for infectiousness (which is longer than previous estimates) and corresponding values for the reproduction number (which is remarkably similar to earlier estimates, presumably because of the different sources of bias in the growth rate and generation time distribution somehow end up canceling each other out).

    However, there are some weaknesses at present. The study correctly flags several potential sources of bias in estimates, but in making adjustments uses estimates from the literature that themselves could suffer from these biases, e.g. the distribution of incubation period from a 2021 meta-analysis. Although the authors conduct some sensitivity analysis it would be worth including some more explicit consideration of whether they would expect any underlying bias to propagate through their calculations. The authors also conduct some sensitivity analysis around the underlying data (e.g. ordering of transmission pairs), but again it would be useful to know whether there could be systematic biases in these early data. Specifically, the paper references Tsang et al (2020), which highlighted variability in early case definitions - is it possible that early generation times are estimated to be longer because intermediate cases in the transmission chain were more likely to go undetected than later in the epidemic?

    We recognize the potential biases in the transmission pairs data. We therefore developed an extensive framework of sensitivity analyses for identifying biases that could substantially affect the results. In the results section and figure 5, we show that the main study result, that the unmitigated generation-interval distribution is longer than previously estimated, is robust to reasonable amounts of ascertainment bias. We discuss this point at length and have added several supplemental figures to support this claim.

    As reviewer #3 mentioned, we conducted a sensitivity analysis for the inclusion of the longest serial intervals, to investigate possible effects of missing links in the longest transmission pairs. We also discuss why we think it’s not necessary to explicitly model the short intervals that may be unobserved due to missing links.

    “Second, we considered the possibility that long serial intervals may be caused by omission of intermediate infections in multiple chains of transmission, which in turn would lead to overestimation of the mean serial and generation intervals. Thus, we refit our model after removing long serial intervals from the data (by varying the maximum serial interval between 14 and 24 days). We also considered “splitting” these intervals into smaller intervals, but decided this was unnecessarily complex, since several choices would need to be made, and the effects would likely be small compared to the effect of the choice of maximum, since the distribution of the resulting split intervals would not differ sharply from that of the remaining observed intervals in most cases.”

    We added to the discussion text regarding the effect of possible bias in the dataset, explicitly specifying the ascertainment bias.

    “Our analysis relies on datasets of transmission pairs gathered from previously published studies and thus has several limitations that are difficult to correct for. Transmission pairs data can be prone to incorrect identification of transmission pairs, including the direction of transmission. In particular, presymptomatic transmission can cause infectors to report symptoms after their infectees, making it difficult to identify who infected whom. Data from the early outbreak might also be sensitive to ascertainment and reporting biases which could lead to missing links in transmission pairs, causing serial intervals to appear longer (For example, people who transmit asymptomatically might not be identified). Moreover, when multiple potential infectors are present, an individual who developed symptoms close to when the infectee became infected is more likely to be identified as the infector. These biases might increase the estimated correlation of the incubation period and the period of infectiousness. We have tried to account for these biases by using a bootstrapping approach, in which some data points are omitted in each bootstrap sample. The relatively narrow ranges of uncertainty suggest that the results are not very sensitive to specific transmission pairs data points being included in the analysis. We also performed a sensitivity analysis to address several potential biases such as the duration of the unmitigated transmission period, the inclusion of long serial intervals in the dataset, and the incorrect ordering of transmission pairs (see Methods). The sensitivity analysis shows that although these biases could decrease the inferred mean generation interval, our main conclusions about the long unmitigated generation intervals (high median length and substantial residual transmission after 14 days) remained robust (Figure 5).”

    It would also be helpful to have some clarifications about methodology, particularly in how the main results about generation time are subsequently analyzed. For example, estimates such as the conversion of generation time to R0 and VOC scalings are described very briefly, so it is currently unclear exactly how these calculations are being performed.

    Following the reviewer comments we made edits to the Methods section in order to make it more readable and clearer. We added subheadings for the various sections. Moreover, we added a section explaining the derivation of the basic reproduction number and clarified the section regarding the VOCs extrapolations.

