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.

A comparison of two frameworks for multi-state modelling, applied to outcomes after hospital admissions with COVID-19.

We compare two multi-state modelling frameworks that can be used to represent dates of events following hospital admission for people infected during an epidemic. The methods are applied to data from people admitted to hospital with COVID-19, to estimate the probability of admission to intensive care unit, the probability of death in hospital for patients before and after intensive care unit admission, the lengths of stay in hospital, and how all these vary with age and gender. One modelling framework is based on defining transition-specific hazard functions for competing risks. A less commonly used framework defines partially-latent subpopulations who will experience each subsequent event, and uses a mixture model to estimate the probability that an individual will experience each event, and the distribution of the time to the event given that it occurs. We compare the advantages and disadvantages of these two frameworks, in the context of the COVID-19 example. The issues include the interpretation of the model parameters, the computational efficiency of estimating the quantities of interest, implementation in software and assessing goodness of fit. In the example, we find that some groups appear to be at very low risk of some events, in particular intensive care unit admission, and these are best represented by using 'cure-rate' models to define transition-specific hazards. We provide general-purpose software to implement all the models we describe in the flexsurv R package, which allows arbitrarily flexible distributions to be used to represent the cause-specific hazards or times to events.

Estimation of the impact of hospital-onset SARS-CoV-2 infections on length of stay in English hospitals using causal inference.

BACKGROUND: From March 2020 through August 2021, 97,762 hospital-onset SARS-CoV-2 infections were detected in English hospitals. Resulting excess length of stay (LoS) created a potentially substantial health and economic burden for patients and the NHS, but we are currently unaware of any published studies estimating this excess. METHODS: We implemented appropriate causal inference methods to determine the extent to which observed additional hospital stay is attributable to the infection rather than the characteristics of the patients. Hospital admissions records were linked to SARS-CoV-2 test data to establish the study population (7.5 million) of all non-COVID-19 admissions to English hospitals from 1st March 2020 to 31st August 2021 with a stay of at least two days. The excess LoS due to hospital-onset SARS-CoV-2 infection was estimated as the difference between the mean LoS observed and in the counterfactual where infections do not occur. We used inverse probability weighted Kaplan-Meier curves to estimate the mean survival time if all hospital-onset SARS-CoV-2 infections were to be prevented, the weights being based on the daily probability of acquiring an infection. The analysis was carried out for four time periods, reflecting phases of the pandemic differing with respect to overall case numbers, testing policies, vaccine rollout and prevalence of variants. RESULTS: The observed mean LoS of hospital-onset cases was higher than for non-COVID-19 hospital patients by 16, 20, 13 and 19 days over the four phases, respectively. However, when the causal inference approach was used to appropriately adjust for time to infection and confounding, the estimated mean excess LoS caused by hospital-onset SARS-CoV-2 was: 2.0 [95% confidence interval 1.8-2.2] days (Mar-Jun 2020), 1.4 [1.2-1.6] days (Sep-Dec 2020); 0.9 [0.7-1.1] days (Jan-Apr 2021); 1.5 [1.1-1.9] days (May-Aug 2021). CONCLUSIONS: Hospital-onset SARS-CoV-2 is associated with a small but notable excess LoS, equivalent to 130,000 bed days. The comparatively high LoS observed for hospital-onset COVID-19 patients is mostly explained by the timing of their infections relative to admission. Failing to account for confounding and time to infection leads to overestimates of additional length of stay and therefore overestimates costs of infections, leading to inaccurate evaluations of control strategies.

Trends in COVID-19 hospital outcomes in England before and after vaccine introduction, a cohort study.

