# Estimate Infections, the Time-Varying Reproduction Number and the Rate of Growth

Source:`R/estimate_infections.R`

`estimate_infections.Rd`

Uses a non-parametric approach to reconstruct cases by date of infection
from reported cases. It uses either a generative Rt model or non-parametric
back calculation to estimate underlying latent infections and then maps
these infections to observed cases via uncertain reporting delays and a
flexible observation model. See the examples and function arguments for th
details of all options. The default settings may not be sufficient for your
use case so the number of warmup samples (`stan_args = list(warmup)`

) may
need to be increased as may the overall number of samples. Follow the links
provided by any warnings messages to diagnose issues with the MCMC fit. It
is recommended to explore several of the Rt estimation approaches supported
as not all of them may be suited to users own use cases. See
here
for an example of using `estimate_infections`

within the `epinow`

wrapper to
estimate Rt for Covid-19 in a country from the ECDC data source.

## Usage

```
estimate_infections(
reported_cases,
generation_time,
delays = delay_opts(),
truncation = trunc_opts(),
rt = rt_opts(),
backcalc = backcalc_opts(),
gp = gp_opts(),
obs = obs_opts(),
stan = stan_opts(),
horizon = 7,
CrIs = c(0.2, 0.5, 0.9),
filter_leading_zeros = TRUE,
zero_threshold = Inf,
id = "estimate_infections",
verbose = interactive()
)
```

## Arguments

- reported_cases
A data frame of confirmed cases (confirm) by date (date). confirm must be integer and date must be in date format.

- generation_time
A list containing the mean, standard deviation of the mean (mean_sd), standard deviation (sd), standard deviation of the standard deviation and the maximum allowed value for the generation time (assuming a gamma distribution).

- delays
A call to

`delay_opts()`

defining delay distributions and options. See the documentation of`delay_opts()`

and the examples below for details.- truncation
A list of options as generated by

`trunc_opts()`

defining the truncation of observed data. Defaults to`trunc_opts()`

. See`estimate_truncation()`

for an approach to estimating truncation from data.- rt
A list of options as generated by

`rt_opts()`

defining Rt estimation. Defaults to`rt_opts()`

. Set to`NULL`

to switch to using back calculation rather than generating infections using Rt.- backcalc
A list of options as generated by

`backcalc_opts()`

to define the back calculation. Defaults to`backcalc_opts()`

.- gp
A list of options as generated by

`gp_opts()`

to define the Gaussian process. Defaults to`gp_opts()`

.Set to NULL to disable the Gaussian process.- obs
A list of options as generated by

`obs_opts()`

defining the observation model. Defaults to`obs_opts()`

.- stan
A list of stan options as generated by

`stan_opts()`

. Defaults to`stan_opts()`

. Can be used to override`data`

,`init`

, and`verbose`

settings if desired.- horizon
Numeric, defaults to 7. Number of days into the future to forecast.

- CrIs
Numeric vector of credible intervals to calculate.

- filter_leading_zeros
Logical, defaults to TRUE. Should zeros at the start of the time series be filtered out.

- zero_threshold
Numeric defaults to Inf. Indicates if detected zero cases are meaningful by using a threshold number of cases based on the 7 day average. If the average is above this threshold then the zero is replaced with the backwards looking rolling average. If set to infinity then no changes are made.

- id
A character string used to assign logging information on error. Used by

`regional_epinow`

to assign errors to regions. Alter the default to run with error catching.- verbose
Logical, defaults to

`TRUE`

when used interactively and otherwise`FALSE`

. Should verbose debug progress messages be printed. Corresponds to the "DEBUG" level from`futile.logger`

. See`setup_logging`

for more detailed logging options.

## Value

A list of output including: posterior samples, summarised posterior samples, data used to fit the model, and the fit object itself.

