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

Time-to-event data are right-truncated if only individuals who have experienced the event by a certain time can be included in the sample. For example, we may be interested in estimating the distribution of time from onset of disease symptoms to death and only have data on individuals who have died. This may be the case, for example, at the beginning of an epidemic. Right truncation causes the distribution of times to event in the sample to be biased towards shorter times compared to the population distribution, and appropriate statistical methods should be used to account for this bias. This article is a review of such methods, particularly in the context of an infectious disease epidemic, like COVID-19. We consider methods for estimating the marginal time-to-event distribution, and compare their efficiencies. (Non-)identifiability of the distribution is an important issue with right-truncated data, particularly at the beginning of an epidemic, and this is discussed in detail. We also review methods for estimating the effects of covariates on the time to event. An illustration of the application of many of these methods is provided, using data on individuals who had died with coronavirus disease by 5 April 2020.

Time between Symptom Onset, Hospitalisation and Recovery or Death: Statistical Analysis of Belgian COVID-19 Patients

There are different patterns in the COVID-19 outbreak in the general population and amongst nursing home patients. We investigate the time from symptom onset to diagnosis and hospitalization or the length of stay (LoS) in the hospital, and whether there are differences in the population. Sciensano collected information on 14,618 hospitalized patients with COVID-19 admissions from 114 Belgian hospitals between 14 March and 12 June 2020. The distributions of different event times for different patient groups are estimated accounting for interval censoring and right truncation of the time intervals. The time between symptom onset and hospitalization or diagnosis are similar, with median length between symptom onset and hospitalization ranging between 3 and 10.4 days, depending on the age of the patient (longest delay in age group 20–60 years) and whether or not the patient lives in a nursing home (additional 2 days for patients from nursing home). The median LoS in hospital varies between 3 and 10.4 days, with the LoS increasing with age. The hospital LoS for patients that recover is shorter for patients living in a nursing home, but the time to death is longer for these patients. Over the course of the first wave, the LoS has decreased.

Epidemiological characteristics of the first 53 laboratory-confirmed cases of COVID-19 epidemic in Hong Kong, 13 February 2020

Background COVID-19, caused by SARS-CoV-2, first appeared in China and subsequently developed into an ongoing epidemic. Understanding epidemiological factors characterising the transmission dynamics of this disease is of fundamental importance. Aims This study aimed to describe key epidemiological parameters of COVID-19 in Hong Kong. Methods We extracted data of confirmed COVID-19 cases and their close contacts from the publicly available information released by the Hong Kong Centre for Health Protection. We used doubly interval censored likelihood to estimate containment delay and serial interval, by fitting gamma, lognormal and Weibull distributions to respective empirical values using Bayesian framework with right truncation. A generalised linear regression model was employed to identify factors associated with containment delay. Secondary attack rate was also estimated. Results The empirical containment delay was 6.39 days; whereas after adjusting for right truncation with the best-fit Weibull distribution, it was 10.4 days (95% CrI: 7.15 to 19.81). Containment delay increased significantly over time. Local source of infection and number of doctor consultations before isolation were associated with longer containment delay. The empirical serial interval was 4.58–6.06 days; whereas the best-fit lognormal distribution to 26 certain-and-probable infector–infectee paired data gave an estimate of 4.77 days (95% CrI: 3.47 to 6.90) with right-truncation. The secondary attack rate among close contacts was 11.7%. Conclusion With a considerable containment delay and short serial interval, contact-tracing effectiveness may not be optimised to halt the transmission with rapid generations replacement. Our study highlights the transmission risk of social interaction and pivotal role of physical distancing in suppressing the epidemic.

Conditional quantiles estimation of the incubation period of COVID-19

Background : In December 2019, some cases of pneumonia with unknown etiology were identified in Wuhan, Hubei province in China. The World Health Organization (WHO) has named this disease as COVID-19, standing for ``2019 coronavirus disease", and announced the disease have become a public health incident on December 31, 2019. This study aimed to investigate the conditional distribution of the incubation period of COVID-19 on the age of infected cases, and estimate its corresponding conditional quantiles from information on 2172 confirmed cases from 29 provinces outside Hubei in China. Methods : We collected data including the infection dates, onset dates, and ages of the confirmed cases from the websites of the centres of disease control, or the daily public reports through February 16th, 2020. A new maximum likelihood method was developed to account for the biased sampling, or right truncation, issue of the data as the epidemic is still ongoing. The estimators can be shown to be consistent asymptotically under mild conditions. Results : Based on the collected data, we found that the conditional quantiles of the incubation period distribution of COVID-19 varies over ages. In detail, the high conditional quantiles of people in the middle age group are shorter than those of others. We estimated that the 0.95-th quantile related to people in the age group 23$\sim$55 is less than 15 days. Conclusions : Observing that the conditional quantiles vary over ages, we may take more precise measures for people of different ages. For example, we may consider carrying out an age-dependent quarantine duration, rather than a uniform 14-days quarantine, in practice. Remarkably, we may need to extend the current quarantine duration for people aged $0\sim22$ and over 55 because the related 0.95-th quantiles are much greater than 14 days.

