Introduction to attrib

In attrib: Attributable Burden of Disease

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(attrib)
library(data.table)

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 fake_data_county and fake_data_nation.

fake_data_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
• week: Week number
• season: Years of the season
• year: Year
• yrwk: Year and week
• x: Number of weeks from the start of the season
• pop: Population size
• pr100_ili: Percentage of doctors consultations diagnosed with influenza like illnesses
• pr100_ili_lag_1: pr_100_ili lagged with one week
• temperature: Temperature
• temperature_high: number of heatwaves
• deaths: number of deaths

fake_data_nation is a similar dataset at the national level.

data_fake_county <- attrib::data_fake_county
data_fake_nation <- attrib::data_fake_nation
head(data_fake_county, 5)

In this example we will look at the exposures pr100_ili_lag_1 and temperature_high 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:
• temperature_high
• pr100_ili_lag_1
• sin(2 * pi * (week - 1) / 52)
• cos(2 * pi * (week - 1) / 52)
• the random effects:
• (1|location_code)
• (pr100_ili_lag_1|season)
• the offset:
• log(pop)

#response
response <- "deaths"

# fixed effects
fixef_county <- " temperature_high +
  pr100_ili_lag_1 +
  sin(2 * pi * (week - 1) / 52) +
  cos(2 * pi * (week - 1) / 52)"


#random effects
ranef_county <- "(1|location_code) +
  (pr100_ili_lag_1|season)"

#offset
offset_county <- "log(pop)"

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

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:
• temperature_high
• pr100_ili_lag_1
• sin(2 * pi * (week - 1) / 52)
• cos(2 * pi * (week - 1) / 52)
• the random effects:
• (pr100_ili_lag_1|season)
• the offset:
• log(pop)

# take in the fixed effects
response = "deaths"
fixef_nation <- "temperature_high +
  pr100_ili_lag_1 +
  sin(2 * pi * (week - 1) / 52) +
  cos(2 * pi * (week - 1) / 52)"


#take in the random effects
ranef_nation <- "(pr100_ili_lag_1|season)"

# take in the offset
offset_nation <- "log(pop)"

  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)

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( "temperature_high" = 0, "pr100_ili_lag_1" = 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)

We can see in the above dataset that the columns id, sim_id, sim_value_exposures=observed, sim_value_temperature_high=0, sim_value_pr100_ili_lag_1=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_temperature_high and sim_value_pr100_ili_lag_1.

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", 
                                                              "season",  
                                                              "x", 
                                                              "week", 
                                                              "id", 
                                                              "sim_id", 
                                                              "deaths", 
                                                              "sim_value_exposures=observed"),
                                           measure.vars = c("sim_value_temperature_high=0", 
                                                            "sim_value_pr100_ili_lag_1=0")) 
data.table::setnames(est_attrib_county_long, "variable", "attr")

head(est_attrib_county_long, 5)

We can see that the columns sim_value_temperature_high=0, sim_value_pr100_ili_lag_1=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", 
                                                              "season",  
                                                              "x", 
                                                              "week", 
                                                              "id", 
                                                              "sim_id", 
                                                              "deaths", 
                                                              "sim_value_exposures=observed"),
                                           measure.vars = c("sim_value_temperature_high=0", 
                                                            "sim_value_pr100_ili_lag_1=0")) 
data.table::setnames(est_attrib_nation_long, "variable", "attr")

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 = sum(deaths)
), 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)

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 = sum(deaths)
), keyby = .(season, attr, sim_id)]

aggregated_nation[, exp_attr:= (`sim_value_exposures=observed` - value)]
aggregated_nation[, tag:= "nation"]
head(aggregated_nation, 5)

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
q05 <- function(x){
  return(quantile(x, 0.05))
}
q95 <- function(x){
  return(quantile(x, 0.95))
}

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")])

aggregated_sim_seasonal_data_national<- data_national[,
                                   unlist(recursive = FALSE, 
                                          lapply(.(median = median, q05 = q05, q95 = q95),
                                                                    function(f) lapply(.SD, f)
                                   )), 
                                   by = eval(data.table::key(data_national)),
                                   .SDcols = c("exp_attr")]

head(aggregated_sim_seasonal_data_national,5)