    We made some edits to the methods section in order to make it more accessible and clear, for example, we added subheadings for the various sections, added a section explaining the derivation of the basic reproduction number, and clarified the section regarding the VOCs extrapolations.

    Reviewer #3 (Public Review):

    Sender & Bar-On et al. perform robust analyses of early SARS-CoV-2 line list data from China to estimate the intrinsic generation interval in the absence of interventions. This is an important topic, as most SARS-CoV-2 data are from periods when transmission-reducing interventions are in place, which will lead to underestimation of the potential infectious period.

    The authors highlight two shortcomings in previous approaches. First, the distribution of 'observed' serial intervals (the time between symptom onset in the infector and symptom onset in the infectee) depends not only on the timeline of each infector's infection, but also the epidemic growth rate, which weights the proportion of observed short vs. long serial intervals. The authors argue that by accounting for this weighting, more accurate estimates of the intrinsic generation interval - the metric on which isolation policies are based - can be obtained. Second, the authors find that the original SARS-CoV-2 generation interval distribution has both a higher mean and longer tail than previous estimates when using only data prior to the introduction of interventions. Finally, the authors use publicly available data on viral load trajectories to extrapolate their estimates to other SARS-CoV-2 variants, finding that alpha, delta, and omicron may have shorter generation intervals than original SARS-CoV-2. These findings are important, as case isolation policies are based on assumptions for how long individuals remain infectious. More broadly, these methods will be important for future work to correctly estimate generation intervals in other outbreaks.

    The conclusions are well supported by the data, and a suite of sensitivity analyses give confidence that the findings are robust to deviations from many of the key assumptions. The code is well documented and publicly available, and thus the findings are easily reproducible. Key strengths of the paper include the clarity and rigor of the modeling methods, and the exhaustive consideration of potential biases and corresponding sensitivity analyses - it is very difficult to think of potential biases that the authors have not already considered! I think this is a well-written and well-executed study. The work is likely to be impactful for reconsidering SARS-CoV-2 isolation policies and revisiting generation interval estimates from other data sources. I also expect this to be a key reference and method for future studies estimating the generation interval.

    I have some minor comments on potential weaknesses and interpretation:

    1. Uncertainty in early generation interval estimates. One of the conclusions is that the estimated mean generation interval is longer than the observed mean serial interval. However, this conclusion does not seem justified given that the observed mean serial interval (9.1 days) is well within the 95% CI of 8.3-11.2 days for the mean generation interval. The confidence intervals for the serial interval in figure 2 are also wide for pre-Jan 17th (though presumably these would be reduced if all pre-Jan 17th serial intervals were combined). Further, only 77 of the ~1000 transmission pairs are actually from pre-January 17th. The actual sample size used for these estimates is much smaller than suggested by Figure S1 and thus this should be made clear. Therefore, although the intuition for why observed serial intervals may differ from the generation interval is correct, I do not think that the data alone demonstrate this. A related issue is on ascertainment bias - could the early serial interval data be biased longer because ascertainment is initially poor and thus more intermediate infectors are missed? The authors consider removing particularly long serial intervals to try and account for this, but that does not deal with e.g. chains of multiple short serial intervals being incorrectly recorded as a single long serial interval (but still within 16 days).

    We agree with the reviewer that due the large uncertainty we cannot deduce that the mean generation interval is longer than the mean serial interval. We changed the phrasing to emphasize this statement is supported by mathematical theory.

    “We note that our estimated mean generation-interval is longer than the observed mean serial-interval (9.1 days) of the period in question. This is supported by the theory (Park et al. 2021) of the dynamical effects of the epidemic -- in contrast to the common assumption that the mean generation and serial intervals are identical. During the exponential growth phase, the mean incubation period of the infectors is expected to be shorter than the mean incubation period of the infectee - this effect causes the mean forward serial interval to become longer than the mean forward generation interval of the cohorts that developed symptoms during the study period. However, these cohorts of infectors with short incubation periods will also have short forward generation (and therefore serial) intervals due to their correlations. When the latter effect is stronger, the mean forward serial interval becomes shorter than the mean intrinsic generation interval, as these findings suggest.“

    Following the comment, we added to Figure S1 the filtering according to date, to reflect the true sample size we use for the main analysis (We renamed it: Appendix 1—figure 1).

