Wednesday 12 February 2020

The Novel Coronavirus (COVID-19) and Problems with Statistics

That there have been over forty-three  thousand confirmed cases of  novel Coronavirus (COVID-19) and over 1,000 deaths is both tragic and troubling. 
   
A number of people have questioned the statistics surrounding the outbreak.  My main concern with the statistics being provided is the estimate that the mortality rate is 2% of confirmed cases.   I am not suggesting that when reported deaths are compared with confirmed cases the death rate does not appear  to be 2 percent.   However, that calculation never took into account  the confirmed cases where the person had neither died nor recovered, and that many of those patients will die.    The simplest way of explaining this is that on February 11th there were  43,103 total cases worldwide, 1,116 deaths and 5,127 recoveries. This leaves 36868 confirmed cases being treated.  It is reasonable to expect that many of those will die, particularly as WHO reports 7333 severe cases in China.  If one applies WHO’s estimate of two percent, then we can expect about 700 of those additional confirmed cases to die, which paradoxically results in a mortality rate of about four percent.

The Mortality Rate has Increased



A second problem with fixating on 2 percent when comparing deaths with confirmed cases is that the death rate is increasing.   This can be seen from the following:
-  As of February 5  there were 24363  confirmed cases in China and 491  deaths in China, which is a death rate of  2.01 % .     
- As of February 7 there were 31 211  confirmed cases in China and 637 deaths in China, which is a death rate of 2.04 %
- As of February 8 there were  34 598 confirmed cases in China and 723 deaths in China, which is a death rate of 2.09 %
 - As of February 9  there were  37 251  confirmed cases in China and  812  deaths in China, which is a death rate of 2.18%.  
 - As of February 10  there were  40 235  confirmed cases in China and  909 deaths in China, which is a death rate of 2.25 %.     
-  As of February 11 there were 42 708  confirmed cases in China and 1017 deaths in China, which is a death rate of 2.38 % .
       
The mortality rate is going up because deaths continue to increase while the increase in the number of confirmed cases has slowed down.   It is reasonable to assume that the mortality rate will keep increasing for at least the next two weeks.  This is because  China’s efforts to quarantine the disease will become even more successful and the number of additional confirmed cases will drop off.   As additional cases drop off, deaths will start to catch up with cases, and the mortality rate will increase.

Severe Cases



An additional  reason to question that the mortality rate will be close to two percent is that China and the World Health Organization are  releasing figures for  severe cases and  recoveries 

WHO’s Novel Coronavirus (2019nCoV) Situation Report –21 which provides  data reported as of February 10th lists 6484 severe cases in China.  WHO’s Situation Report -22 which provides  data reported as of February 11th lists 7333 severe cases in China   If one assumes that all of the Severe cases result in death, then the mortality rate for Coronavirus for February 10th is 18 percent [= 100 (909  + 6484)/ 40 235] and for  February 11th is 19.5 percent [= 100 (1017  + 7333)/ 42708].   However, as WHO defines a Severe illness according to any of the following criteria: (1)  shortness of breath ; (2) respiratory rate more than 30 bpm; (3) hypoxemia; (4) chest X-ray with multilobar infiltrates or pulmonary infiltration progressed more than 50% within 24 - 48 hours,  not all with severe coronavirus will die.   Conversely, not all confirmed cases have yet had time to develop into severe cases, and one would expect many recent cases to become severe.

A recent study of 138 patients with confirmed coronavirus  admitted to Zhongnan Hospital of Wuhan University from January 1 to January 28, 2020 provides some guidance on the mortality rate for severe cases.   As of February 3 (the closing date for the study), Dr. Dawei Wang and the additional  authors found that 36  of the patients (26%) required admission to the intensive care unit, 6 had died (4.3%), 85 patients (61.6%) were still hospitalized, and 47 patients (34.1%) had been discharged.  Of the 36 patients admitted to the ICU, 11 were still in the ICU, 9 had been discharged to home, 10 had been transferred to the general wards, and 6 had died. Of the 11 patients who remained in the ICU, 6 received invasive ventilation and 5 noninvasive. 