## Examples

```
# \donttest{
# set number of cores to use
old_opts <- options()
options(mc.cores = ifelse(interactive(), 4, 1))
# get example case counts
reported_cases <- example_confirmed[1:60]
# set up example generation time
generation_time <- get_generation_time(disease = "SARS-CoV-2", source = "ganyani")
# set delays between infection and case report
incubation_period <- get_incubation_period(disease = "SARS-CoV-2", source = "lauer")
reporting_delay <- list(
mean = convert_to_logmean(2, 1), mean_sd = 0.1,
sd = convert_to_logsd(2, 1), sd_sd = 0.1, max = 10
)
# default setting
# here we assume that the observed data is truncated by the same delay as
def <- estimate_infections(reported_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
rt = rt_opts(prior = list(mean = 2, sd = 0.1)),
stan = stan_opts(control = list(adapt_delta = 0.95))
)
# real time estimates
summary(def)
#> measure estimate
#> 1: New confirmed cases by infection date 2203 (1148 -- 3902)
#> 2: Expected change in daily cases Likely decreasing
#> 3: Effective reproduction no. 0.86 (0.6 -- 1.1)
#> 4: Rate of growth -0.04 (-0.12 -- 0.036)
#> 5: Doubling/halving time (days) -17 (19 -- -5.9)
# summary plot
plot(def)
# decreasing the accuracy of the approximate Gaussian to speed up computation.
# These settings are an area of active research. See ?gp_opts for details.
agp <- estimate_infections(reported_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
rt = rt_opts(prior = list(mean = 2, sd = 0.1)),
gp = gp_opts(ls_min = 10, basis_prop = 0.1),
stan = stan_opts(control = list(adapt_delta = 0.95))
)
#> Warning: There were 4 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
summary(agp)
#> measure estimate
#> 1: New confirmed cases by infection date 2184 (1096 -- 4057)
#> 2: Expected change in daily cases Likely decreasing
#> 3: Effective reproduction no. 0.85 (0.59 -- 1.1)
#> 4: Rate of growth -0.041 (-0.12 -- 0.04)
#> 5: Doubling/halving time (days) -17 (17 -- -5.7)
plot(agp)
# Adjusting for future susceptible depletion
dep <- estimate_infections(reported_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
rt = rt_opts(
prior = list(mean = 2, sd = 0.1),
pop = 1000000, future = "latest"
),
gp = gp_opts(ls_min = 10, basis_prop = 0.1), horizon = 21,
stan = stan_opts(control = list(adapt_delta = 0.95))
)
#> Warning: There were 2 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
plot(dep)
# Adjusting for truncation of the most recent data
# See estimate_truncation for an approach to estimating this from data
trunc_dist <- list(
mean = convert_to_logmean(0.5, 0.5), mean_sd = 0.1,
sd = convert_to_logsd(0.5, 0.5), sd_sd = 0.1,
max = 3
)
trunc <- estimate_infections(reported_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
truncation = trunc_opts(trunc_dist),
rt = rt_opts(prior = list(mean = 2, sd = 0.1)),
gp = gp_opts(ls_min = 10, basis_prop = 0.1),
stan = stan_opts(control = list(adapt_delta = 0.95))
)
#> Warning: There were 2 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
plot(trunc)
# using back calculation (combined here with under reporting)
# this model is in the order of 10 ~ 100 faster than the gaussian process method
# it is likely robust for retrospective Rt but less reliable for real time estimates
# the width of the prior window controls the reliance on observed data and can be
# optionally switched off using backcalc_opts(prior = "none"), see ?backcalc_opts for
# other options
backcalc <- estimate_infections(reported_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
rt = NULL, backcalc = backcalc_opts(),
obs = obs_opts(scale = list(mean = 0.4, sd = 0.05)),
horizon = 0
)
plot(backcalc)
# Rt projected into the future using the Gaussian process
project_rt <- estimate_infections(reported_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
rt = rt_opts(
prior = list(mean = 2, sd = 0.1),
future = "project"
)
)
#> Warning: There were 2 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
plot(project_rt)
# default settings on a later snapshot of data
snapshot_cases <- example_confirmed[80:130]
snapshot <- estimate_infections(snapshot_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
rt = rt_opts(prior = list(mean = 1, sd = 0.1))
)
#> Warning: There were 22 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
plot(snapshot)
# stationary Rt assumption (likely to provide biased real-time estimates)
stat <- estimate_infections(reported_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
rt = rt_opts(prior = list(mean = 2, sd = 0.1), gp_on = "R0")
)
plot(stat)
# no gaussian process (i.e fixed Rt assuming no breakpoints)
fixed <- estimate_infections(reported_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
gp = NULL
)
plot(fixed)
# no delays
no_delay <- estimate_infections(reported_cases, generation_time = generation_time)
#> Warning: There were 11 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
plot(no_delay)
# break point but otherwise static Rt
bp_cases <- data.table::copy(reported_cases)
bp_cases <- bp_cases[, breakpoint := ifelse(date == as.Date("2020-03-16"), 1, 0)]
bkp <- estimate_infections(bp_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
rt = rt_opts(prior = list(mean = 2, sd = 0.1)),
gp = NULL
)
# break point effect
summary(bkp, type = "parameters", params = "breakpoints")
#> date variable strat type median mean sd lower_90
#> 1: <NA> breakpoints 1 <NA> -0.6298554 -0.6298413 0.02757524 -0.6747835
#> lower_50 lower_20 upper_20 upper_50 upper_90
#> 1: -0.6486451 -0.6378769 -0.6227737 -0.6105377 -0.584764
plot(bkp)
# weekly random walk
rw <- estimate_infections(reported_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
rt = rt_opts(prior = list(mean = 2, sd = 0.1), rw = 7),
gp = NULL
)
# random walk effects
summary(rw, type = "parameters", params = "breakpoints")
#> date variable strat type median mean sd lower_90
#> 1: <NA> breakpoints 1 <NA> -0.25957458 -0.26128588 0.06770300 -0.37537835
#> 2: <NA> breakpoints 2 <NA> -0.22350648 -0.22318097 0.08134202 -0.35408200
#> 3: <NA> breakpoints 3 <NA> -0.28068369 -0.27859517 0.08974259 -0.42207879
#> 4: <NA> breakpoints 4 <NA> -0.02670933 -0.02694557 0.09485745 -0.17708652
#> 5: <NA> breakpoints 5 <NA> 0.04724248 0.04753704 0.09284697 -0.09892788
#> 6: <NA> breakpoints 6 <NA> -0.07298442 -0.07748014 0.11239513 -0.27027613
#> 7: <NA> breakpoints 7 <NA> -0.01709740 -0.01554207 0.18070172 -0.30632987
#> lower_50 lower_20 upper_20 upper_50 upper_90
#> 1: -0.30631351 -0.27725794 -0.244008940 -0.2132743510 -0.15479016
#> 2: -0.27767709 -0.24618521 -0.204075318 -0.1673509709 -0.08915599
#> 3: -0.33458995 -0.30167596 -0.259230703 -0.2209283993 -0.13045074
#> 4: -0.09269798 -0.05088761 -0.001496799 0.0383167319 0.12419378
#> 5: -0.01812776 0.02062275 0.069063901 0.1057235476 0.20431283
#> 6: -0.15059813 -0.10164015 -0.045132330 -0.0001959052 0.09890684
#> 7: -0.13578045 -0.05972906 0.025330201 0.1034133639 0.28332325
plot(rw)
options(old_opts)
# }
```