    We recognize the potential biases in the transmission pairs data. We therefore developed an extensive framework of sensitivity analyses for identifying biases that could substantially affect the results. In the results section and figure 5, we show that the main study result, that the unmitigated generation-interval distribution is longer than previously estimated, is robust to reasonable amounts of ascertainment bias. We discuss this point at length and have added several supplemental figures to support this claim.

    As reviewer #3 mentioned, we conducted a sensitivity analysis for the inclusion of the longest serial intervals, to investigate possible effects of missing links in the longest transmission pairs. We also discuss why we think it’s not necessary to explicitly model the short intervals that may be unobserved due to missing links.

    “Second, we considered the possibility that long serial intervals may be caused by omission of intermediate infections in multiple chains of transmission, which in turn would lead to overestimation of the mean serial and generation intervals. Thus, we refit our model after removing long serial intervals from the data (by varying the maximum serial interval between 14 and 24 days). We also considered “splitting” these intervals into smaller intervals, but decided this was unnecessarily complex, since several choices would need to be made, and the effects would likely be small compared to the effect of the choice of maximum, since the distribution of the resulting split intervals would not differ sharply from that of the remaining observed intervals in most cases.”

    We added to the discussion text regarding the effect of possible bias in the dataset, explicitly specifying the ascertainment bias.

    “Our analysis relies on datasets of transmission pairs gathered from previously published studies and thus has several limitations that are difficult to correct for. Transmission pairs data can be prone to incorrect identification of transmission pairs, including the direction of transmission. In particular, presymptomatic transmission can cause infectors to report symptoms after their infectees, making it difficult to identify who infected whom. Data from the early outbreak might also be sensitive to ascertainment and reporting biases which could lead to missing links in transmission pairs, causing serial intervals to appear longer (For example, people who transmit asymptomatically might not be identified). Moreover, when multiple potential infectors are present, an individual who developed symptoms close to when the infectee became infected is more likely to be identified as the infector. These biases might increase the estimated correlation of the incubation period and the period of infectiousness. We have tried to account for these biases by using a bootstrapping approach, in which some data points are omitted in each bootstrap sample. The relatively narrow ranges of uncertainty suggest that the results are not very sensitive to specific transmission pairs data points being included in the analysis. We also performed a sensitivity analysis to address several potential biases such as the duration of the unmitigated transmission period, the inclusion of long serial intervals in the dataset, and the incorrect ordering of transmission pairs (see Methods). The sensitivity analysis shows that although these biases could decrease the inferred mean generation interval, our main conclusions about the long unmitigated generation intervals (high median length and substantial residual transmission after 14 days) remained robust (Figure 5).”

    1. Frailty of using viral loads to extrapolate generation intervals. The authors take the observation that variants of concern demonstrate faster viral clearance on average to estimate shorter generation intervals for alpha, delta, and omicron. The authors rightly point out in the discussion that using viral load as a proxy for infectiousness has many limitations. I would emphasize even further that it is very difficult to extrapolate from viral load data in this way, as infectiousness appears to vary far more between variants than can be explained by duration positive or peak viral load. Other factors are potentially at play, such as compartmentalization in the respiratory tract, aerosolization, receptor binding, immunity, etc. Further, there is considerable individual-level variation in viral trajectories and thus the use of a population-mean model overlooks a key component of SARS-CoV-2 infection dynamics. An important reference, which came out recently and thus makes sense to have been missed from the initial submission, is Puhach et al. Nature Medicine 2022 https://doi.org/10.1038/s41591-022-01816-0.