Widespread vaccination campaigns have changed the landscape for COVID-19, vastly altering symptoms and reducing morbidity and mortality. We estimate trends in mortality by month of admission and vaccination status among those hospitalised with COVID-19 in England between March 2020 to September 2021, controlling for demographic factors and hospital load. Among 259,727 hospitalised COVID-19 cases, 51,948 (20.0%) experienced mortality in hospital. Hospitalised fatality risk ranged from 40.3% (95% confidence interval 39.4-41.3%) in March 2020 to 8.1% (7.2-9.0%) in June 2021. Older individuals and those with multiple co-morbidities were more likely to die or else experienced longer stays prior to discharge. Compared to unvaccinated people, the hazard of hospitalised mortality was 0.71 (0.67-0.77) with a first vaccine dose, and 0.56 (0.52-0.61) with a second vaccine dose. Compared to hospital load at 0-20% of the busiest week, the hazard of hospitalised mortality during periods of peak load (90-100%), was 1.23 (1.12-1.34). The prognosis for people hospitalised with COVID-19 in England has varied substantially throughout the pandemic and according to case-mix, vaccination, and hospital load. Our estimates provide an indication for demands on hospital resources, and the relationship between hospital burden and outcomes.

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.

Hospitalization and Mortality Risk for COVID-19 Cases With SARS-CoV-2 AY.4.2 (VUI-21OCT-01) Compared to Non-AY.4.2 Delta Variant Sublineages.

To investigate if the AY.4.2 sublineage of the SARS-CoV-2 delta variant is associated with hospitalization and mortality risks that differ from non-AY.4.2 delta risks, we performed a retrospective cohort study of sequencing-confirmed COVID-19 cases in England based on linkage of routine health care datasets. Using stratified Cox regression, we estimated adjusted hazard ratios (aHR) of hospital admission (aHR = 0.85; 95% confidence interval [CI], .77-.94), hospital admission or emergency care attendance (aHR = 0.87; 95% CI, .81-.94), and COVID-19 mortality (aHR = 0.85; 95% CI, .71-1.03). The results indicate that the risks of hospitalization and mortality are similar or lower for AY.4.2 compared to cases with other delta sublineages.

Comparative analysis of the risks of hospitalisation and death associated with SARS-CoV-2 omicron (B.1.1.529) and delta (B.1.617.2) variants in England: a cohort study.

BACKGROUND: The omicron variant (B.1.1.529) of SARS-CoV-2 has demonstrated partial vaccine escape and high transmissibility, with early studies indicating lower severity of infection than that of the delta variant (B.1.617.2). We aimed to better characterise omicron severity relative to delta by assessing the relative risk of hospital attendance, hospital admission, or death in a large national cohort. METHODS: Individual-level data on laboratory-confirmed COVID-19 cases resident in England between Nov 29, 2021, and Jan 9, 2022, were linked to routine datasets on vaccination status, hospital attendance and admission, and