Attribute premature deaths or YLL to an environmental stressor using a life table approach

This function assesses premature deaths or years of life lost (YLL) attributable to exposure to an environmental stressor using a life table approach.

Usage

attribute_lifetable(
  age_group,
  sex,
  bhd_central,
  bhd_lower = NULL,
  bhd_upper = NULL,
  population,
  health_outcome = NULL,
  min_age = NULL,
  max_age = NULL,
  approach_exposure = "single_year",
  approach_newborns = "without_newborns",
  year_of_analysis,
  time_horizon = NULL,
  fraction_lived = 0.5,
  exp_central = NULL,
  exp_lower = NULL,
  exp_upper = NULL,
  cutoff_central = 0,
  cutoff_lower = NULL,
  cutoff_upper = NULL,
  threshold = NULL,
  erf_eq_central = NULL,
  erf_eq_lower = NULL,
  erf_eq_upper = NULL,
  rr_central = NULL,
  rr_lower = NULL,
  rr_upper = NULL,
  rr_increment = NULL,
  erf_shape = NULL,
  prop_pop_exp = 1,
  geo_id_micro = "a",
  geo_id_macro = NULL,
  info = NULL,
  main_results_by = NULL
)

Arguments

age_group

Numeric vector or string vector providing the age groups considered in the assessment. In case of use in attribute_lifetable)(), it must be a numeric and contain single year age groups. See Details for more info. Optional argument for attribute_health(); needed for attribute_lifetable().

sex

Numeric vector or string vector specifying the sex of the groups considered in the assessment.Optional argument.

bhd_central, bhd_lower, bhd_upper

Numeric value or numeric vector providing the baseline health data of the health outcome of interest in the study population and (optionally) the corresponding lower bound and the upper 95% confidence interval bounds. See Details for more info. Only applicable in RR pathways; always required.

population

Numeric vector For attribute_lifetable(), it is an obligatory argument specifying the mid-year populations per age (i.e. age group size = 1 year) for the (first) year of analysis. For attribute_health() it is an optional argument which specifies the population used to calculate attributable impacts rate per 100 000 population. See Details for more info.

health_outcome

String specifying the desired result of the life table assessment. Options: "deaths" (premature deaths), "yll" (years of life lost).

min_age, max_age

Numeric value specifying the minimum and maximum age for which the exposure will affect the exposed population, respectively. See Details for more info.

approach_exposure

String specifying whether exposure is constant or only in one year. Options: "single_year" (default), "constant".

approach_newborns

String specifying whether newborns are to be considered in the years after the year of analysis or not. Options: "without_newborns" (default), "with_newborns". See Details for more info.

year_of_analysis

Numeric value providing the first with exposure to the environmental stressor.

time_horizon

Numeric value specifying the time horizon (number of years) for which the attributable YLL or premature deaths are to be considered. See Details for more info. Optional argument.

fraction_lived

Numeric vector Numeric vector or single numeric scalar referring to the average fraction of the age interval lived by individuals who die within that interval. Default is 0.5.

exp_central, exp_lower, exp_upper

Numeric value or numeric vector specifying the exposure level(s) to the environmental stressor and (optionally) the corresponding lower and upper bound of the 95% confidence interval. See Details for more info.

cutoff_central, cutoff_lower, cutoff_upper

Numeric value specifying the exposure cut-off value, i.e. the exposure level below which no health impacts are quantified, and (optionally) the corresponding lower and upper 95% confidence interval bounds. Default: 0, or same value as threshold, if it is entered. If cutoff is higher than threshold, the exposure-response function is truncated at the cut-off value. Expressed in the same unit as the exposure. See the vignette chapter Cut-off vs. threshold.

threshold

Numeric value specifying the effect threshold, i.e. the exposure level from which the exposure-response function starts to show an effect. It is the anchor of the curve and is therefore subtracted from the exposure. Default: same value as the cut-off. Expressed in the same unit as the exposure. See the vignette chapter Cut-off vs. threshold.

erf_eq_central, erf_eq_lower, erf_eq_upper

String or function specifying the exposure-response function and (optionally) the corresponding lower and upper 95% confidence interval functions. See Details for more info. Required in AR pathways; in RR pathways required only if rr_... argument(s) not specified.

rr_central, rr_lower, rr_upper

Numeric value specifying the central relative risk estimate and (optionally) the corresponding lower and upper 95% confidence interval bounds. Only applicable in RR pathways; not required if erf_eq_... argument(s) already specified.

rr_increment

Numeric value specifying the exposure increment for which the provided relative risk is valid. See Details for more info. Only applicable in RR pathways; not required if erf_eq_... argument(s) already specified.

erf_shape

String value specifying the exposure-response function shape to be assumed. Options (no default): "linear", log_linear", "linear_log", "log_log". Input exposure values must be expressed in same unit as the increment of the relative risk. The re-scale of the relative risk is unbounded above and users are responsible for the plausible range. Only applicable in RR pathways; not required if erf_eq_... argument(s) already specified.