    We agree with the reviewer about the frailty of using viral loads to extrapolate generation intervals. We therefore expanded our discussion of the limitation of using viral load data for inferring infectiousness including many of the points mentioned by the reviewer. We use viral load data in the most minimal way to try to enable some discussion of new VOC, and try to emphasize the needed caution.

    Viral load trajectories data have potential for informing estimates of the infectiousness profile. However the relationship between viral load, culture positivity, symptom onset, and infectivity is complex and not well characterized. Due to this limitation we tried to use viral loads in a more limited way, extrapolating our results to variants of concerns (which lack unmitigated transmission data). Following the comment, we added a detailed discussion of the limitations of using viral loads as a proxy for infectiousness, including the variation of viral loads across individuals. We also added supplementary figures (Figure 6—figure supplements 1-2) to show the possible effect of an individual's viral loads in relation to the infectiousness and for comparison with new viral load and culture results (Chu et al. 2022; Killingley et al. 2022). As the viral load trajectories data for the different VOC is given only as a function of time from the onset of symptoms, it is not possible to directly link it to the fraction of transmission post 14 days from infection. We made changes to Figure 6 to clarify the possible connection of viral load with the TOST (time from symptoms onset to transmission) distribution and the resulting extrapolation to the unmitigated generation-interval distributions.

    “SARS-CoV-2 viral load trajectories serve an important role in understanding the dynamics of the disease and modeling its infectiousness (Quilty et al. 2021; Cleary et al. 2021). Indeed, the general shapes of the mean viral load trajectories and culture positivity, based on longitudinal studies, are comparable with our estimated unmitigated infectiousness profile (Figure 6—figure supplements 1-2, comparison with (Chu et al. 2022; Killingley et al. 2022; Kissler et al. 2021)). However, the nature of the relationship between viral load, culture positivity, symptom onset, and real-world infectivity is complex and not well characterized. Therefore, the ability to infer infectiousness from viral load data is very limited, especially near the tail of infectiousness, several days following symptom onset and peak viral loads. Viral load models are usually made to fit the measurements during an initial exponential clearance phase and in many cases miss a later slow decay (Kissler et al. 2021). Furthermore, there is considerable individual-level variation in viral trajectories that isn’t accounted for in population-mean models (Kissler et al. 2021; Singanayagam et al. 2021). Other factors limiting the ability to compare generation-interval estimates with viral loads models are the variability of the incubation periods and its relation to the timing of the peak of the viral loads, and the great uncertainty and apparent non-linearity of the relation between viral loads and culture positivity (Jaafar et al. 2021; Jones et al. 2021). Due to these caveats and in order to avoid over interpretation of viral load data, we restrict our extrapolation of new VOCs’ infectiousness to a single parameter characterizing the viral duration of clearance.”

    We also edited another paragraph in the discussion:

    “Our extrapolations are necessarily crude given the complex relationship between viral load, symptomaticity, and infectiousness discussed above. Moreover, compartmentalization in the respiratory tract, aerosolization, receptor binding affinity, and immune history can also play important roles in determining the infectiousness profiles of SARS-CoV-2 variants (Puhach et al. ). ”

    1. Lack of validation with other datasets This study hinges on data from a single setting in a short window of time. Although the data are from multiple publications, the fact that so many reported the same transmission pair data demonstrates that these are overlapping datasets. As the authors note, there are potential biases e.g., ascertainment rates and behavioral changes which will impact the generation interval estimates. Thus, generalizability to other settings is limited.

    We agree with the reviewer that the dataset used in our study is limited, and consists of overlapping transmission pairs. We perform some analysis of the possible bias caused by inclusion of each dataset, as can be seen in Appendix 1—figure 4.

    The best validation would have been a comparison with another independent dataset from the early spread of the epidemic, but no such dataset exists. We added a sentence to the discussion to emphasize this point.

    “Due to the nature of early spread of a new unknown disease it is nearly impossible to find two completely unrelated datasets from the period prior to mitigation, limiting the ability of further validation of the current results.”

