Introduction to Attrib

library(attrib)
#> attrib 2023.6.8
#> https://www.csids.no/attrib/

Introduction

attrib provides a way of estimating what the mortality would have been if some given exposures are set to a reference value. By using simulations from the posterior distribution of all coefficients we can easily aggregate over time and locations while still estimating valid credible intervals.

This vignette will go through:

how to use fit_attrib to fit the model to the data
how to use est_attrib to estimate the mortality under different scenarios (i.e. when the exposures are at reference values and at observed values)
some examples of usages of the resulting dataset

Data example

We will use the datasets data_fake_attrib_county and data_fake_attrib_nation.

data_fake_attrib_county consists of fake mortality data for all counties of Norway on a weekly basis from 2010 until 2020. The dataset consists of the following features:

location_code: Location code of the different counties
isoyear: Isoyear
isoweek: Week number
isoyearweek: Isoyear and isoweek
season: Years of the season
seasonweek: Number of weeks from the start of the season
pop_jan1_n: Population size
ili_isoweekmean0_6_pr100: Percentage of doctors consultations diagnosed with influenza like illnesses
ili_isoweekmean7_13_pr100: ili_isoweekmean0_6_pr100 lagged with one week
heatwavedays_n: number of heatwaves
deaths_n: number of deaths

data_fake_attrib_nation is a similar dataset at the national level.

data_fake_county <- attrib::data_fake_attrib_county
data_fake_nation <- attrib::data_fake_attrib_nation
head(data_fake_county, 5)
#>    location_code isoyear isoweek isoyearweek    season seasonweek pop_jan1_n
#> 1:  county_nor03    2010       1     2010-01 2009/2010         24     693494
#> 2:  county_nor03    2011       1     2011-01 2010/2011         24     693494
#> 3:  county_nor03    2012       1     2012-01 2011/2012         24     693494
#> 4:  county_nor03    2013       1     2013-01 2012/2013         24     693494
#> 5:  county_nor03    2014       1     2014-01 2013/2014         24     693494
#>    ili_isoweekmean0_6_pr100 ili_isoweekmean7_13_pr100 heatwavedays_n deaths_n
#> 1:                0.9231202                 0.8146507              0      112
#> 2:                1.8997241                 1.7890927              0      113
#> 3:                1.3924947                 1.6017501              0      128
#> 4:                0.9296033                 0.7167721              0      126
#> 5:                1.3933639                 1.1638354              0      115

In this example we will look at the exposures ili_isoweekmean7_13_pr100 and heatwavedays_n and calculate the attributable mortality due to these exposures.

Fitting using fit_attrib

County level

We want to estimate the attributable mortality due to ILI and heatwaves. attrib lets us fit models with both fixed and random effect and offsets using linear mixed models (LMM).

We use the glmer function from the lme4 package. In practice, this means we must specify the response, offsets, the fixed effects, and the random effects. In our case we will model the response deaths as a function of:

the fixed effects:
- heatwavedays_n
- ili_isoweekmean7_13_pr100
- sin(2 * pi * (isoweek - 1) / 52)
- cos(2 * pi * (isoweek - 1) / 52)
the random effects:
- (1|location_code)
- (ili_isoweekmean7_13_pr100|season)
the offset:
- log(pop_jan1_n)

#response
response <- "deaths_n"

# fixed effects
fixef_county <- " heatwavedays_n +
  ili_isoweekmean7_13_pr100 +
  sin(2 * pi * (isoweek - 1) / 52) +
  cos(2 * pi * (isoweek - 1) / 52)"


#random effects
ranef_county <- "(1|location_code) +
  (ili_isoweekmean7_13_pr100|season)"

#offset
offset_county <- "log(pop_jan1_n)"

# Now we fit the model using `fit_attrib`. 
fit_county <- fit_attrib(
  data_fake_county, 
  response = response, 
  fixef = fixef_county, 
  ranef = ranef_county, 
  offset = offset_county
)

This results in the following fit:

fit_county
#> Generalized linear mixed model fit by maximum likelihood (Laplace
#>   Approximation) [glmerMod]
#>  Family: poisson  ( log )
#> Formula: deaths_n ~ heatwavedays_n + ili_isoweekmean7_13_pr100 + sin(2 *  
#>     pi * (isoweek - 1)/52) + cos(2 * pi * (isoweek - 1)/52) +  
#>     offset(log(pop_jan1_n)) + (1 | location_code) + (ili_isoweekmean7_13_pr100 |  
#>     season)
#>    Data: data
#>       AIC       BIC    logLik  deviance  df.resid 
#>  44402.03  44462.79 -22192.02  44384.03      6305 
#> Random effects:
#>  Groups        Name                      Std.Dev. Corr 
#>  location_code (Intercept)               0.001725      
#>  season        (Intercept)               0.002016      
#>                ili_isoweekmean7_13_pr100 0.005003 -1.00
#> Number of obs: 6314, groups:  location_code, 11; season, 11
#> Fixed Effects:
#>                    (Intercept)                  heatwavedays_n  
#>                       -8.79945                         0.07321  
#>      ili_isoweekmean7_13_pr100  sin(2 * pi * (isoweek - 1)/52)  
#>                        0.03429                         0.01448  
#> cos(2 * pi * (isoweek - 1)/52)  
#>                        0.06784  
#> optimizer (Nelder_Mead) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings

Note that fit has the added attributes offset (saving the offset name) and fit_fix (the coefficients of the linear model fitted on only the fixed effects). These are needed by est_attrib to create the dataset containing only the fixed effects.

