Estimating a time-to-event distribution from right-truncated data in an epidemic: A review of methods

Generative Bayesian modeling to nowcast the effective reproduction number from line list data with missing symptom onset dates

The time-varying effective reproduction number Rt is a widely used indicator of transmission dynamics during infectious disease outbreaks. Timely estimates of Rt can be obtained from reported cases counted by their date of symptom onset, which is generally closer to the time of infection than the date of report. Case counts by date of symptom onset are typically obtained from line list data, however these data can have missing information and are subject to right truncation. Previous methods have addressed these problems independently by first imputing missing onset dates, then adjusting truncated case counts, and finally estimating the effective reproduction number. This stepwise approach makes it difficult to propagate uncertainty and can introduce subtle biases during real-time estimation due to the continued impact of assumptions made in previous steps. In this work, we integrate imputation, truncation adjustment, and Rt estimation into a single generative Bayesian model, allowing direct joint inference of case counts and Rt from line list data with missing symptom onset dates. We then use this framework to compare the performance of nowcasting approaches with different stepwise and generative components on synthetic line list data for multiple outbreak scenarios and across different epidemic phases. We find that under reporting delays realistic for hospitalization data (50% of reports delayed by more than a week), intermediate smoothing, as is common practice in stepwise approaches, can bias nowcasts of case counts and Rt, which is avoided in a joint generative approach due to shared regularization of all model components. On incomplete line list data, a fully generative approach enables the quantification of uncertainty due to missing onset dates without the need for an initial multiple imputation step. In a real-world comparison using hospitalization line list data from the COVID-19 pandemic in Switzerland, we observe the same qualitative differences between approaches. The generative modeling components developed in this work have been integrated and further extended in the R package epinowcast, providing a flexible and interpretable tool for real-time surveillance.

On a simple estimation of the proportional odds model under right truncation

Retrospective sampling can be useful in epidemiological research for its convenience to explore an etiological association. One particular retrospective sampling is that disease outcomes of the time-to-event type are collected subject to right truncation, along with other covariates of interest. For regression analysis of the right-truncated time-to-event data, the so-called proportional reverse-time hazards model has been proposed, but the interpretation of its regression parameters tends to be cumbersome, which has greatly hampered its application in practice. In this paper, we instead consider the proportional odds model, an appealing alternative to the popular proportional hazards model. Under the proportional odds model, there is an embedded relationship between the reverse-time hazard function and the usual hazard function. Building on this relationship, we provide a simple procedure to estimate the regression parameters in the proportional odds model for the right truncated data. Weighted estimations are also studied.

Transmission dynamics of monkeypox in the United Kingdom: contact tracing study

OBJECTIVE

To analyse the transmission dynamics of the monkeypox outbreak in the UK, declared a Public Health Emergency of International Concern in July 2022.

DESIGN

Contact tracing study, linking data on case-contact pairs and on probable exposure dates.

SETTING

Case questionnaires from the UK Health Security Agency (UKHSA), United Kingdom.

PARTICIPANTS

2746 people with polymerase chain reaction confirmed monkeypox virus in the UK between 6 May and 1 August 2022.

MAIN OUTCOME MEASURES

The incubation period and serial interval of a monkeypox infection using two bayesian time delay models-one corrected for interval censoring (ICC-interval censoring corrected) and one corrected for interval censoring, right truncation, and epidemic phase bias (ICRTC-interval censoring right truncation corrected). Growth rates of cases by reporting date, when monkeypox virus was confirmed and reported to UKHSA, were estimated using generalised additive models.