    1. The impact of epidemic dynamics on infector vs. infectee serial intervals. It took me a long time to get my head around the assertion that the forward serial interval distribution will be longer during epidemic growth due to the overrepresentation of short incubation periods among infectors relative to infectees. A supplementary figure, similar to the way Figure 1 is laid out, to illustrate this concept may go a long way to aid the reader's understanding.

    We added an explanation to the paragraph in order to make it clearer:

    “A cohort of individuals that develop symptoms on a given day is a sample of all individuals who have been previously infected. When the incidence of infection is increasing, recently infected individuals represent a bigger fraction of this population and thus are over-represented in this cohort. Therefore, we are more likely to encounter infected individuals with a short incubation period in this cohort compared to an unbiased sample. The forward serial-interval is calculated for a cohort of infectors who developed symptoms at the same time and therefore is sensitive to this bias. These dynamical biases are demonstrated using epidemic simulations by Park et al."

    1. Simulations to illustrate concepts and power Given the assertion that observed serial intervals will depend on epidemic growth rates, reporting, and timing of interventions, I think a simple simulation to illustrate some of these ideas would be very helpful. For example, a simple agent-based model with simulated infectivity profiles and incubation periods using the estimated bivariate distribution would be extremely helpful in illustrating how serial intervals and estimates of the generation interval can differ from the true intrinsic generation interval (I coded such a simulation to help me understand this paper in a couple of hours with <100 lines of R code, so I do not think this would be much work). This would also be very helpful for illustrating statistical power re. comment 1.

    The current paper is based on a strong theoretical foundation provided by previous works, specifically Park et al. 2021, which used simulations similar to the reviewer’s suggestions to demonstrate the dynamical biases. We now mention these simulations somewhere in the introduction section:

    “These dynamical biases are demonstrated using epidemic simulations by Park et al."

  3. eLife

    Evaluation Summary:

    A pathogen's generation interval directly affects estimates of its transmissibility (R), and the period of self-isolation or quarantine needed to prevent transmission. This study shows that the unmitigated generation interval of the original variant of SARS-CoV-2 is several days longer than previously estimated and that interventions have substantially decreased the effective generation interval. These findings improve our ability to model counterfactual intervention-free scenarios. Overall technically sound analyses support the conclusions, and extensive sensitivity analyses show that the findings are robust. However, sampling or ascertainment bias in this relatively small pre-intervention dataset or biased inputs could affect the accuracy of the reported estimates.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)

  4. eLife

    Reviewer #1 (Public Review):

    The authors show that the unmitigated generation interval of the original variant of SARS-CoV-2 is longer than originally thought. They argue that in the absence of interventions that limit transmission late in the course of infection, the fraction of transmission events that occur before symptom onset would be considerably lower, and the fraction of transmission events occurring 10 days or more after infection of the index case would be substantially higher.

    These findings improve our ability to accurately estimate the basic reproductive number (R0), to evaluate quarantine and isolation policies, and to model counterfactual intervention-free scenarios. Many applied analyses rely on accurate generation interval estimates. To head off confusion, it would be helpful if the authors could provide more comprehensive guidance about which applied analyses should be informed by the unmitigated generation interval, or the observed generation interval. (E.g. the unmitigated interval is useful for quarantine and isolation policies, but would we ever want to use the unmitigated interval to estimate R?).

    The analysis estimates a longer generation interval after accounting for three main sources of bias or error that are common in other analyses:
    1. Recently infected individuals are intrinsically overrepresented in data on a growing epidemic. Thus, shorter incubation periods and forward serial intervals are more likely to be observed, even in the absence of interventions. This analysis adjusts for these dynamical biases.
    2. Interventions or behavioral changes can prevent transmission late in the course of infection. This can shorten the generation and serial intervals over the course of an epidemic. This analysis focuses specifically on transmission pairs observed very early, before the adoption of interventions.
    3. The incubation period and generation interval should be correlated - infectors that progress relatively quickly to symptoms should also become infectious sooner (symptom onset occurs near the peak of viral titers). Most existing analyses assume these intervals are uncorrelated, but this analysis accounts for their correlation.