National level

We estimate the same as before But on a national level, meaning we remove the random effect (1|location_code) since we only have one location code. This gives the following features:

the fixed effects:
- heatwavedays_n
- ili_isoweekmean7_13_pr100
- sin(2 * pi * (isoweek - 1) / 52)
- cos(2 * pi * (isoweek - 1) / 52)
the random effects:
- (ili_isoweekmean7_13_pr100|season)
the offset:
- log(pop_jan1_n)

#response
response <- "deaths_n"

# fixed effects
fixef_nation <- " heatwavedays_n +
  ili_isoweekmean7_13_pr100 +
  sin(2 * pi * (isoweek - 1) / 52) +
  cos(2 * pi * (isoweek - 1) / 52)"


#random effects
ranef_nation <- "(ili_isoweekmean7_13_pr100|season)"

#offset
offset_nation <- "log(pop_jan1_n)"

# Now we fit the model using `fit_attrib`. 
fit_nation <- fit_attrib(
  data_fake_nation, 
  response = response, 
  fixef = fixef_nation, 
  ranef = ranef_nation, 
  offset = offset_nation
)

Using the sim function

The sim function can be used to generate simulations for all the rows in our data.

It first generates n_sim simulations from the posterior distribution of the coefficients from out fit before applying these coefficients on our dataset generating n_sim simulations and expected mortality for each line. This is quite generic. Hence if the goal is to compute attributable mortality or incident risk ratios we use est_attrib as shown in a later part of the vignette.

n_sim <- 20
sim_data <- sim(fit_nation, data_fake_nation, n_sim)
head(sim_data[id_row == 1], 5)
#>    location_code isoyear isoweek isoyearweek    season seasonweek pop_jan1_n
#> 1:    nation_nor    2009      30     2009-30 2009/2010          1    5367580
#> 2:    nation_nor    2009      30     2009-30 2009/2010          1    5367580
#> 3:    nation_nor    2009      30     2009-30 2009/2010          1    5367580
#> 4:    nation_nor    2009      30     2009-30 2009/2010          1    5367580
#> 5:    nation_nor    2009      30     2009-30 2009/2010          1    5367580
#>    ili_isoweekmean0_6_pr100 ili_isoweekmean7_13_pr100 heatwavedays_n deaths_n
#> 1:              8.98914e-07                         0      0.8181818      827
#> 2:              8.98914e-07                         0      0.8181818      827
#> 3:              8.98914e-07                         0      0.8181818      827
#> 4:              8.98914e-07                         0      0.8181818      827
#> 5:              8.98914e-07                         0      0.8181818      827
#>    id_row sim_id sim_value
#> 1:      1      1  807.3156
#> 2:      1      2  810.0678
#> 3:      1      3  802.7396
#> 4:      1      4  803.5876
#> 5:      1      5  805.2850

We can see that we now have multiple expected mortalities for the same dataline. This is due to the coefficient simulations.

Estimating attributable mortality using est_attrib

To estimate attributable mortality we simulate:

the estimated mortality for observed exposures
the estimated mortality for the exposures set to reference values

This is easily done using est_attrib.

We need to give the fit, the dataset, the exposures with reference values, and the number of simulations. est_attrib will then using the arm::sim function to generate simulations of the underlying posterior distribution. attrib::sim will then combine the simulated coefficients to estimate the modeled outcome (i.e. number of deaths) for each simulation.

exposures <- list( "heatwavedays_n" = 0, "ili_isoweekmean7_13_pr100" = 0)
n_sim <- 20
est_attrib_sim_county <- attrib::est_attrib(
  fit_county, 
  data_fake_county, 
  exposures = exposures, 
  n_sim = n_sim
)

est_attrib_sim_nation <- attrib::est_attrib(
  fit_nation, 
  data_fake_nation, 
  exposures = exposures,
  n_sim = n_sim
)

head(est_attrib_sim_county, 5)
#>    location_code isoyear isoweek isoyearweek    season seasonweek pop_jan1_n
#> 1:  county_nor03    2010       1     2010-01 2009/2010         24     693494
#> 2:  county_nor03    2011       1     2011-01 2010/2011         24     693494
#> 3:  county_nor03    2012       1     2012-01 2011/2012         24     693494
#> 4:  county_nor03    2013       1     2013-01 2012/2013         24     693494
#> 5:  county_nor03    2014       1     2014-01 2013/2014         24     693494
#>    ili_isoweekmean0_6_pr100 ili_isoweekmean7_13_pr100 heatwavedays_n deaths_n
#> 1:                0.9231202                 0.8146507              0      112
#> 2:                1.8997241                 1.7890927              0      113
#> 3:                1.3924947                 1.6017501              0      128
#> 4:                0.9296033                 0.7167721              0      126
#> 5:                1.3933639                 1.1638354              0      115
#>    id sim_id sim_value_exposures=observed sim_value_heatwavedays_n=0
#> 1:  1      1                     114.2379                   114.2379
#> 2:  2      1                     117.9895                   117.9895
#> 3:  3      1                     117.1525                   117.1525
#> 4:  4      1                     114.7316                   114.7316
#> 5:  5      1                     117.5407                   117.5407
#>    sim_value_ili_isoweekmean7_13_pr100=0
#> 1:                              111.9369
#> 2:                              113.1031
#> 3:                              112.3154
#> 4:                              112.8651
#> 5:                              113.4813