RESULTS

The mean age of participants was 37.8 years and 95% reported being gay, bisexual, and other men who have sex with men (1160 out of 1213 reporting). The mean incubation period was estimated to be 7.6 days (95% credible interval 6.5 to 9.9) using the ICC model and 7.8 days (6.6 to 9.2) using the ICRTC model. The estimated mean serial interval was 8.0 days (95% credible interval 6.5 to 9.8) using the ICC model and 9.5 days (7.4 to 12.3) using the ICRTC model. Although the mean serial interval was longer than the incubation period for both models, short serial intervals were more common than short incubation periods, with the 25th centile and the median of the serial interval shorter than the incubation period. For the ICC and ICRTC models, the corresponding estimates ranged from 1.8 days (95% credible interval 1.5 to 1.8) to 1.6 days (1.4 to 1.6) shorter at the 25th centile and 1.6 days (1.5 to 1.7) to 0.8 days (0.3 to 1.2) shorter at the median. 10 out of 13 linked patients had documented pre-symptomatic transmission. Doubling times of cases declined from 9.07 days (95% confidence interval 12.63 to 7.08) on the 6 May, when the first case of monkeypox was reported in the UK, to a halving time of 29 days (95% confidence interval 38.02 to 23.44) on 1 August.

CONCLUSIONS

Analysis of the instantaneous growth rate of monkeypox incidence indicates that the epidemic peaked in the UK as of 9 July and then started to decline. Short serial intervals were more common than short incubation periods suggesting considerable pre-symptomatic transmission, which was validated through linked patient level records. For patients who could be linked through personally identifiable data, four days was the maximum time that transmission was detected before symptoms manifested. An isolation period of 16 to 23 days would be required to detect 95% of people with a potential infection. The 95th centile of the serial interval was between 23 and 41 days, suggesting long infectious periods.

Adjusting for time of infection or positive test when estimating the risk of a post-infection outcome in an epidemic

When comparing the risk of a post-infection binary outcome, for example, hospitalisation, for two variants of an infectious pathogen, it is important to adjust for calendar time of infection. Typically, the infection time is unknown and positive test time used as a proxy for it. Positive test time may also be used when assessing how risk of the outcome changes over calendar time. We show that if time from infection to positive test is correlated with the outcome, the risk conditional on positive test time is a function of the trajectory of infection incidence. Hence, a risk ratio adjusted for positive test time can be quite different from the risk ratio adjusted for infection time. We propose a simple sensitivity analysis that indicates how risk ratios adjusted for positive test time and infection time may differ. This involves adjusting for a shifted positive test time, shifted to make the difference between it and infection time uncorrelated with the outcome. We illustrate this method by reanalysing published results on the relative risk of hospitalisation following infection with the Alpha versus pre-existing variants of SARS-CoV-2. Results indicate the relative risk adjusted for infection time may be lower than that adjusted for positive test time.

Trends in outcomes following COVID-19 symptom onset in Milan: a cohort study

BACKGROUND

For people with symptomatic COVID-19, the relative risks of hospital admission, death without hospital admission and recovery without admission, and the times to those events, are not well understood. We describe how these quantities varied with individual characteristics, and through the first wave of the pandemic, in Milan, Italy.

METHODS

A cohort study of 27 598 people with known COVID-19 symptom onset date in Milan, Italy, testing positive between February and June 2020 and followed up until 17 July 2020. The probabilities of different events, and the times to events, were estimated using a mixture multistate model.

RESULTS

The risk of death without hospital admission was higher in March and April (for non-care home residents, 6%-8% compared with 2%-3% in other months) and substantially higher for care home residents (22%-29% in March). For all groups, the probabilities of hospitalisation decreased from February to June. The probabilities of hospitalisation also increased with age, and were higher for men, substantially lower for healthcare workers and care home residents, and higher for people with comorbidities. Times to hospitalisation and confirmed recovery also decreased throughout the first wave. Combining these results with our previously developed model for events following hospitalisation, the overall symptomatic case fatality risk was 15.8% (15.4%-16.2%).

CONCLUSIONS

The highest risks of death before hospital admission coincided with periods of severe burden on the healthcare system in Lombardy. Outcomes for care home residents were particularly poor. Outcomes improved as the first wave waned, community healthcare resources were reinforced and testing became more widely available.