mortality. The relative risk of hospital attendance or admission within 14 days, or death within 28 days after confirmed infection, was estimated using proportional hazards regression. Analyses were stratified by test date, 10-year age band, ethnicity, residential region, and vaccination status, and were further adjusted for sex, index of multiple deprivation decile, evidence of a previous infection, and year of age within each age band. A secondary analysis estimated variant-specific and vaccine-specific vaccine effectiveness and the intrinsic relative severity of omicron infection compared with delta (ie, the relative risk in unvaccinated cases). FINDINGS: The adjusted hazard ratio (HR) of hospital attendance (not necessarily resulting in admission) with omicron compared with delta was 0·56 (95% CI 0·54-0·58); for hospital admission and death, HR estimates were 0·41 (0·39-0·43) and 0·31 (0·26-0·37), respectively. Omicron versus delta HR estimates varied with age for all endpoints examined. The adjusted HR for hospital admission was 1·10 (0·85-1·42) in those younger than 10 years, decreasing to 0·25 (0·21-0·30) in 60-69-year-olds, and then increasing to 0·47 (0·40-0·56) in those aged at least 80 years. For both variants, past infection gave some protection against death both in vaccinated (HR 0·47 [0·32-0·68]) and unvaccinated (0·18 [0·06-0·57]) cases. In vaccinated cases, past infection offered no additional protection against hospital admission beyond that provided by vaccination (HR 0·96 [0·88-1·04]); however, for unvaccinated cases, past infection gave moderate protection (HR 0·55 [0·48-0·63]). Omicron versus delta HR estimates were lower for hospital admission (0·30 [0·28-0·32]) in unvaccinated cases than the corresponding HR estimated for all cases in the primary analysis. Booster vaccination with an mRNA vaccine was highly protective against hospitalisation and death in omicron cases (HR for hospital admission 8-11 weeks post-booster vs unvaccinated: 0·22 [0·20-0·24]), with the protection afforded after a booster not being affected by the vaccine used for doses 1 and 2. INTERPRETATION: The risk of severe outcomes following SARS-CoV-2 infection is substantially lower for omicron than for delta, with higher reductions for more severe endpoints and significant variation with age. Underlying the observed risks is a larger reduction in intrinsic severity (in unvaccinated individuals) counterbalanced by a reduction in vaccine effectiveness. Documented previous SARS-CoV-2 infection offered some protection against hospitalisation and high protection against death in unvaccinated individuals, but only offered additional protection in vaccinated individuals for the death endpoint. Booster vaccination with mRNA vaccines maintains over 70% protection against hospitalisation and death in breakthrough confirmed omicron infections. FUNDING: Medical Research Council, UK Research and Innovation, Department of Health and Social Care, National Institute for Health Research, Community Jameel, and Engineering and Physical Sciences Research Council.