We can see in the above dataset that the columns id, sim_id, sim_value_exposures=observed, sim_value_heatwavedays_n=0, sim_value_ili_isoweekmean7_13_pr100=0 are added to the previous set of columns. For each row in the original dataset we now have 20 rows, one for each of the simulations done by est_attrib. In each row we see the estimate of the number of deaths given a reference value for sim_value_heatwavedays_n and sim_value_ili_isoweekmean7_13_pr100.

To make the data processing easier later we convert the dataset from wide to long form and collapse the estimated mortality

est_attrib_county_long <- data.table::melt.data.table(
  est_attrib_sim_county, 
  id.vars = c(
    "location_code", 
    "isoyear",
    "isoweek",
    "isoyearweek",
    "season",  
    "seasonweek", 
    "id", 
    "sim_id", 
    "deaths_n", 
    "sim_value_exposures=observed"
  ),
  measure.vars = c(
    "sim_value_heatwavedays_n=0", 
    "sim_value_ili_isoweekmean7_13_pr100=0"
  )
) 
data.table::setnames(est_attrib_county_long, "variable", "attr")

head(est_attrib_county_long, 5)
#>    location_code isoyear isoweek isoyearweek    season seasonweek id sim_id
#> 1:  county_nor03    2010       1     2010-01 2009/2010         24  1      1
#> 2:  county_nor03    2011       1     2011-01 2010/2011         24  2      1
#> 3:  county_nor03    2012       1     2012-01 2011/2012         24  3      1
#> 4:  county_nor03    2013       1     2013-01 2012/2013         24  4      1
#> 5:  county_nor03    2014       1     2014-01 2013/2014         24  5      1
#>    deaths_n sim_value_exposures=observed                       attr    value
#> 1:      112                     114.2379 sim_value_heatwavedays_n=0 114.2379
#> 2:      113                     117.9895 sim_value_heatwavedays_n=0 117.9895
#> 3:      128                     117.1525 sim_value_heatwavedays_n=0 117.1525
#> 4:      126                     114.7316 sim_value_heatwavedays_n=0 114.7316
#> 5:      115                     117.5407 sim_value_heatwavedays_n=0 117.5407

We can see that the columns sim_value_heatwavedays_n=0, sim_value_ili_isoweekmean7_13_pr100=0 are now collapsed into the new column attr and value with attr describing which exposure we have and value giving the corresponding reference value.

est_attrib_nation_long <- data.table::melt.data.table(
  est_attrib_sim_nation, 
  id.vars = c(
    "location_code", 
    "isoyear",
    "isoweek",
    "isoyearweek",
    "season",  
    "seasonweek", 
    "id", 
    "sim_id", 
    "deaths_n", 
    "sim_value_exposures=observed"
  ),
  measure.vars = c(
    "sim_value_heatwavedays_n=0", 
    "sim_value_ili_isoweekmean7_13_pr100=0"
  )
) 
data.table::setnames(est_attrib_nation_long, "variable", "attr")

head(est_attrib_nation_long, 5)
#>    location_code isoyear isoweek isoyearweek    season seasonweek id sim_id
#> 1:    nation_nor    2009      30     2009-30 2009/2010          1  1      1
#> 2:    nation_nor    2009      31     2009-31 2009/2010          2  2      1
#> 3:    nation_nor    2009      32     2009-32 2009/2010          3  3      1
#> 4:    nation_nor    2009      33     2009-33 2009/2010          4  4      1
#> 5:    nation_nor    2009      34     2009-34 2009/2010          5  5      1
#>    deaths_n sim_value_exposures=observed                       attr    value
#> 1:      827                     808.3530 sim_value_heatwavedays_n=0 761.6070
#> 2:      751                     794.0040 sim_value_heatwavedays_n=0 763.0903
#> 3:      811                     785.7890 sim_value_heatwavedays_n=0 765.2585
#> 4:      787                     799.2017 sim_value_heatwavedays_n=0 768.0857
#> 5:      828                     792.2368 sim_value_heatwavedays_n=0 771.5378

Compare the national data to data aggregated from county to national level.

We will now aggregate our two simulated datasets (one on a county level and one on a national level) to aid in comparison.

Aggregate from county/weekly to national/seasonal

We proceed by aggregating the county dataset to the national/seasonal level. Afterwards we calculate the expected attributable mortality, exp_attr, by subtracting value (the simulated expected number of deaths given the reference value of the exposure) from the sim_value_exposures=observed.

