Corona virus survival analysis
Jan. 27, 2021. United Kingdom survival analysis before and after B.1.1.7 variant
May 6, 2021. India survival analysis after latest surge (March 15, 2021)
India reported case fatality rate was over 3% a year ago. It is now 0.71%. The survival function nonparametric least squares estimate (nplse), P[Days from case to death <= 50] = 1.55%, in the latest surge, looking back 7 days. (The npmle starts March 15.)
Graph shows UK survival function simultaneous estimates from Sept.-Dec. and Dec.-Jan. 2021, when B.1.1.7 variant was widespread. September surge fatality rate was 2.53%, and Dec.-Jan. is 5.23%. Survival function estimates are close for first few weeks of illness.
The report "These are Generic Maximum Likeli..." in the attachments gives "survival" function estimates and forecasts, for both death and recovery, and their applications to test treatment hypotheses and vaccine efficacy, resource allocation, and logistics and risk. Data are daily confirmed case, death, and recovery counts. Methods are nonparametric maximum likelihood and least squares estimation, ergodicity, bootstrap, and matrix algebra for logistics and transient Markov SIR model of Susceptible, Infectious, and Removed (by death, cure, or quarantine).
Infections have been increasing. This requires modified least-squares using deaths since Sept. 13 in US and since Oct. 3 in California. If you want specific locality survival function estimates, please let me know. I have updated US, California, Sweden, Norway, DR Congo, and UK.
CFR (Case Fatality Rate = deaths/cases) is biased until an epidemic is over, because of cycles and because not every case has died or recovered. Survival function estimates, P[Death date – Confirmed case date > t] or
P[Recovery date – Confirmed case date > t], provide time-specific information relevant for hypothesis testing, resource allocation, SIR actuarial transition rates, and unbiased CFR.
Table 1. Biased CFR and unbiased survival function death rate per confirmed case (nonparametric least squares).
SARS (2006) survival function was ~91% 5 weeks from case confirmation; i.e., CFR = 9%. MERS (2013-2014) survival function was ~60% 3 weeks; i.e., CFR = 40%. These estimates agree with CFRs published after the epidemics ended [Fauci et al., NEJM editorial March 27, 2020]. Closeness of biased CFR to unbiased is a lagging indicator of epidemic end.
When will it end?
Different countries and epidemics have different trajectories. China’s Hubei Province, home of the Wuhan market, reported no confirmed cases for over a week and then quit reporting. The percentage of Hubei Province population cases is 0.12%. It took 6-8 weeks of quarantine to apparently control the corona virus in China.
How long will I be sick?
The US means conditional on death or recovery are 16 and 26 days. The modes are 7 (death) and 9 (recovery) days. California death forecasts:
Figure 2. Simultaneous estimates of death and cure survival functions.
Please see *.docx or *.pdf file below for details and recommendations.
Figure 3. US County survival function estimates. Lowest curves are Santa Clara, San Mateo, San Bernardino, and Los Angeles counties
Broom chart of survival function estimates from subsets of data is in figure 4. All except Feb-Mar R(t) are from beginning of March to end of 1st, 2nd, 3rd weeks and March 31. Pre-March cases were added to March case counts, multiplied by 1-CFR. The lower, shorter lines indicate that the survival function estimates are improving over time, currently P[Life > 60 days] = 89%.
Figure 4. Early US survival function broom chart. Later broom charts indicate convergence of estimates.
Please read either attachment "These are generic...*" for details, explanations, "Why Kill Controls?" https://sites.google.com/site/fieldreliability/why-kill-controls, and additional information on COVID-19 survival analyses and their applications. The Aug2020.* files are presentation to ASQ Silicon Valley statistics discussion group August 12.