    Overall, the conclusions seem reasonable and well-supported. The observation that the generation interval decreases over the course of an epidemic is also consistent with existing studies that show the serial interval has similarly decreased over time. But given the implications of the findings, I hope the authors can address a few questions about potential additional sources of bias:

    1. It is somewhat reassuring that the generation interval decreases relatively smoothly as the cutoff date increases (Fig. S6), but it would be helpful if the authors address the potential impact of ascertainment biases. One of the main reasons that the authors estimate a shorter generation interval is that they define January 17th, early in the outbreak before interventions and behavioral changes had taken place, as the cutoff point for the infector's date of symptom onset. This cutoff eliminates biases from interventions, but it also severely limits the size of the transmission-pair dataset (Fig. S3), and focusing on this very early subset of cases may increase the influence of ascertainment bias. Prior to January 17th, should we expect observed transmission pairs to involve more severe cases on average? And is the unmitigated generation interval correlated with case severity?

    2. The analysis assumes the incubation period follows a fixed distribution, whose parameterization comes from a meta-analysis of previously estimated incubation periods. But p.5 discusses the idea that observed incubation periods are affected by the same dynamical biases as forward serial intervals,

    "For example, when the incidence of infection is increasing exponentially, individuals are more likely to have been infected recently. Therefore, a cohort of infectors that developed symptoms at the same time will have shorter incubation periods than their infectees on average, which will, in turn, affect the shape of the forward serial-interval distribution."

    Has the incubation period been adjusted for these dynamical biases, or should it be?

    3. It appears that correlation parameter estimates co-vary with estimates of the mean generation interval (Fig. S6; S13b). Are the authors confident that the correlation parameter is identifiable? How much would the median generation interval estimate in the main analysis change if the correlation parameter had been fixed to 0 (which isn't realistic) or to 0.5 (which might be plausible)?

  5. eLife

    Reviewer #2 (Public Review):

    There have been several estimates of the generation time and serial interval published for SARS-CoV-2, but as the authors note, estimates can be subject to biases including shifted event timing depending on the phase of the epidemic, correlation in characteristics between infector and infectee, and impact of control measures on truncating potential infectiousness. This study, therefore, has several strengths. It first collates data on transmission events from the earliest phase of the COVID-19 pandemic, then makes adjustments for these potential biases to estimate the generation time in absence of control measures, and finally discusses implications for transmission.

    Given many subsequent aspects of the COVID-19 pandemic have been defined relative to earlier phases (e.g. relative transmissibility of variants, relative duration of infectiousness), understanding the baseline characteristics of the infection is crucial. I thought this paper makes a useful contribution to this understanding, generating adjusted estimates for infectiousness (which is longer than previous estimates) and corresponding values for the reproduction number (which is remarkably similar to earlier estimates, presumably because of the different sources of bias in the growth rate and generation time distribution somehow end up cancelling each other out).

    However, there are some weaknesses at present. The study correctly flags several potential sources of bias in estimates, but in making adjustments uses estimates from the literature that themselves could suffer from these biases, e.g. the distribution of incubation period from a 2021 meta-analysis. Although the authors conduct some sensitivity analysis it would be worth including some more explicit consideration of whether they would expect any underlying bias to propagate through their calculations. The authors also conduct some sensitivity analysis around the underlying data (e.g. ordering of transmission pairs), but again it would be useful to know whether there could be systematic biases in these early data. Specifically, the paper references Tsang et al (2020), which highlighted variability in early case definitions - is it possible that early generation times are estimated to be longer because intermediate cases in the transmission chain were more likely to go undetected than later in the epidemic?

    It would also be helpful to have some clarifications about methodology, particularly in how the main results about generation time are subsequently analysed. For example, estimates such as the conversion of generation time to R0 and VOC scalings are described very briefly, so it is currently unclear exactly how these calculations are being performed.