To be able to separate this dataset from the other we add a tag.

aggregated_county_to_nation <-  est_attrib_county_long[,.(
  "sim_value_exposures=observed" = sum(`sim_value_exposures=observed`),
  value = sum(value), 
  deaths_n = sum(deaths_n)
), keyby = .(season, attr, sim_id)]

# Add exp_attr, exp_irr and a tag.
aggregated_county_to_nation[, exp_attr:= (`sim_value_exposures=observed` - value)]
aggregated_county_to_nation[, tag := "aggregated_from_county"]

head(aggregated_county_to_nation, 5)
#>       season                       attr sim_id sim_value_exposures=observed
#> 1: 2009/2010 sim_value_heatwavedays_n=0      1                     43768.73
#> 2: 2009/2010 sim_value_heatwavedays_n=0      2                     44070.95
#> 3: 2009/2010 sim_value_heatwavedays_n=0      3                     44455.71
#> 4: 2009/2010 sim_value_heatwavedays_n=0      4                     44195.52
#> 5: 2009/2010 sim_value_heatwavedays_n=0      5                     44709.98
#>       value deaths_n exp_attr                    tag
#> 1: 43355.27    44006 413.4645 aggregated_from_county
#> 2: 43670.21    44006 400.7446 aggregated_from_county
#> 3: 44023.37    44006 432.3361 aggregated_from_county
#> 4: 43801.03    44006 394.4844 aggregated_from_county
#> 5: 44267.72    44006 442.2571 aggregated_from_county

Aggregating the national model per season

For the national model we aggregate over seasons and create exp_attr in the same way as above.

aggregated_nation <-  est_attrib_nation_long[, .(
  "sim_value_exposures=observed" = sum(`sim_value_exposures=observed`),
  value = sum(value), 
  deaths_n = sum(deaths_n)
), keyby = .(season, attr, sim_id)]

aggregated_nation[, exp_attr:= (`sim_value_exposures=observed` - value)]
aggregated_nation[, tag:= "nation"]
head(aggregated_nation, 5)
#>       season                       attr sim_id sim_value_exposures=observed
#> 1: 2009/2010 sim_value_heatwavedays_n=0      1                     44484.64
#> 2: 2009/2010 sim_value_heatwavedays_n=0      2                     44297.66
#> 3: 2009/2010 sim_value_heatwavedays_n=0      3                     43880.36
#> 4: 2009/2010 sim_value_heatwavedays_n=0      4                     44188.17
#> 5: 2009/2010 sim_value_heatwavedays_n=0      5                     44156.80
#>       value deaths_n exp_attr    tag
#> 1: 44076.80    44006 407.8435 nation
#> 2: 43797.77    44006 499.8873 nation
#> 3: 43435.57    44006 444.7890 nation
#> 4: 43636.87    44006 551.2955 nation
#> 5: 43733.17    44006 423.6221 nation

For simplicity we data.table::rbindlist the two datasets together.

library(ggplot2)
data_national<- data.table::rbindlist(list(aggregated_county_to_nation, aggregated_nation))

Calculate simulation quantiles.

The next thing to do is to aggregate away the simulations. The benefits of having the simulations is the possibility it gives to efficiently compute all desired quantiles. For this example we will use the .05, .5 and .95 quantiles.

# Quantile functins
q025 <- function(x){
  return(quantile(x, 0.025))
}
q975 <- function(x){
  return(quantile(x, 0.975))
}

We compute the quantiles for exp_attr in the following way.

col_names <- colnames(data_national)
data.table::setkeyv(
  data_national, 
  col_names[!col_names %in% c(
    "exp_attr", 
    "sim_id", 
    "sim_value_exposures=observed", 
    "value", 
    "deaths_n"
  )]
)

aggregated_sim_seasonal_data_national<- data_national[
  ,
  unlist(
    recursive = FALSE, 
    lapply(.(median = median, q025 = q025, q975 = q975), function(f) lapply(.SD, f))
  ), 
  by = eval(data.table::key(data_national)),
  .SDcols = c("exp_attr")
]

head(aggregated_sim_seasonal_data_national,5)
#>       season                                  attr                    tag
#> 1: 2009/2010            sim_value_heatwavedays_n=0 aggregated_from_county
#> 2: 2009/2010            sim_value_heatwavedays_n=0                 nation
#> 3: 2009/2010 sim_value_ili_isoweekmean7_13_pr100=0 aggregated_from_county
#> 4: 2009/2010 sim_value_ili_isoweekmean7_13_pr100=0                 nation
#> 5: 2010/2011            sim_value_heatwavedays_n=0 aggregated_from_county
#>    median.exp_attr q025.exp_attr q975.exp_attr
#> 1:        412.6411      390.4961      442.6492
#> 2:        471.0203      365.0025      534.5972
#> 3:        711.2374      555.2749      836.0516
#> 4:        733.5690      512.9498      972.1955
#> 5:        468.3495      437.6797      495.9044

We can now see that we have credible intervals and estimates for attributable deaths for all exposures.