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_pr100_ili_lag_1=0"], 
                       aes(x = season, y = median.exp_attr, group = tag, color = tag)) 
q <- q + geom_pointrange(aes(x = season, y = median.exp_attr, ymin = q05.exp_attr, ymax = q95.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 = sum(deaths)
), keyby = .(season, x, week, 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)

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, q05 = q05, q95 = q95),
                                               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_q05 := cumsum(q05.exp_attr), by = .( attr, season)]
aggregated_county_to_nation_weekly[, cumsum_q95 := cumsum(q95.exp_attr), by = .( attr, season)]

head(aggregated_county_to_nation_weekly, 5)

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_pr100_ili_lag_1=0"
  ],
  aes(
    x = x, 
    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_pr100_ili_lag_1=0"
  ],
  aes(
    ymin = cumsum_q05, 
    ymax = cumsum_q95
  ), 
  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_pr100_ili_lag_1=0"], 
  aes(x = x, y = cumsum, group = season)
  ) 
q <- q + geom_line(
  data = aggregated_county_to_nation_weekly[
    season != "2019/2020" &
    attr == "sim_value_pr100_ili_lag_1=0"
  ],
  aes(
    x = x, 
    y = median.exp_attr, 
    group = season
  ), 
  color = "grey"
)
q <- q + geom_line(
  data = aggregated_county_to_nation_weekly[
    season == "2019/2020" &
    attr == "sim_value_pr100_ili_lag_1=0"
  ], 
  aes(
    x = x,
    y = median.exp_attr,
    group = season
  ), 
  color = "blue"
)
q <- q + geom_ribbon(
  data = aggregated_county_to_nation_weekly[
    season == "2019/2020" &
    attr == "sim_value_pr100_ili_lag_1=0"
  ],
  aes(
    x = x,
    ymin = q05.exp_attr,
    ymax = q95.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 pr100_ili_lag_1. To do this we will use the fit made by fit_attrib on the county dataset but we will change the values for pr100_ili_lag_1 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[, pr100_ili_lag_1 := 1]
head(data_fake_county_irr, 5)

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

exposures_irr = c(pr100_ili_lag_1 = 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)

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 pr100_ili_lag_1=0 and pr100_ili_lag_1=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_pr100_ili_lag_1=0"= sum(`sim_value_pr100_ili_lag_1=0`), 
  deaths = sum(deaths)
), keyby = .(season, sim_id)]

Here we generate the IRR:

aggregated_county_to_nation_sim_irr[, exp_irr:= (`sim_value_exposures=observed`/`sim_value_pr100_ili_lag_1=0`
)]
head(aggregated_county_to_nation_sim_irr,5)

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_pr100_ili_lag_1=0")]
)

aggregated_county_to_nation_irr <- aggregated_county_to_nation_sim_irr[,
  unlist(recursive = FALSE, lapply(.(median = median, q05 = q05, q95 = q95), 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

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 pr100_ili_lag_1.

coef_fit_county <- data.table::as.data.table(coef(fit_county)$season)
col_names_coef <- c("pr100_ili_lag_1")
coef_irr_data <- coef_fit_county[, ..col_names_coef]
coef_irr_data[, irr := exp(pr100_ili_lag_1)]
coef_irr_data[, q05 := exp(pr100_ili_lag_1 - 1.645 *0.003761)]  # 0.003761 is the standard deviation from coef(fit_county)
coef_irr_data[, q95 := exp(pr100_ili_lag_1 + 1.645 *0.003761)]
coef_irr_data[, tag := "from_coef"]
coef_irr_data

Add the correct seasons to the data.

coef_irr_data <- cbind(season = aggregated_county_to_nation_irr$season, coef_irr_data)
coef_irr_data

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[, pr100_ili_lag_1 := NULL]
total_data_irr

q <- ggplot(
  data = total_data_irr, 
  aes(
    x = season,
    group = tag, 
    color = tag
  )
) 
q <- q +  geom_pointrange(
  aes(
    y = irr,
    ymin = q05,
    ymax = q95
  ),
  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.

attrib documentation built on March 30, 2021, 5:11 p.m.