Quantifying Efficiency Gains of Innovative Designs of Two-Arm Vaccine Trials for COVID-19 Using an Epidemic Simulation Model

Clinical trials of a vaccine during an epidemic face particular challenges, such as the pressure to identify an effective vaccine quickly to control the epidemic, and the effect that time-space-varying infection incidence has on the power of a trial. We illustrate how the operating characteristics of different trial design elements maybe evaluated using a network epidemic and trial simulation model, based on COVID-19 and individually randomized two-arm trials with a binary outcome. We show that “ring” recruitment strategies, prioritizing participants at an imminent risk of infection, can result in substantial improvement in terms of power in the model we present. In addition, we introduce a novel method to make more efficient use of the data from the earliest cases of infection observed in the trial, whose infection may have been too early to be vaccine-preventable. Finally, we compare several methods of response-adaptive randomization (RAR), discussing their advantages and disadvantages in the context of our model and identifying particular adaptation strategies that preserve power and estimation properties, while slightly reducing the number of infections, given an effective vaccine.

Hospital admission and emergency care attendance risk for SARS-CoV-2 delta (B.1.617.2) compared with alpha (B.1.1.7) variants of concern: a cohort study.

BACKGROUND: The SARS-CoV-2 delta (B.1.617.2) variant was first detected in England in March, 2021. It has since rapidly become the predominant lineage, owing to high transmissibility. It is suspected that the delta variant is associated with more severe disease than the previously dominant alpha (B.1.1.7) variant. We aimed to characterise the severity of the delta variant compared with the alpha variant by determining the relative risk of hospital attendance outcomes. METHODS: This cohort study was done among all patients with COVID-19 in England between March 29 and May 23, 2021, who were identified as being infected with either the alpha or delta SARS-CoV-2 variant through whole-genome sequencing. Individual-level data on these patients were linked to routine health-care datasets on vaccination, emergency care attendance, hospital admission, and mortality (data from Public Health England's Second Generation Surveillance System and COVID-19-associated deaths dataset; the National Immunisation Management System; and NHS Digital Secondary Uses Services and Emergency Care Data Set). The risk for hospital admission and emergency care attendance were compared between patients with sequencing-confirmed delta and alpha variants for the whole cohort and by vaccination status subgroups. Stratified Cox regression was used to adjust for age, sex, ethnicity, deprivation, recent international travel, area of residence, calendar week, and vaccination status. FINDINGS: Individual-level data on 43 338 COVID-19-positive patients (8682 with the delta variant, 34 656 with the alpha variant; median age 31 years [IQR 17-43]) were included in our analysis. 196 (2·3%) patients with the delta variant versus 764 (2·2%) patients with the alpha variant were admitted to hospital within 14 days after the specimen was taken (adjusted hazard ratio [HR] 2·26 [95% CI 1·32-3·89]). 498 (5·7%) patients with the delta variant versus 1448 (4·2%) patients with the alpha variant were admitted to hospital or attended emergency care within 14 days (adjusted HR 1·45 [1·08-1·95]). Most patients were unvaccinated (32 078 [74·0%] across both groups). The HRs for vaccinated patients with the delta variant versus the alpha variant (adjusted HR for hospital admission 1·94 [95% CI 0·47-8·05] and for hospital admission or emergency care attendance 1·58 [0·69-3·61]) were similar to the HRs for unvaccinated patients (2·32 [1·29-4·16] and 1·43 [1·04-1·97]; p=0·82 for both) but the precision for the vaccinated subgroup was low. INTERPRETATION: This large national study found a higher hospital admission or emergency care attendance risk for patients with COVID-19 infected with the delta variant compared with the alpha variant. Results suggest that outbreaks of the delta variant in unvaccinated populations might lead to a greater burden on health-care services than the alpha variant. FUNDING: Medical Research Council; UK Research and Innovation; Department of Health and Social Care; and National Institute for Health Research.

Decreasing hospital burden of COVID-19 during the first wave in Regione Lombardia: an emergency measures context.

BACKGROUND: The aim of this study is to quantify the hospital burden of COVID-19 during the first wave and how it changed over calendar time; to interpret the results in light of the emergency measures introduced to manage the strain on secondary healthcare. METHODS: This is a cohort study of hospitalised confirmed cases of COVID-19 admitted from February-June 2020 and followed up till 17th July 2020, analysed using a mixture multi-state model. All hospital patients with confirmed COVID-19 disease in Regione Lombardia were involved, admitted from February-June 2020, with non-missing hospital of admission and non-missing admission date. RESULTS: The cohort consists of 40,550 patients hospitalised during the first wave. These patients had a median age of 69 (interquartile range 56-80) and were more likely to be men (60%) than women (40%). The hospital-fatality risk, averaged over all pathways through hospital, was 27.5% (95% CI 27.1-28.0%); and steadily decreased from 34.6% (32.5-36.6%) in February to 7.6% (6.3-10.6%) in June. Among surviving patients, median length of stay in hospital was 11.8 (11.6-12.3) days, compared to 8.1 (7.8-8.5) days in non-survivors. Averaged over final outcomes, median length of stay in hospital decreased from 21.4 (20.5-22.8) days in February to 5.2 (4.7-5.8) days in June. CONCLUSIONS: The hospital burden, in terms of both risks of poor outcomes and lengths of stay in hospital, has been demonstrated to have decreased over the months of the first wave, perhaps reflecting improved treatment and management of COVID-19 cases, as well as reduced burden as the first wave waned. The quantified burden allows for planning of hospital beds needed for current and future waves of SARS-CoV-2 i.

Risk factors associated with severe hospital burden of COVID-19 disease in Regione Lombardia: a cohort study.