Plot to compare the national with the aggregated county to national model

To be able to compare the two models we make a point range plot using ggplot2.

q <- ggplot(
  aggregated_sim_seasonal_data_national[attr == "sim_value_ili_isoweekmean7_13_pr100=0"], 
  aes(x = season, y = median.exp_attr, group = tag, color = tag)
)
q <- q + geom_pointrange(
  aes(x = season, y = median.exp_attr, ymin = q025.exp_attr, ymax = q975.exp_attr), 
  position = position_dodge(width = 0.3)
  )
q <- q + ggtitle("Attributable mortality due to ILI in Norway according to 2 models") 
q <- q +  scale_y_continuous("Estimated attributable mortality") 
q <- q +  theme(axis.text.x = element_text(angle = 90),axis.title.x=element_blank()) 
q <- q +  labs(caption = glue::glue("Aggregated county model: Attributable mortality modeled on a county level before beeing aggregated up to a national level.\n National model: Attributable mortality modeled on a national level."))
q

Comparing cumulative sums over seasons

When operating on the national level, we prefer to aggregate the county model to national level (instead of using the national model). This ensures consistent results at all geographical levels.

aggregated_county_to_nation <-  est_attrib_county_long[, .(
  "sim_value_exposures=observed" = sum(`sim_value_exposures=observed`),
  value = sum(value), 
  deaths_n = sum(deaths_n)
), keyby = .(season, seasonweek, isoweek, attr, sim_id)]

aggregated_county_to_nation[, exp_attr:= (`sim_value_exposures=observed` - value)]
aggregated_county_to_nation[, exp_irr:= (`sim_value_exposures=observed` /value)]
head(aggregated_county_to_nation,5)
#>       season seasonweek isoweek                       attr sim_id
#> 1: 2009/2010          1      30 sim_value_heatwavedays_n=0      1
#> 2: 2009/2010          1      30 sim_value_heatwavedays_n=0      2
#> 3: 2009/2010          1      30 sim_value_heatwavedays_n=0      3
#> 4: 2009/2010          1      30 sim_value_heatwavedays_n=0      4
#> 5: 2009/2010          1      30 sim_value_heatwavedays_n=0      5
#>    sim_value_exposures=observed    value deaths_n exp_attr  exp_irr
#> 1:                     786.3562 747.5979      827 38.75835 1.051844
#> 2:                     794.6368 757.0525      827 37.58435 1.049646
#> 3:                     803.1978 762.6508      827 40.54697 1.053166
#> 4:                     791.2099 754.2325      827 36.97745 1.049027
#> 5:                     806.7873 765.1923      827 41.59499 1.054359

Again we compute the quantiles.


col_names <- colnames(aggregated_county_to_nation)
data.table::setkeyv(aggregated_county_to_nation, col_names[!col_names %in% c("exp_attr", "exp_irr","sim_id", "exposures", "sim_value_exposures=observed", "value")])

aggregated_county_to_nation_weekly <- aggregated_county_to_nation[,
              unlist(recursive = FALSE, lapply(.(median = median, q025 = q025, q975 = q975),
                                               function(f) lapply(.SD, f)
              )), 
              by=eval(data.table::key(aggregated_county_to_nation)),
              .SDcols = c("exp_attr", "exp_irr")]

We then estimate the cumulative sums of attributable mortality and corresponding credible intervals.

aggregated_county_to_nation_weekly[, cumsum := cumsum(median.exp_attr), by = .( attr, season)]
aggregated_county_to_nation_weekly[, cumsum_q025 := cumsum(q025.exp_attr), by = .( attr, season)]
aggregated_county_to_nation_weekly[, cumsum_q975 := cumsum(q975.exp_attr), by = .( attr, season)]

head(aggregated_county_to_nation_weekly, 5)
#>       season seasonweek isoweek                                  attr deaths_n
#> 1: 2009/2010          1      30            sim_value_heatwavedays_n=0      827
#> 2: 2009/2010          1      30 sim_value_ili_isoweekmean7_13_pr100=0      827
#> 3: 2009/2010          2      31            sim_value_heatwavedays_n=0      751
#> 4: 2009/2010          2      31 sim_value_ili_isoweekmean7_13_pr100=0      751
#> 5: 2009/2010          3      32            sim_value_heatwavedays_n=0      811
#>    median.exp_attr median.exp_irr q025.exp_attr q025.exp_irr q975.exp_attr
#> 1:    3.869028e+01       1.051496  3.661640e+01     1.048323  4.157655e+01
#> 2:    0.000000e+00       1.000000  0.000000e+00     1.000000  0.000000e+00
#> 3:    2.645599e+01       1.035102  2.510310e+01     1.033077  2.833190e+01
#> 4:    1.786682e-05       1.000000  1.403088e-05     1.000000  2.112109e-05
#> 5:    2.168157e+01       1.028680  2.051557e+01     1.026964  2.322068e+01
#>    q975.exp_irr       cumsum  cumsum_q025  cumsum_q975
#> 1:     1.054744 3.869028e+01 3.661640e+01 4.157655e+01
#> 2:     1.000000 0.000000e+00 0.000000e+00 0.000000e+00
#> 3:     1.037239 6.514627e+01 6.171950e+01 6.990845e+01
#> 4:     1.000000 1.786682e-05 1.403088e-05 2.112109e-05
#> 5:     1.030436 8.682784e+01 8.223507e+01 9.312912e+01