  6. eLife

    Reviewer #3 (Public Review):

    Sender & Bar-On et al. perform robust analyses of early SARS-CoV-2 line list data from China to estimate the intrinsic generation interval in the absence of interventions. This is an important topic, as most SARS-CoV-2 data are from periods when transmission-reducing interventions are in place, which will lead to underestimation of the potential infectious period.

    The authors highlight two shortcomings in previous approaches. First, the distribution of 'observed' serial intervals (the time between symptom onset in the infector and symptom onset in the infectee) depends not only on the timeline of each infector's infection, but also the epidemic growth rate, which weights the proportion of observed short vs. long serial intervals. The authors argue that by accounting for this weighting, more accurate estimates of the intrinsic generation interval - the metric on which isolation policies are based - can be obtained. Second, the authors find that the original SARS-CoV-2 generation interval distribution has both a higher mean and longer tail than previous estimates when using only data prior to the introduction of interventions. Finally, the authors use publicly available data on viral load trajectories to extrapolate their estimates to other SARS-CoV-2 variants, finding that alpha, delta, and omicron may have shorter generation intervals than original SARS-CoV-2. These findings are important, as case isolation policies are based on assumptions for how long individuals remain infectious. More broadly, these methods will be important for future work to correctly estimate generation intervals in other outbreaks.

    The conclusions are well supported by the data, and a suite of sensitivity analyses give confidence that the findings are robust to deviations from many of the key assumptions. The code is well documented and publicly available, and thus the findings are easily reproducible. Key strengths of the paper include the clarity and rigor of the modeling methods, and the exhaustive consideration of potential biases and corresponding sensitivity analyses - it is very difficult to think of potential biases that the authors have not already considered! I think this is a well-written and well-executed study. The work is likely to be impactful for reconsidering SARS-CoV-2 isolation policies and revisiting generation interval estimates from other data sources. I also expect this to be a key reference and method for future studies estimating the generation interval.

    I have some minor comments on potential weaknesses and interpretation:

    1. Uncertainty in early generation interval estimates
    One of the conclusions is that the estimated mean generation interval is longer than the observed mean serial interval. However, this conclusion does not seem justified given that the observed mean serial interval (9.1 days) is well within the 95% CI of 8.3-11.2 days for the mean generation interval. The confidence intervals for the serial interval in figure 2 are also wide for pre-Jan 17th (though presumably these would be reduced if all pre-Jan 17th serial intervals were combined). Further, only 77 of the ~1000 transmission pairs are actually from pre-January 17th. The actual sample size used for these estimates is much smaller than suggested by Figure S1 and thus this should be made clear. Therefore, although the intuition for why observed serial intervals may differ from the generation interval is correct, I do not think that the data alone demonstrate this.

    A related issue is on ascertainment bias - could the early serial interval data be biased longer because ascertainment is initially poor and thus more intermediate infectors are missed? The authors consider removing particularly long serial intervals to try and account for this, but that does not deal with e.g. chains of multiple short serial intervals being incorrectly recorded as a single long serial interval (but still within 16 days).

    2. Frailty of using viral loads to extrapolate generation intervals
    The authors take the observation that variants of concern demonstrate faster viral clearance on average to estimate shorter generation intervals for alpha, delta, and omicron. The authors rightly point out in the discussion that using viral load as a proxy for infectiousness has many limitations. I would emphasize even further that it is very difficult to extrapolate from viral load data in this way, as infectiousness appears to vary far more between variants than can be explained by duration positive or peak viral load. Other factors are potentially at play, such as compartmentalization in the respiratory tract, aerosolization, receptor binding, immunity, etc. Further, there is considerable individual-level variation in viral trajectories and thus the use of a population-mean model overlooks a key component of SARS-CoV-2 infection dynamics. An important reference, which came out recently and thus makes sense to have been missed from the initial submission, is Puhach et al. Nature Medicine 2022 https://doi.org/10.1038/s41591-022-01816-0.

