| Title: | The BETS Model for Early Epidemic Data |
|---|---|
| Description: | Implements likelihood inference for early epidemic analysis. BETS is short for the four key epidemiological events being modeled: Begin of exposure, End of exposure, time of Transmission, and time of Symptom onset. The package contains a dataset of the trajectory of confirmed cases during the coronavirus disease (COVID-19) early outbreak. More detail of the statistical methods can be found in Zhao et al. (2020) <arXiv:2004.07743>. |
| Authors: | Qingyuan Zhao [aut, cre], Nianqiao Ju [aut] |
| Maintainer: | Qingyuan Zhao <[email protected]> |
| License: | CC BY 4.0 |
| Version: | 1.0.0 |
| Built: | 2024-08-19 04:47:11 UTC |
| Source: | https://github.com/qingyuanzhao/bets.covid19 |
Processing age to print its distribution
age.process(age)age.process(age)
age |
a vector of age, each entry is either a number (like 34) or age by decade (like 30s) |
each age is either repeated 10 times or expanded to 10 numbers (for example, 30s is expanded to 30, 31, ..., 39).
The BETSbets.covid19 package provides likelihood inference for early epidemic data with four key epidemiological events: Beginning of exposure, End of exposure, time of Transmission, and time of Symptom onset. It jointly estimates the epidemic doubling time and incubation period and is able to correct for different kinds of sample selection.
Qingyuan Zhao, Nianqiao Ju, Sergio Bacallado, and Rajen Shah. "BETS: The dangers of selection bias in early analyses of the coronavirus disease (COVID-19) pandemic", 2020. arXiv:2004.07743.
Likelihood inference
bets.inference( data, likelihood = c("conditional", "unconditional"), ci = c("lrt", "point", "bootstrap"), M = Inf, r = NULL, L = NULL, level = 0.95, bootstrap = 1000, mc.cores = 1 )bets.inference( data, likelihood = c("conditional", "unconditional"), ci = c("lrt", "point", "bootstrap"), M = Inf, r = NULL, L = NULL, level = 0.95, bootstrap = 1000, mc.cores = 1 )
data |
A data.frame with three columns: B, E, S. |
likelihood |
Conditional on B and E? |
ci |
How to compute the confidence interval? |
M |
Right truncation for symptom onset (only available for conditional likelihood) |
r |
Parameter for epidemic growth (overrides |
L |
Time of travel restriction (required for unconditional likelihood) |
level |
Level of the confidence interval (default 0.95). |
bootstrap |
Number of bootstrap resamples. |
mc.cores |
Number of cores used for computing the bootstrap confidence interval. |
The confidence interval is either not computed ("point"), or computed by inverting the likelihood ratio test ("lrt") or basic bootstrap ("bootstrap")
Results of the likelihood inference, including maximum likelihood estimators and individual confidence intervals for the model parameters based on inverting the likelihood ratio test.
data(wuhan_exported) data <- subset(wuhan_exported, Location == "Hefei") data$B <- data$B - 0.75 data$E <- data$E - 0.25 data$S <- data$S - 0.5 # Conditional likelihood inference bets.inference(data, "conditional") bets.inference(data, "conditional", "bootstrap", bootstrap = 100, level = 0.5) # Unconditional likelihood inference bets.inference(data, "unconditional", L = 54) # Conditional likelihood inference for data with right truncation bets.inference(subset(data, S <= 60), "conditional", M = 60) # Conditional likelihood inference with r fixed at 0 (not recommended) bets.inference(data, "conditional", r = 0)data(wuhan_exported) data <- subset(wuhan_exported, Location == "Hefei") data$B <- data$B - 0.75 data$E <- data$E - 0.25 data$S <- data$S - 0.5 # Conditional likelihood inference bets.inference(data, "conditional") bets.inference(data, "conditional", "bootstrap", bootstrap = 100, level = 0.5) # Unconditional likelihood inference bets.inference(data, "unconditional", L = 54) # Conditional likelihood inference for data with right truncation bets.inference(subset(data, S <= 60), "conditional", M = 60) # Conditional likelihood inference with r fixed at 0 (not recommended) bets.inference(data, "conditional", r = 0)
(Profile) Likelihood function
bets.likelihood( params, data, likelihood = c("conditional", "unconditional"), M = Inf, r = NULL, L = NULL, params_init = NULL )bets.likelihood( params, data, likelihood = c("conditional", "unconditional"), M = Inf, r = NULL, L = NULL, params_init = NULL )
params |
A vector of parameters (with at least one of the following entries: rho, r, ip_q50, ip_q95) |
data |
A data frame with three columns: B, E, S |
likelihood |
Use the conditional or unconditional likelihood function |
M |
Right truncation for symptom onset |
r |
Parameter for epidemic growth (overrides |
L |
Day of travel quarantine |
params_init |
Initial parameters for computing the profile likelihood |
Non-default values of M and r are only available for conditional likelihood.