We can then plot the estimated cumulative attributable mortality over influenza seasons in Norway

library(ggplot2)
q <- ggplot(
  data = aggregated_county_to_nation_weekly[
    season %in% c(
      "2015/2016",
      "2016/2017",
      "2017/2018",
      "2018/2019",
      "2019/2020"
    ) &
    attr == "sim_value_ili_isoweekmean7_13_pr100=0"
  ],
  aes(
    x = seasonweek, 
    y = cumsum, 
    group = season, 
    color = season, 
    fill = season
  )
)
q <- q + geom_line()
q <- q + geom_ribbon(
  data = aggregated_county_to_nation_weekly[
    season %in% c("2019/2020") &
    attr == "sim_value_ili_isoweekmean7_13_pr100=0"
  ],
  aes(
    ymin = cumsum_q025, 
    ymax = cumsum_q975
  ), 
  alpha = 0.4, 
  colour = NA
)
q <- q + scale_y_continuous("Estimated cumulative attributable mortality")
q <- q + ggtitle("Estimated cumulative attributable mortality over influenza seasons in Norway")
q

We can also plot the estimated weekly attributable mortality in Norway

q <- ggplot(
  data = aggregated_county_to_nation_weekly[attr == "sim_value_ili_isoweekmean7_13_pr100=0"], 
  aes(x = seasonweek, y = cumsum, group = season)
  ) 
q <- q + geom_line(
  data = aggregated_county_to_nation_weekly[
    season != "2019/2020" &
    attr == "sim_value_ili_isoweekmean7_13_pr100=0"
  ],
  aes(
    x = seasonweek, 
    y = median.exp_attr, 
    group = season
  ), 
  color = "grey"
)
q <- q + geom_line(
  data = aggregated_county_to_nation_weekly[
    season == "2019/2020" &
    attr == "sim_value_ili_isoweekmean7_13_pr100=0"
  ], 
  aes(
    x = seasonweek,
    y = median.exp_attr,
    group = season
  ), 
  color = "blue"
)
q <- q + geom_ribbon(
  data = aggregated_county_to_nation_weekly[
    season == "2019/2020" &
    attr == "sim_value_ili_isoweekmean7_13_pr100=0"
  ],
  aes(
    x = seasonweek,
    ymin = q025.exp_attr,
    ymax = q975.exp_attr
  ),
  fill = "blue",
  alpha=0.4
)
q <- q + scale_y_continuous("Estimated attributable mortality")
q <- q + ggtitle("Estimated mortality due to ILI per week")
q

Incident rate ratio

Until now we have focused on estimating attributable mortality. Now we will investigate computing the incident rate ratio (IRR) for ili_isoweekmean7_13_pr100. To do this we will use the fit made by fit_attrib on the county dataset but we will change the values for ili_isoweekmean7_13_pr100 to 1 (IRRs are generally expressed as the effect of the exposure changing from 0 to 1).

data_fake_county_irr <- data.table::copy(data_fake_county)
data_fake_county_irr[, ili_isoweekmean7_13_pr100 := 1]
head(data_fake_county_irr, 5)
#>    location_code isoyear isoweek isoyearweek    season seasonweek pop_jan1_n
#> 1:  county_nor03    2010       1     2010-01 2009/2010         24     693494
#> 2:  county_nor03    2011       1     2011-01 2010/2011         24     693494
#> 3:  county_nor03    2012       1     2012-01 2011/2012         24     693494
#> 4:  county_nor03    2013       1     2013-01 2012/2013         24     693494
#> 5:  county_nor03    2014       1     2014-01 2013/2014         24     693494
#>    ili_isoweekmean0_6_pr100 ili_isoweekmean7_13_pr100 heatwavedays_n deaths_n
#> 1:                0.9231202                         1              0      112
#> 2:                1.8997241                         1              0      113
#> 3:                1.3924947                         1              0      128
#> 4:                0.9296033                         1              0      126
#> 5:                1.3933639                         1              0      115

Then we can set the reference value to zero and hence obtain the IRR for the given exposure.

exposures_irr = c(ili_isoweekmean7_13_pr100 = 0)

Now we use est_attrib to create the simulations.

