Estimating the infection and case fatality ratio for COVID-19 using age-adjusted data from the outbreak on the Diamond Princess cruise ship

Abstract

Adjusting for delay from confirmation-to-death, we estimated case and infection fatality ratios (CFR, IFR) for COVID-19 on the Diamond Princess ship as 2.3% (0.75%–5.3%) and 1.2% (0.38–2.7%). Comparing deaths onboard with expected deaths based on naive CFR estimates using China data, we estimate IFR and CFR in China to be 0.5% (95% CI: 0.2–1.2%) and 1.1% (95% CI: 0.3–2.4%) respectively.

Aim
To estimate the infection and case fatality ratio of COVID-19, using data from passengers of the Diamond Princess cruise ship while correcting for delays between confirmation-and-death, and age-structure of the population.

Full text

Estimating the infection and case fatality ratio for COVID-19
using age-adjusted data from the outbreak on the Diamond
Princess cruise ship
Timothy W Russell1*, Joel Hellewell1†, Christopher I Jarvis1†, Kevin Van Zandvoort1†, Sam
Abbott1, Ruwan Ratnayake1,2, CMMID COVID-19 working group, Stefan Flasche1, Rosalind
M Eggo1, W John Edmunds1, Adam J Kucharski1
* corresponding author: timothy.russell@lshtm.ac.uk
1 Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious
Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, United
Kingdom
2 Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical
Medicine, London, United Kingdom
3 The members of the Centre for the Mathematical Modelling of Infectious Diseases
(CMMID) COVID-19 working group are listed at the end of the article
† authors contributed equally
Aim
To estimate the infection and case fatality ratio of COVID-19, using data from passengers of
the Diamond Princess cruise ship while correcting for delays between confirmation-and-
death, and age-structure of the population.
Abstract
Adjusting for delay from confirmation-to-death, we estimated case and infection fatality ratios
(CFR, IFR) for COVID-19 on the Diamond Princess ship as 1.2% (0.38–2.7%) and 2.3%
(0.75%–5.3%). Comparing deaths onboard with expected deaths based on naive CFR
estimates using China data, we estimate IFR and CFR in China to be 0.5% (95% CI: 0.2–
1.2%) and 1.1% (95% CI: 0.3–2.4%) respectively.
Main text
In real-time, estimates of the case fatality ratio (CFR) and infection fatality ratio (IFR) can be
biased upwards by under-reporting of cases and downwards by failure to account for the delay
from confirmation-to-death. Collecting detailed epidemiological information from a closed
population such as the quarantined Diamond Princess can produce a more comprehensive
description of asymptomatic and symptomatic cases and their subsequent outcomes. Using data
from the Diamond Princess, and adjusting for delay from confirmation-to-outcome and age-
structure of the ship’s occupants, we estimated the IFR and CFR for the outbreak in China.
As of 3rd March 2020, there have been 92,809 confirmed cases of coronavirus disease 2019
(COVID-19), with 3,164 deaths [1]. On 1st February 2020, a patient tested positive for COVID-19
in Hong Kong; they disembarked from the Diamond Princess cruise ship on the 25th January
[2,3]. This patient had onset of symptoms on the 19th January, one day before boarding the ship
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[2]. Upon returning to Yokohama, Japan, on February 3rd, the ship was held in quarantine,
during which testing was performed in order to measure COVID-19 infections among the 3,711
passengers and crew members onboard.
Passengers were initially to be held in quarantine for 14 days. However, those that had intense
exposure to the confirmed case-patient, such as sharing a cabin, were held in quarantine beyond
the initial 14-day window [3]. By 20th February, there were 634 confirmed cases onboard (17%),
with 328 of these asymptomatic (asymptomatic cases were either self-assessed or tested
positive before symptom onset) [3]. Overall 3,063 PCR tests were performed among passengers
and crew members. Testing started among the elderly passengers, descending by age [3]. For
details on the testing procedure, see [2] and [3].
Adjusting for outcome delay in CFR estimates
During an outbreak, the so-called naive CFR (nCFR), i.e. the ratio of reported deaths date to
reported cases to date, will underestimate the true CFR because the outcome (recovery or
death) is not known for all cases [4,5]. We can therefore estimate the true denominator for the
CFR (i.e. the number of cases with known outcomes) by accounting for the delay from
confirmation-to-death [5].
We assumed the delay from confirmation-to-death followed the same distribution as estimated
hospitalisation-to-death, based on data from the COVID-19 outbreak in Wuhan, China, between
the 17th December 2019 and the 22th January 2020, accounting right-censoring in the data as a
result of as-yet-unknown disease outcomes (Figure 1, panels A and B) [6]. As a sensitivity
analysis, we also consider raw “non-truncated” distributions, which do not account for censoring;
the raw and truncated distributions have a mean of 8.6 days and 13 days respectively.
To correct the CFR, we use the case and death incidence data to estimate the number of cases
with known outcomes [5]:
where is the daily case incidence at time , is the proportion of cases with delay between
onset or hospitalisation and death. represents the underestimation of the known outcomes [5]
and is used to scale the value of the cumulative number of cases in the denominator in the
calculation of the cCFR. Finally, we used the measured proportions of asymptomatic to
symptomatic cases on the Diamond Princess to scale the corrected CFR (cCFR) to estimate the