Incubation Period and Other Epidemiological Characteristics of 2019 Novel Coronavirus Infections with Right Truncation: A Statistical Analysis of Publicly Available Case Data

The geographic spread of 2019 novel coronavirus (COVID-19) infections from the epicenter of Wuhan, China, has provided an opportunity to study the natural history of the recently emerged virus. Using publicly available event-date data from the ongoing epidemic, the present study investigated the incubation period and other time intervals that govern the epidemiological dynamics of COVID-19 infections. Our results show that the incubation period falls within the range of 2–14 days with 95% confidence and has a mean of around 5 days when approximated using the best-fit lognormal distribution. The mean time from illness onset to hospital admission (for treatment and/or isolation) was estimated at 3–4 days without truncation and at 5–9 days when right truncated. Based on the 95th percentile estimate of the incubation period, we recommend that the length of quarantine should be at least 14 days. The median time delay of 13 days from illness onset to death (17 days with right truncation) should be considered when estimating the COVID-19 case fatality risk.

Serial interval of novel coronavirus (COVID-19) infections

ObjectiveTo estimate the serial interval of novel coronavirus (COVID-19) from information on 28 infector-infectee pairs.MethodsWe collected dates of illness onset for primary cases (infectors) and secondary cases (infectees) from published research articles and case investigation reports. We subjectively ranked the credibility of the data and performed analyses on both the full dataset (n=28) and a subset of pairs with highest certainty in reporting (n=18). In addition, we adjusting for right truncation of the data as the epidemic is still in its growth phase.ResultsAccounting for right truncation and analyzing all pairs, we estimated the median serial interval at 4.0 days (95% credible interval [CrI]: 3.1, 4.9). Limiting our data to only the most certain pairs, the median serial interval was estimated at 4.6 days (95% CrI: 3.5, 5.9).ConclusionsThe serial interval of COVID-19 is shorter than its median incubation period. This suggests that a substantial proportion of secondary transmission may occur prior to illness onset. The COVID-19 serial interval is also shorter than the serial interval of severe acute respiratory syndrome (SARS), indicating that calculations made using the SARS serial interval may introduce bias.Highlights-The serial interval of novel coronavirus (COVID-19) infections was estimated from a total of 28 infector-infectee pairs.-The median serial interval is shorter than the median incubation period, suggesting a substantial proportion of pre-symptomatic transmission.-A short serial interval makes it difficult to trace contacts due to the rapid turnover of case generations.

Power calculations for cluster randomized trials (CRTs) with right-truncated Poisson-distributed outcomes: a motivating example from a malaria vector control trial

Background Cluster randomized trials (CRTs) are increasingly used to study the efficacy of interventions targeted at the population level. Formulae exist to calculate sample sizes for CRTs, but they assume that the domain of the outcomes being considered covers the full range of values of the considered distribution. This assumption is frequently incorrect in epidemiological trials in which counts of infection episodes are right-truncated due to practical constraints on the number of times a person can be tested. Methods Motivated by a malaria vector control trial with right-truncated Poisson-distributed outcomes, we investigated the effect of right-truncation on power using Monte Carlo simulations. Results The results demonstrate that the adverse impact of right-truncation is directly proportional to the magnitude of the event rate, λ, with calculations of power being overestimated in instances where right-truncation was not accounted for. The severity of the adverse impact of right-truncation on power was more pronounced when the number of clusters was ≤30 but decreased the further the right-truncation point was from zero. Conclusions Potential right-truncation should always be accounted for in the calculation of sample size requirements at the study design stage.

Incubation Period and Other Epidemiological Characteristics of 2019 Novel Coronavirus Infections with Right Truncation: A Statistical Analysis of Publicly Available Case Data

The geographic spread of 2019 novel coronavirus (COVID-19) infections from the epicenter of Wuhan, China, has provided an opportunity to study the natural history of the recently emerged virus. Using publicly available event-date data from the ongoing epidemic, the present study investigated the incubation period and other time intervals that govern the epidemiological dynamics of COVID-19 infections. Our results show that the incubation period falls within the range of 2–14 days with 95% confidence and has a mean of around 5 days when approximated using the best-fit lognormal distribution. The mean time from illness onset to hospital admission (for treatment and/or isolation) was estimated at 3–4 days without truncation and at 5–9 days when right truncated. Based on the 95th percentile estimate of the incubation period, we recommend that the length of quarantine should be at least 14 days. The median time delay of 13 days from illness onset to death (17 days with right truncation) should be considered when estimating the COVID-19 case fatality risk.