est_attrib_sim_county_irr <- attrib::est_attrib(
  fit_county, 
  data_fake_county_irr, 
  exposures = exposures_irr,
  n_sim = 100
)
head(est_attrib_sim_county_irr, 5)
#>    location_code isoyear isoweek isoyearweek    season seasonweek pop_jan1_n
#> 1:  county_nor03    2010       1     2010-01 2009/2010         24     693494
#> 2:  county_nor03    2011       1     2011-01 2010/2011         24     693494
#> 3:  county_nor03    2012       1     2012-01 2011/2012         24     693494
#> 4:  county_nor03    2013       1     2013-01 2012/2013         24     693494
#> 5:  county_nor03    2014       1     2014-01 2013/2014         24     693494
#>    ili_isoweekmean0_6_pr100 ili_isoweekmean7_13_pr100 heatwavedays_n deaths_n
#> 1:                0.9231202                         1              0      112
#> 2:                1.8997241                         1              0      113
#> 3:                1.3924947                         1              0      128
#> 4:                0.9296033                         1              0      126
#> 5:                1.3933639                         1              0      115
#>    id sim_id sim_value_exposures=observed sim_value_ili_isoweekmean7_13_pr100=0
#> 1:  1      1                     115.0372                              111.4212
#> 2:  2      1                     116.8059                              113.2856
#> 3:  3      1                     117.3511                              113.5094
#> 4:  4      1                     115.0757                              111.6920
#> 5:  5      1                     115.8099                              111.5854

We see we have obtained values for the reference of the exposure in the same way as before. The difference is that we changed the dataset before running est_attrib. This means we will now be observing the difference between ili_isoweekmean7_13_pr100=0 and ili_isoweekmean7_13_pr100=1.

We now aggregate to the national seasonal level.

aggregated_county_to_nation_sim_irr <-  est_attrib_sim_county_irr[, .(
  "sim_value_exposures=observed" = sum(`sim_value_exposures=observed`),
  "sim_value_ili_isoweekmean7_13_pr100=0"= sum(`sim_value_ili_isoweekmean7_13_pr100=0`), 
  deaths_n = sum(deaths_n)
), keyby = .(season, sim_id)]

Here we generate the IRR:

aggregated_county_to_nation_sim_irr[, exp_irr:= (`sim_value_exposures=observed`/`sim_value_ili_isoweekmean7_13_pr100=0`
)]
head(aggregated_county_to_nation_sim_irr,5)
#>       season sim_id sim_value_exposures=observed
#> 1: 2009/2010      1                     44601.63
#> 2: 2009/2010      2                     44623.96
#> 3: 2009/2010      3                     44827.63
#> 4: 2009/2010      4                     45239.76
#> 5: 2009/2010      5                     44872.28
#>    sim_value_ili_isoweekmean7_13_pr100=0 deaths_n  exp_irr
#> 1:                              43199.65    44006 1.032453
#> 2:                              43345.84    44006 1.029486
#> 3:                              43352.20    44006 1.034034
#> 4:                              43586.40    44006 1.037933
#> 5:                              43385.19    44006 1.034276

Now we can compute the quantiles:


col_names <- colnames(aggregated_county_to_nation_sim_irr)
data.table::setkeyv(
  aggregated_county_to_nation_sim_irr,
  col_names[!col_names %in% c("exp_irr", "sim_id", "sim_value_exposures=observed", "sim_value_ili_isoweekmean7_13_pr100=0")]
)

aggregated_county_to_nation_irr <- aggregated_county_to_nation_sim_irr[,
  unlist(recursive = FALSE, lapply(.(median = median, q025 = q025, q975 = q975), function(f) lapply(.SD, f))),
  by = eval(data.table::key(aggregated_county_to_nation_sim_irr)),
  .SDcols = c("exp_irr")
]
aggregated_county_to_nation_irr[, tag := "aggregated"]

aggregated_county_to_nation_irr
#>        season deaths_n median.exp_irr q025.exp_irr q975.exp_irr        tag
#>  1: 2009/2010    44006       1.034434     1.024874     1.042590 aggregated
#>  2: 2010/2011    43316       1.033053     1.023506     1.041198 aggregated
#>  3: 2011/2012    43221       1.035828     1.026256     1.043996 aggregated
#>  4: 2012/2013    43020       1.032271     1.022731     1.040410 aggregated
#>  5: 2013/2014    43309       1.039849     1.030240     1.048048 aggregated
#>  6: 2014/2015    43234       1.032363     1.022822     1.040503 aggregated
#>  7: 2015/2016    44320       1.038316     1.028721     1.046503 aggregated
#>  8: 2016/2017    43468       1.032752     1.023208     1.040895 aggregated
#>  9: 2017/2018    43438       1.039011     1.029409     1.047204 aggregated
#> 10: 2018/2019    43350       1.030513     1.020990     1.038639 aggregated
#> 11: 2019/2020    43707       1.035991     1.026417     1.044160 aggregated

Now we compare the resulting values for IRR with the ones obtained by coef(fit_county)$season and the 90 percent credible interval computed manually using the standard deviation given by summary(fit_county) for ili_isoweekmean7_13_pr100.