infection fatality ratio (IFR).
Corrected IFR and CFR estimates
We estimated that the all-age cIFR on the Diamond Princess was 1.2% (0.38–2.7%) and the
cCFR was 2.3% (0.75–5.3%) (Table 1). Using the age distribution of cases and deaths on the
ship [2,3], we estimated that for individuals aged 70 and over, the cIFR was 9.0% (3.8–17%) and
the cCFR was 18% (7.3–33%) (Table 1). The 95% confidence intervals were calculated with an
exact binomial test with death count and either cases or known outcomes (depending on whether
it was an interval for the naive or corrected estimate).
Using the age-stratified nCFR estimates reported in a large study in China [7], we then
calculated the expected number of deaths of people who were onboard the ship in each age
group, assuming this nCFR estimate was accurate. This produced a total of 15.15 expected
deaths, which gives a nCFR estimate of 5% (15.15/301) for Diamond Princess (Table 2), which
falls within the top end of our 95% CI. As our corrected cCFR for Diamond Princess was 2.3%
(0.75% - 5.3%), this suggests we need to multiply the nCFR estimates in China [7] by a factor
46% (95% CI: 15–105%) to obtain the correct value. As the raw overall nCFR reported in the
China data was 2.3% [7], this suggests the cCFR in China during that period was 1.1% (95% CI:
0.3-2.4%) and the IFR was 0.5% (95% CI: 0.2-1.2%). Based on cases and deaths reported in
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China up to 4th March 2020, nCFR = 2984/80422*100 = 3.71% (95% CI 3.58% - 3.84%); this
naive value is significantly higher than the corrected CFR we estimate here.
Age Range cIFR cCFR
Hospitalisation
-
to
-
death
Distribution
All ages
combined 0.91% (0.11% -
4.3%) 1.9% (0.60% -
4.3%) Non-truncated (Figure 1A)
1.2% (0.39% -
2.7%) 2.3% (0.75% -
5.3%) Truncated (Figure 1B)
70+
7.3% (3.0%
-
14%)
14% (6.0%
-
27%)
Non
-
truncated (Figure 1A)
9.0% (3.8% - 17%)
18% (7.3% - 33%)
Truncated (Figure 1B)
Table 1: cIFR and cCFR estimates calculated using the reported case and death data on the
Diamond Princess cruise ship [2]. Correction was performed using equation (1) and the
hospitalisation-to-death distribution in [6].
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Figure 1: The time-to-death distributions and case and death data used to calculate the cCFR
estimates. Panel A: the delay distributions of hospitalisation-to-death; both are lognormal
distributions fitted and reported in Linton et al. using data from the outbreak in Wuhan, China.
The non-truncated distribution has a mean of 8.6 days and SD of 6.7 days; the right-truncated
distribution has a mean of 13 days and SD of 12.7 days. Panels B and C: the case and death
timeseries (respectively) of passengers onboard the ship.
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Age
Range No. of
passengers Symp.
cases Asymp.
cases nCFR
Expected
deaths using
nCFR
Observed
deaths on
cruise ship
0 - 9
16
0
1
0.0%
(0.0% -
0.9%)
0 (0 - 0)
0
10 - 19
23
2
3
0.2%
(0.0% -
1.0%)
0 (0 - 0)
0
20 - 29
347
25
3
0.2%
(0.1% -
0.4%)
0.05 (0.02 -
0.10)
0
30 - 39
428
27
7
0.2%
(0.1% -
0.4%)
0.06 (0.04 -
0.10)
0
40
-
49
334
19
8
0.4%
(0.3% -
0.6%)
0.08 (0.06
-
0.12)
0
50
-
59
398
28
31
1.3%
(1.1% -
1.5%)
0.36 (0.31
-
0.43)
0
60 - 69
923
76
101
3.6%
(3.2% -
4.0%)
2.74 (2.5 - 3.1)
0
70
-
79
1015
95
139
8.0%
(7.2% -
8.9%)
7.6 (6.8
-
8.4)
6
80
-
89
216
29
25
14.8%
(13.0% -
16.7%)
4.28 (3.8
-
4.9)
1
Totals
3711
301
318
15.15 (13.5
-
17.1)
7
Table 2: Age stratified data of symptomatic (symp.) and asymptomatic (asymp.) cases on-board
the Diamond Princess [2], [3], along with the nCFR estimates given in [7], the expected number
of cases in each age group if the nCFR estimates were correct where the total number of
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expected deaths under these estimates was 15.15 and age stratified observed/expected death
ratios.
The case fatality ratio is challenging to accurately estimate in real time [8], especially for an
infection with attributes similar to SARS-CoV-2, which has a delay of almost two weeks between
confirmation and death, strong effects of age-dependence and comorbidities on mortality risk,
and likely under-reporting of cases in many settings [6]. Using an age-stratified adjustment, we
accounted for changes in known outcomes over time. By applying the method to Diamond
Princess data, we focus on a setting that is likely to have lower reporting error because large
numbers were tested and the test has high sensitivity.
The average age onboard the ship was 58, so our estimates of cCFR cannot directly be applied
to a younger population; we therefore scaled our estimates to obtain values for a population
equivalent to those in the early China outbreak. There were some limitations to our analysis.
Cruise ship passengers may have a different health status to the general population of their
home countries, due to health requirements to embark on a multi-week holiday, or differences
related to socio-economic status or comborbities. Deaths only occurred in individuals 70 years or
older, so we were not able to generate age-specific cCFRs; the fatality risk may also be
influenced by differences in healthcare between countries. Because of likely age-specific
differences in reporting, we focused on overall cCFR in China, rather than calculating age-
specific cCFRs [7].
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author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the(which was not peer-reviewed) The copyright holder for this preprint .https://doi.org/10.1101/2020.03.05.20031773doi: medRxiv preprint