If one splits the 36 ICU patients into two groups [Dead plus invasive ventilation ] and [ discharged, plus transferred to general ward, plus noninvasive] this suggests a mortality rate of 33%  [= 12/36 x 100] for severe cases.   If one compares only those who died with the total of those who had been discharged from ICU and those transferred to general ward, this suggests a mortality rate of 24  % [= 100x 6/(6+9+10)]

If one then recalculates the death rate for Situation report 21 (February 10th) assuming 33% of severe cases are considered likely to die, then the mortality rate is 7.6%   [= 100 (909 + .33 x 6484) / 40235] resulting from 3048 actual and estimated deaths.  If one recalculates the death rate for Situation report 21 assuming 24% of severe cases are considered likely to die, then the mortality rate is 6%   [= 100 (909 + .24 x 6484) / 40235] resulting from 2465 actual and estimated deaths.

Recoveries


As of February 11th  there were 1018 deaths worldwide and 5,127  recoveries worldwide.   Assuming that  those still undergoing treatment will show the same ratio between deaths and recovery, those numbers  equate to a mortality rate of 16.5%.

On a positive note, the mortality rate based on that calculation appears to be dropping. 
                                   

Deaths Trail New Cases


Another reason to question that the death rate is two percent is that deaths always trail new cases. By this I mean that it takes weeks for a person infected with the disease to either recover or die.    A tragic example of this is the recent death of doctor Li Wenliang, the person who first raised the alarm.  It is reasonable to assume that he was infected in December or the first two weeks of January.   He died on February 7th.   He may not have shown symptoms until about ten to fourteen days after infection.   If so then his treatment lasted about two to  three weeks.

At this point in time there is no way of calculating the  average length of time that it takes for those who are confirmed with Coronavirus to die (or recover).  In their paper Dr. Dawei Wang and the other medical doctors report the time from onset to dyspnea was 5 days and 8 days to ARDS (acute respiratory distress syndrome ).    For the purpose of an example, I will assume that on average it takes on average ten days for those who are confirmed with Coronavirus to die (or recover).  On February 1st there were 11821 confirmed  cases in China.  If one assumes that the total deaths in China as of February 11  mainly result from those that were reported cases on February 1st, then the mortality rate is 5.9%.   [= 100 x 1017/ 11831].
   

Comparison with SARS and MERS

   
Severe acute respiratory syndrome (SARS) is a viral  disease caused by the SARS coronavirus (SARS-CoV).    Middle East respiratory syndrome (MERS) ] is a viral infection caused by the MERS coronavirus (MERS-CoV).   For SARS there were 774 deaths out of 8,096 reported cases for a mortality rate of 9.6 percent.  Over 2,000 cases of MERS were  reported with about 600 deaths, with a mortality rate of about 30%.    A mortality rate of from 6% to 16.5% for the current coronavirus outbreak  accords with the mortality rates for SARS and MERS.

Perplexingly, my calculations are only applicable to confirmed coronavirus cases in China.  The mortality rate outside China appears to be less than one percent.

Sincerely,
Christopher Brett
Ottawa
   

References


Dawei Wang, MD ; Bo Hu, MD ; Chang Hu, MD ;   Fangfang Zhu, MD ; Xing Liu, MD; Jing Zhang, MD ; Binbin Wang, MD; Hui Xiang, MD; Zhenshun Cheng, MD; Yong Xiong, MD; Yan Zhao, MD; Yirong Li, MD; Xinghuan Wang, MD; Zhiyong Peng, MD, 2020
Clinical Characteristics of 138 Hospitalized Patients With 2019 Novel Coronavirus–Infected Pneumonia in Wuhan, China | Critical Care Medicine | JAMA | 
JAMA. Published online February 7, 2020. doi:10.1001/jama.2020.1585
https://jamanetwork.com/journals/jama/fullarticle/2761044

World Health Organization
SITUATION REPORT  - 5 ;  25  JANUARY 2020
Severe illness: According to any of the following criteria:  (1)  shortness of breath ; (2) respiratory rate more than 30 bpm; (3) hypoxemia; (4) chest X-ray with multilobar infiltrates or pulmonary infiltration progressed more than 50% within 24 - 48 hours.