    3. Lack of validation with other datasets
    This study hinges on data from a single setting in a short window of time. Although the data are from multiple publications, the fact that so many reported the same transmission pair data demonstrates that these are overlapping datasets. As the authors note, there are potential biases e.g., ascertainment rates and behavioral changes which will impact the generation interval estimates. Thus, generalizability to other settings is limited.

    4. The impact of epidemic dynamics on infector vs. infectee serial intervals
    It took me a long time to get my head around the assertion that the forward serial interval distribution will be longer during epidemic growth due to the overrepresentation of short incubation periods among infectors relative to infectees. A supplementary figure, similar to the way Figure 1 is laid out, to illustrate this concept may go a long way to aid the reader's understanding.

    5. Simulations to illustrate concepts and power
    Given the assertion that observed serial intervals will depend on epidemic growth rates, reporting, and timing of interventions, I think a simple simulation to illustrate some of these ideas would be very helpful. For example, a simple agent-based model with simulated infectivity profiles and incubation periods using the estimated bivariate distribution would be extremely helpful in illustrating how serial intervals and estimates of the generation interval can differ from the true intrinsic generation interval (I coded such a simulation to help me understand this paper in a couple of hours with <100 lines of R code, so I do not think this would be much work). This would also be very helpful for illustrating statistical power re. comment 1.

  7. Version published to 10.1101/2021.11.17.21266051v2 on medRxiv
  8. ScreenIT

    SciScore for 10.1101/2021.11.17.21266051: (What is this?)

    Please note, not all rigor criteria are appropriate for all manuscripts.

    Table 1: Rigor

    NIH rigor criteria are not applicable to paper type.

    Table 2: Resources

    Software and Algorithms
    SentencesResources
    We then chose the parameters that maximize the likelihood of the observed serial intervals (the maximum likelihood estimate): Sequential Least Squares Programming method, implemented in Python, was used to maximize the log-likelihood33.
    Python
    suggested: (IPython, RRID:SCR_001658)

    Results from OddPub: Thank you for sharing your data.

    Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:
    Our analysis relies on datasets of transmission pairs gathered from previously published studies and thus has several limitations that are difficult to correct for. Transmission pairs data can be prone to incorrect identification of transmission pairs, including the direction of transmission. In particular, presymptomatic transmission can cause infectors to develop symptoms after their infectees, making it difficult to identify who infected whom. Data from the early outbreak might also be sensitive to ascertainment and reporting biases. For example, people who transmit asymptomatically might not be identified. Moreover, when multiple potential infectors are present, an individual who developed symptoms close to when the infectee became infected is more likely to be identified as the infector. These biases might increase the estimated correlation of the incubation period and the period of infectiousness. We have tried to deal with these biases by using a bootstrapping approach, in which some data points are omitted in each bootstrap sample. The relatively narrow ranges of uncertainty suggest that the results are not very sensitive to specific transmission pairs data points being included in the analysis. We also performed a thorough sensitivity analysis to address several of the potential biases such as the determination of period corresponding to unmitigated transmission, the inclusion of long serial intervals in the dataset, and the incorrect orderings of transmission pairs ...

    Results from TrialIdentifier: No clinical trial numbers were referenced.

    Results from Barzooka: We did not find any issues relating to the usage of bar graphs.

    Results from JetFighter: We did not find any issues relating to colormaps.

    Results from rtransparent:
    • Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
    • Thank you for including a funding statement. Authors are encouraged to include this statement when submitting to a journal.
    • No protocol registration statement was detected.

    Results from scite Reference Check: We found no unreliable references.

    About SciScore

    SciScore is an automated tool that is designed to assist expert reviewers by finding and presenting formulaic information scattered throughout a paper in a standard, easy to digest format. SciScore checks for the presence and correctness of RRIDs (research resource identifiers), and for rigor criteria such as sex and investigator blinding. For details on the theoretical underpinning of rigor criteria and the tools shown here, including references cited, please follow this link.

  9. Version published to 10.1101/2021.11.17.21266051v1 on medRxiv