prop_pop_exp

Numeric value or numeric vector specifying the population fraction(s) exposed for each exposure (category), i.e. the proportion of the total population that falls in each exposure category. Default: 1. The fractions do not have to add up to 1: the part of the population that they do not cover is treated as unexposed, i.e. it gets the relative risk of the reference level. E.g, in air pollution assessments everybody is usually exposed and the fractions add up to 1, whereas in noise assessments they typically add up to less than 1, because exposure is only reported above a given level. Accordingly, bhd_... must always refer to the total population. See Details for more info. Only applicable in RR pathways.

geo_id_micro, geo_id_macro

Numeric vector or string vector providing unique IDs of the geographic area considered in the assessment (geo_id_micro) and (optionally) providing higher-level IDs (geo_id_macro) to aggregate the geographic areas at. See Details for more info. Only applicable in assessments with multiple geographic units.

info

String, data frame or tibble providing information about the assessment. This will be added to the results table as column(s) keeping the name(s) that you entered with the prefix info_ (e.g. a column education becomes info_education) if a data frame is entered, or as one single column called info if a vector is entered. These additional columns can be used to further stratify the analysis in a secondary step. Optional argument.

main_results_by

Character vector naming the dimensions that the main results are reported by, i.e. the dimensions whose impacts must never be added together, e.g. different exposure-outcome pairs. By default all dimensions except the geographic units and the uncertainty (_ci) columns are summed in the main results. Names entered here are kept as separate rows instead. Options: the columns of info (named as you named them, or "info" if you entered a vector instead of a data frame), "sex", "age_group", "exp_category", "geo_id_micro", "geo_id_macro" and, in attribute_lifetable(), "year". Note that this argument does not create the results_by_... tables of the detailed output, which are available anyway: it determines which dimensions survive in health_main and in all of them. See the vignette chapter Multiple exposure-outcome pairs. Optional argument.

Value

This function returns a list containing:

1) health_main (tibble) containing the main results;

• impact (numeric column) attributable health burden/impact

• pop_fraction (numeric column) population attributable fraction; only applicable in relative risk assessments

• And many more

2) health_detailed (list) containing detailed (and interim) results.

• input_args (list) containing all the argument inputs used in the background

• input_table (tibble) containing the inputs after preparation

• results_raw (tibble) containing results for all combinations of input (geo units, uncertainty, age and sex specific data...)

• results_by_... (tibble) containing results stratified by each geographic unit, age or sex.

Details

Function arguments

age_group The numeric values must refer to 1 year age groups, e.g. c(0:99). To convert multi-year/larger age groups to 1 year age groups use the function prepare_lifetable() (see its function documentation for more info).

main_results_by Optional argument. By default the impacts of all subgroups, and of all the years of the time horizon, are added up in the main results. That is not meaningful for subgroups that quantify overlapping people in different ways, e.g. different exposure-outcome pairs. Enter their names here to keep them as separate rows. Entering "year" shows the impacts per year of the time horizon. See the vignette chapter Multiple exposure-outcome pairs.

Last age group The life table is closed at the last age group, i.e. its survivors are not projected into a further age. Therefore, the last age group must be one in which essentially all remaining deaths occur, as in most national life tables. Otherwise the attributable health impacts are underestimated. If needed, condensate the last age group (i.e. sum the populations and the deaths of the highest ages into it) instead of adding age groups beyond the data. More information in the vignette.

bhd_central,bhd_lower,bhd_upper Deaths per age must be inputted with 1 value per age (i.e. age group size = 1 year). There must be greater than or equal to 1 deaths per age to avoid issues during the calculation of survival probabilities. If zeros show up in the last ages (e.g. age 98 = 0 deaths, 99 years old = 1), please sum the values and condensate last category (e.g. age 98 = 1).

population The population data must be inputted with 1 value per age (i.e. age group size = 1 year). The values must be greater than or equal to 1 per age to avoid issues during the calculation of survival probabilities. Mid-year population of year x can be approximated as the mean of either end-year populations of years x-1 and x or start-of-year populations of years x and x+1. For each age, the inputted values must be greater than or equal to 1 to avoid issues during the calculation of survival probabilities.

approach_newborns If "with_newborns" is selected, it is assumed that for each year after the year of analysis n babies (population aged 0) are born.

approach_exposure Strategy for modeling exposure over time:

• "single_year": Air pollution exposure is evaluated for a single year (year of analysis). Attributable premature deaths are calculated for this year only.