coef_fit_county <- data.table::as.data.table(coef(fit_county)$season)
col_names_coef <- c("ili_isoweekmean7_13_pr100")
coef_irr_data <- coef_fit_county[, ..col_names_coef]
coef_irr_data[, irr := exp(ili_isoweekmean7_13_pr100)]
coef_irr_data[, q025 := exp(ili_isoweekmean7_13_pr100 - 1.96 *0.003761)]  # 0.003761 is the standard deviation from coef(fit_county)
coef_irr_data[, q975 := exp(ili_isoweekmean7_13_pr100 + 1.96 *0.003761)]
coef_irr_data[, tag := "from_coef"]
coef_irr_data
#>     ili_isoweekmean7_13_pr100      irr     q025     q975       tag
#>  1:                0.03380077 1.034379 1.026782 1.042032 from_coef
#>  2:                0.03246441 1.032997 1.025410 1.040640 from_coef
#>  3:                0.03514786 1.035773 1.028166 1.043436 from_coef
#>  4:                0.03170748 1.032216 1.024634 1.039853 from_coef
#>  5:                0.03902228 1.039794 1.032157 1.047487 from_coef
#>  6:                0.03179648 1.032307 1.024726 1.039945 from_coef
#>  7:                0.03754698 1.038261 1.030635 1.045943 from_coef
#>  8:                0.03217375 1.032697 1.025112 1.040338 from_coef
#>  9:                0.03821602 1.038956 1.031325 1.046643 from_coef
#> 10:                0.03000346 1.030458 1.022890 1.038082 from_coef
#> 11:                0.03530514 1.035936 1.028327 1.043600 from_coef

Add the correct seasons to the data.

coef_irr_data <- cbind(season = aggregated_county_to_nation_irr$season, coef_irr_data)
coef_irr_data
#>        season ili_isoweekmean7_13_pr100      irr     q025     q975       tag
#>  1: 2009/2010                0.03380077 1.034379 1.026782 1.042032 from_coef
#>  2: 2010/2011                0.03246441 1.032997 1.025410 1.040640 from_coef
#>  3: 2011/2012                0.03514786 1.035773 1.028166 1.043436 from_coef
#>  4: 2012/2013                0.03170748 1.032216 1.024634 1.039853 from_coef
#>  5: 2013/2014                0.03902228 1.039794 1.032157 1.047487 from_coef
#>  6: 2014/2015                0.03179648 1.032307 1.024726 1.039945 from_coef
#>  7: 2015/2016                0.03754698 1.038261 1.030635 1.045943 from_coef
#>  8: 2016/2017                0.03217375 1.032697 1.025112 1.040338 from_coef
#>  9: 2017/2018                0.03821602 1.038956 1.031325 1.046643 from_coef
#> 10: 2018/2019                0.03000346 1.030458 1.022890 1.038082 from_coef
#> 11: 2019/2020                0.03530514 1.035936 1.028327 1.043600 from_coef

rbindlist the two datasets together.

total_data_irr <- data.table::rbindlist(list(coef_irr_data, aggregated_county_to_nation_irr), use.names = FALSE)
total_data_irr[, ili_isoweekmean7_13_pr100 := NULL]
total_data_irr
#>        season      irr     q025     q975        tag
#>  1: 2009/2010 1.034379 1.026782 1.042032  from_coef
#>  2: 2010/2011 1.032997 1.025410 1.040640  from_coef
#>  3: 2011/2012 1.035773 1.028166 1.043436  from_coef
#>  4: 2012/2013 1.032216 1.024634 1.039853  from_coef
#>  5: 2013/2014 1.039794 1.032157 1.047487  from_coef
#>  6: 2014/2015 1.032307 1.024726 1.039945  from_coef
#>  7: 2015/2016 1.038261 1.030635 1.045943  from_coef
#>  8: 2016/2017 1.032697 1.025112 1.040338  from_coef
#>  9: 2017/2018 1.038956 1.031325 1.046643  from_coef
#> 10: 2018/2019 1.030458 1.022890 1.038082  from_coef
#> 11: 2019/2020 1.035936 1.028327 1.043600  from_coef
#> 12: 2009/2010 1.034434 1.024874 1.042590 aggregated
#> 13: 2010/2011 1.033053 1.023506 1.041198 aggregated
#> 14: 2011/2012 1.035828 1.026256 1.043996 aggregated
#> 15: 2012/2013 1.032271 1.022731 1.040410 aggregated
#> 16: 2013/2014 1.039849 1.030240 1.048048 aggregated
#> 17: 2014/2015 1.032363 1.022822 1.040503 aggregated
#> 18: 2015/2016 1.038316 1.028721 1.046503 aggregated
#> 19: 2016/2017 1.032752 1.023208 1.040895 aggregated
#> 20: 2017/2018 1.039011 1.029409 1.047204 aggregated
#> 21: 2018/2019 1.030513 1.020990 1.038639 aggregated
#> 22: 2019/2020 1.035991 1.026417 1.044160 aggregated
#>        season      irr     q025     q975        tag

q <- ggplot(
  data = total_data_irr, 
  aes(
    x = season,
    group = tag, 
    color = tag
  )
) 
q <- q +  geom_pointrange(
  aes(
    y = irr,
    ymin = q025,
    ymax = q975
  ),
  position = position_dodge(width = 0.3)
)
q <- q + theme(axis.text.x = element_text(angle = 90),axis.title.x=element_blank())
q <- q + labs(y = "Incident risk ratio")
q <- q + ggtitle("Incident risk ratio for ILI per season")
q

As we can see these intervals are very similar.

The benefit of the simulated approach is that this process will be equally easy no matter the complexity of what we want to compute the IRR for. We do not have to take into account the variance-covariance matrix at any stage.

Aurora Christine Hofman

2020-07-21