Author contributions:
TWR, AJK and WJE conceived of the study and collected the data. TWR, AJK and SA coded the
methods. TWR and JH wrote the first draft of the manuscript with feedback from all other
authors. KvZ, TWR, SA and CIJ worked on the statistical aspects of the study. All authors read
and approved the final version of the manuscript. Each member of the CMMID COVID-19
working group contributed in processing, cleaning an interpretation of data, interpreted findings,
contributed to the manuscript, and approved the work for publication.
Acknowledgements:
TWR, JH SA, SF and AJK are supported by the Wellcome Trust (grant numbers: 206250/Z/17/Z,
210758/Z/18/Z, 210758/Z/18/Z, 210758/Z/18/Z, 208812/Z/17/Z, 206250/Z/17/Z). CIJ is supported
by Global Challenges Research Fund (GCRF) project ‘RECAP’ managed through RCUK and
ESRC (ES/P010873/1). KvZ is supported by Elrha’s Research for Health in Humanitarian Crises
(R2HC) Programme, which aims to improve health outcomes by strengthening the evidence
base for public health interventions in humanitarian crises. The R2HC programme is funded by
the UK Government (DFID), the Wellcome Trust, and the UK National Institute for Health
Research (NIHR). RR is supported by Canadian Institutes of Health Research (Award no. DFS-
164266). RME is supported by HDR UK (grant: MR/S003975/1)
CMMID nCoV working group funding statements: Thibaut Jombart (RCUK/ESRC (grant:
ES/P010873/1); UK PH RST; NIHR HPRU Modelling Methodology), Amy Gimma (GCRF
(ES/P010873/1)), Nikos I Bosse (no funding statement to declare), Alicia Rosello (NIHR (grant:
PR-OD-1017-20002)), Mark Jit (Gates (INV-003174), NIHR (16/137/109)), James D Munday
(Wellcome Trust (grant: 210758/Z/18/Z)), Billy J Quilty (NIHR (16/137/109)), Petra Klepac (Gates
(INV-003174)), Hamish Gibbs (NIHR (ITCRZ 03010)), Yang Liu (Gates (INV-003174), NIHR
(16/137/109)), Sebasitan Funk (Wellcome Trust (grant: 210758/Z/18/Z)), Samuel Clifford
(Wellcome Trust (grant: 208812/Z/17/Z)), Fiona Sun (NIHR EPIC grant (16/137/109)), Kiesha
Prem (Gates (INV-003174)), Charlie Diamond (NIHR (16/137/109)), Nicholas Davies (NIHR
(HPRU-2012-10096)), Carl A B Pearson
Code Availability
All of the data and the code required to reproduce the figures and results of this study can be
found at the public github repository: https://github.com/thimotei/cCFRDiamondPrincess.
Members of the Centre for the Mathematical Modelling of
Infectious Diseases (CMMID) nCoV working group:
The following authors were part of the Centre for Mathematical Modelling of Infectious Disease
2019-nCoV working group. Thibaut Jombart, Amy Gimma, Nikos I Bosse, Alicia Rosello, Mark
Jit, James D Munday, Billy J Quilty, Petra Klepac, Hamish Gibbs, Yang Liu, Sebasitan Funk,
Samuel Clifford, Fiona Sun, Kiesha Prem, Charlie Diamond, Nicholas Davies, Carl A B Pearson.
Conflict of interest:
None declared.
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