• "constant": Air pollution exposure is sustained across the full projection horizon. Attributable premature deaths and YLLs are accumulated across all years within time_horizon.

time_horizon Applicable for the following cases:

• YLL: single_year or constant exposure

• premature deaths: constant exposure

For example, if 10 is entered one is interested in the impacts of exposure during the year of analysis and the next 9 years (= 10 years in total). Default value: the number of age groups entered in the age_group argument.

min_age, max_age Both bounds are inclusive, e.g. min_age = 30 implies that all adults aged 30 or older will be affected by the exposure and max_age = 69 that no health effects are considered above the age of 69. By default the exposure affects all age groups, i.e. min_age is the youngest and max_age the oldest age group entered in age_group.

fraction_lived is by default 0.5 for all age groups, i.e. the value that AirQ+ assumes. It determines the survival probabilities and matters most in the age groups with the highest mortality, i.e. the last ones. See the vignette for how to choose it.

If the single-year age groups were obtained with prepare_lifetable(), enter here the same fraction_lived that was used there, which is available in the output column fraction_lived_for_attribute. Otherwise the life table would be built with an assumption that differs from the one used for the conversion.

Methodology

The life table approach to obtain YLL and deaths requires population and baseline mortality data to be stratified by one year age groups. This function applies the same approach as the on applied in the WHO tool AirQ+ (WHO 2020) , which is described in previous literature (Miller and Hurley 2003) .

Detailed information about the methodology (including equations) is available in the package vignette. More specifically, see chapters:

• YLL and deaths with life table

• Fraction of the age interval lived

• Cut-off vs. threshold

Conversion of multi-year to single year age groups

To convert multi-year/larger age groups to 1 year age groups, use the healthiar function prepare_lifetable().

Note

For this specific function, the return object health_detailed also contains intermediate_calculations. This is a nested tibble containing intermediate results, such as population projections and impact by age/year.

References

Miller BG, Hurley JF (2003). “Life table methods for quantitative impact assessments in chronic mortality.” Journal of Epidemiology and Community Health, 57(3), 200–206. ISSN 0143-005X. doi:10.1136/jech.57.3.200 .

WHO (2020). “Health impact assessment of air pollution: AirQ+ life table manual.” World Health Organization - Regional Office for Europe. https://www.who.int/europe/publications/i/item/WHO-EURO-2020-1559-41310-56212.

See also

• Upstream: prepare_exposure (only if no exposure data available)

• Alternative: attribute_health, get_paf, get_risk

• Downstream: attribute_mod, compare, daly, multiexpose, standardize, monetize, socialize

Author

Alberto Castro & Axel Luyten

Examples

# Goal: determine YLL attributable to air pollution exposure during one year
# using the life table approach
results <- attribute_lifetable(
  health_outcome = "yll",
  approach_exposure = "single_year",
  approach_newborns = "without_newborns",
  exp_central = 8.85,
  prop_pop_exp = 1,
  cutoff_central = 5,
  rr_central =  1.118,
  rr_increment = 10,
  erf_shape = "log_linear",
  age_group = exdat_lifetable$age_group,
  sex = exdat_lifetable$sex,
  bhd_central = exdat_lifetable$deaths,
  population = exdat_lifetable$midyear_population,
  year_of_analysis = 2019,
  min_age = 20
)
results$health_main$impact # Attributable YLL
#> [1] 28809.87


# Goal: determine attributable premature deaths due to air pollution exposure
# during one year using the life table approach
results_pm_deaths <- attribute_lifetable(
  health_outcome = "deaths",
  approach_exposure = "single_year",
  exp_central = 8.85,
  prop_pop_exp = 1,
  cutoff_central = 5,
  rr_central =  1.118,
  rr_increment = 10,
  erf_shape = "log_linear",
  age_group = exdat_lifetable$age_group,
  sex = exdat_lifetable$sex,
  bhd_central = exdat_lifetable$deaths,
  population = exdat_lifetable$midyear_population,
  year_of_analysis = 2019,
  min_age = 20
)
results_pm_deaths$health_main$impact # Attributable premature deaths
#> [1] 2599.366


# Goal: determine YLL attributable to air pollution exposure (exposure distribution)
# during one year using the life table approach
results <- attribute_lifetable(
  health_outcome = "yll",
  exp_central = rep(c(8, 9, 10), each = 100*2), # each = length of sex or age_group vector
  prop_pop_exp = rep(c(0.2, 0.3, 0.5), each = 100*2), # each = length of sex or age_group vector
  cutoff_central = 5,
  rr_central = 1.118,
  rr_lower = 1.06,
  rr_upper = 1.179,
  rr_increment = 10,
  erf_shape = "log_linear",
  age_group = rep(
    exdat_lifetable$age_group,
    times = 3), # times = number of exposure categories
  sex = rep(
    exdat_lifetable$sex,
    times = 3), # times = number of exposure categories
  population = rep(
    exdat_lifetable$midyear_population,
    times = 3), # times = number of exposure categories
  bhd_central = rep(
    exdat_lifetable$deaths,
    times = 3), # times = number of exposure categories
  year_of_analysis = 2019,
  min_age = 20
)
results$health_main$impact_rounded # Attributable YLL
#> [1] 32185 16849 47413