Log-likelihood function if params has all four entries, rho, r, ip_q50, ip_q95 (or three entires—r, ip_q50, ip_q95—if computing the conditional likelihood). Otherwise returns the profile likelihood for the parameters in params.
data(wuhan_exported) data <- wuhan_exported data$B <- data$B - 0.75 data$E <- data$E - 0.25 data$S <- data$S - 0.5 params <- c(r = 0.2, ip_q50 = 5, ip_q95 = 12) # Conditional likelihood bets.likelihood(params, data) # Conditional likelihood with right truncation bets.likelihood(params, subset(data, S <= 60), M = 60) # Conditional likelihood with fixed r (not recommended) bets.likelihood(params, data, r = 0) # Unconditional likelihood params["rho"] <- 1 bets.likelihood(params, data, likelihood = "unconditional", L = 54) # Profile conditional likelihood bets.likelihood(c(r = 0.2), data, params_init = params)data(wuhan_exported) data <- wuhan_exported data$B <- data$B - 0.75 data$E <- data$E - 0.25 data$S <- data$S - 0.5 params <- c(r = 0.2, ip_q50 = 5, ip_q95 = 12) # Conditional likelihood bets.likelihood(params, data) # Conditional likelihood with right truncation bets.likelihood(params, subset(data, S <= 60), M = 60) # Conditional likelihood with fixed r (not recommended) bets.likelihood(params, data, r = 0) # Unconditional likelihood params["rho"] <- 1 bets.likelihood(params, data, likelihood = "unconditional", L = 54) # Profile conditional likelihood bets.likelihood(c(r = 0.2), data, params_init = params)
A dataset containing the trajectory of cases of COVID-19.
covid19_datacovid19_data
A data frame with 1091 rows and 20 variables:
Label of the case, in the format of Country-Case number.
Nationality or residence of the patient.
Male (M) or Female (F).
Age of the patient, either an integer or age by decade (for example, 40s).
Other confirmed cases that this patient had contacts with.
Whether the case has contact with earlier confirmed cases or visited Hubei province.
Was the patient infected outside Wuhan? Yes (Y), Likely (L), or No (empty string and the default).
Begin of stay in Wuhan.
End of Stay in Wuhan.
When was the patient infected? Can be an interval or multiple dates.
When did the patient arrive in the country where he/she was confirmed a 2019-nCoV case?
When did the patient first show symptoms of 2019-nCoV (cough, fever, fatigue, etc.)?
After developing symptoms, when was the patient first went to (or taken to) a medical institution?
If the patient was not admitted to or isolated in a hospital after the initial medical visit, when was the patient finally admitted or isolated?
When was the patient confirmed as a case of 2019-nCoV?
When was the patient discharged from hospital?
When did the patient die?
Has this information been verified by another data collector?
URLs to the information recorded (usually government websites or news reports).
Transform date to numeric
date.process(date)date.process(date)
date |
a vector of dates of the form "DD-MMM" (for example, 23-Jan). |
a vector of days since December 1st, 2019 (or example, 23-Jan is converted to 23+31 = 52).
Prepare data frame for analysis
preprocess.data( data, infected_in = c("Wuhan", "Outside"), symptom_impute = FALSE )preprocess.data( data, infected_in = c("Wuhan", "Outside"), symptom_impute = FALSE )
data |
A data frame |
infected_in |
Either "Wuhan" or "Outside" |
symptom_impute |
Whether to use initial medical visit and confirmation to impute missing symptom onset. |
A summary of the procedures:
Convert all dates to number of days since 1-Dec-2019.
Separates data into those returned from Wuhan and those infected outside of wuhan.
Restrict to cases with a known symptom onset date.
Parse column 'Infected' into two columns: Infected_first and Infected_last.
For all cases, set Infected_first to 1 if it is missing.
For outside cases, set Infected_last to be no later than symptom onset.
For Wuhan-exported cases, set Infected_last to no later than symptom onset and end of Wuhan stay.
A data frame
Nianqiao Ju <[email protected]>, Qingyuan Zhao <[email protected]>
data(covid19_data) head(data <- preprocess.data(covid19_data)) ## This is how the wuhan_exported data frame is created data <- subset(data, Symptom < Inf) data <- subset(data, Arrived <= 54) data$Location <- do.call(rbind, strsplit(as.character(data$Case), "-"))[, 1] wuhan_exported <- data.frame(Location = data$Location, B = data$Begin_Wuhan, E = data$End_Wuhan, S = data$Symptom) ## devtools::use_data(wuhan_exported)data(covid19_data) head(data <- preprocess.data(covid19_data)) ## This is how the wuhan_exported data frame is created data <- subset(data, Symptom < Inf) data <- subset(data, Arrived <= 54) data$Location <- do.call(rbind, strsplit(as.character(data$Case), "-"))[, 1] wuhan_exported <- data.frame(Location = data$Location, B = data$Begin_Wuhan, E = data$End_Wuhan, S = data$Symptom) ## devtools::use_data(wuhan_exported)
Constructed from covid19_data, see example(preprocess.data).
wuhan_exportedwuhan_exported
A data frame with 378 rows and 4 variables:
Where the case is confirmed.
Gender of the patient.
Age of the patient.
Beginning of stay in Wuhan.
End of stay in Wuhan.
Symptom onset.