BACKGROUND: Understanding the risk factors associated with hospital burden of COVID-19 is crucial for healthcare planning for any future waves of infection. METHODS: An observational cohort study is performed, using data on all PCR-confirmed cases of COVID-19 in Regione Lombardia, Italy, during the first wave of infection from February-June 2020. A multi-state modelling approach is used to simultaneously estimate risks of progression through hospital to final outcomes of either death or discharge, by pathway (via critical care or not) and the times to final events (lengths of stay). Logistic and time-to-event regressions are used to quantify the association of patient and population characteristics with the risks of hospital outcomes and lengths of stay respectively. RESULTS: Risks of severe outcomes such as ICU admission and mortality have decreased with month of admission (for example, the odds ratio of ICU admission in June vs March is 0.247 [0.120-0.508]) and increased with age (odds ratio of ICU admission in 45-65 vs 65 + age group is 0.286 [0.201-0.406]). Care home residents aged 65 + are associated with increased risk of hospital mortality and decreased risk of ICU admission. Being a healthcare worker appears to have a protective association with mortality risk (odds ratio of ICU mortality is 0.254 [0.143-0.453] relative to non-healthcare workers) and length of stay. Lengths of stay decrease with month of admission for survivors, but do not appear to vary with month for non-survivors. CONCLUSIONS: Improvements in clinical knowledge, treatment, patient and hospital management and public health surveillance, together with the waning of the first wave after the first lockdown, are hypothesised to have contributed to the reduced risks and lengths of stay over time.

Risk of hospital admission for patients with SARS-CoV-2 variant B.1.1.7: cohort analysis.

OBJECTIVE: To evaluate the relation between diagnosis of covid-19 with SARS-CoV-2 variant B.1.1.7 (also known as variant of concern 202012/01) and the risk of hospital admission compared with diagnosis with wild-type SARS-CoV-2 variants. DESIGN: Retrospective cohort analysis. SETTING: Community based SARS-CoV-2 testing in England, individually linked with hospital admission data. PARTICIPANTS: 839 278 patients with laboratory confirmed covid-19, of whom 36 233 had been admitted to hospital within 14 days, tested between 23 November 2020 and 31 January 2021 and analysed at a laboratory with an available TaqPath assay that enables assessment of S-gene target failure (SGTF), a proxy test for the B.1.1.7 variant. Patient data were stratified by age, sex, ethnicity, deprivation, region of residence, and date of positive test. MAIN OUTCOME MEASURES: Hospital admission between one and 14 days after the first positive SARS-CoV-2 test. RESULTS: 27 710 (4.7%) of 592 409 patients with SGTF variants and 8523 (3.5%) of 246 869 patients without SGTF variants had been admitted to hospital within one to 14 days. The stratum adjusted hazard ratio of hospital admission was 1.52 (95% confidence interval 1.47 to 1.57) for patients with covid-19 infected with SGTF variants, compared with those infected with non-SGTF variants. The effect was modified by age (P<0.001), with hazard ratios of 0.93-1.21 in patients younger than 20 years with versus without SGTF variants, 1.29 in those aged 20-29, and 1.45-1.65 in those aged ≥30 years. The adjusted absolute risk of hospital admission within 14 days was 4.7% (95% confidence interval 4.6% to 4.7%) for patients with SGTF variants and 3.5% (3.4% to 3.5%) for those with non-SGTF variants. CONCLUSIONS: The results suggest that the risk of hospital admission is higher for people infected with the B.1.1.7 variant compared with wild-type SARS-CoV-2, likely reflecting a more severe disease. The higher severity may be specific to adults older than 30 years.

Quantifying Efficiency Gains of Innovative Designs of Two-Arm Vaccine Trials for COVID-19 Using an Epidemic Simulation Model.

Clinical trials of a vaccine during an epidemic face particular challenges, such as the pressure to identify an effective vaccine quickly to control the epidemic, and the effect that time-space-varying infection incidence has on the power of a trial. We illustrate how the operating characteristics of different trial design elements maybe evaluated using a network epidemic and trial simulation model, based on COVID-19 and individually randomized two-arm trials with a binary outcome. We show that "ring" recruitment strategies, prioritizing participants at an imminent risk of infection, can result in substantial improvement in terms of power in the model we present. In addition, we introduce a novel method to make more efficient use of the data from the earliest cases of infection observed in the trial, whose infection may have been too early to be vaccine-preventable. Finally, we compare several methods of response-adaptive randomization (RAR), discussing their advantages and disadvantages in the context of our model and identifying particular adaptation strategies that preserve power and estimation properties, while slightly reducing the number of infections, given an effective vaccine.