Skip to contents

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

Source: R/attribute_lifetable.R
attribute_lifetable.Rd

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,
  exp_central = NULL,
  exp_lower = NULL,
  exp_upper = NULL,
  cutoff_central = 0,
  cutoff_lower = NULL,
  cutoff_upper = 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
)

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

Numberic value specifying the minimum and maximum age for which the exposure will affect the exposed population, respectively. Default min_age: 30. Default max_age: none. 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.

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 and (optionally) the corresponding lower and upper 95% confidence interval bounds. Default: 0. See Details for more info.

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". 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). Default: 1. 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. See Details for more info. 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.

  • results_raw (tibble) containing results for each combination of input uncertainty

  • results_by_geo_id_micro (tibble) containing results for each geographic unit under analysis (specified in geo_id_micro argument)

  • results_by_year (tibble) containing results by year

  • results_by_sex (tibble) containing results by sex

  • results_by_age_group (tibble) containing results by age group

  • intermediate_calculations (tibble) containing intermediate results, among others population projections (for both the exposed and unexposed scenarios) and impact by age and year stored in nested tibbles

  • input_table (tibble) containing the inputs to each relevant argument

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

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).

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.

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.

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: length of the numeric vector specified in the age_group argument.

min_age, max_age The min_age default value 30 implies that all adults aged 30 or older will be affected by the exposure; max_age analogeously specifies the age above which no health effects of the exposure are considered.

Conversion of multi-year to single year age groups

To convert multi-year/larger age groups to 1 year age groups use the function prepare_lifetable() and see its function documentation for more info.

Life table methodology

The life table methodology of attribute_lifetable() follows that of the WHO tool AirQ+, and is described in more detail by Miller & Hurley (2003, https://doi.org/10.1136/jech.57.3.200).

In short, two scenarios are compared: 1) a scenario with the exposure level specified in the function ("exposed scenario") and 2) a scenario with no exposure ("unexposed scenario"). First, the entry and mid-year populations of the (first) year of analysis in the unexposed scenario is determined using modified survival probabilities. Second, age-specific population projections using scenario-specific survival probabilities are done for both scenarios. Third, by subtracting the populations in the unexposed scenario from the populations in the exposed scenario the premature deaths/years of life lost attributable to the exposure are determined.

An expansive life table case study by Miller (2010) is available here: https://cleanair.london/app/uploads/CAL-098-Mayors-health-study-report-June-2010-1.pdf.

Determination of populations in the (first) year of analysis

The entry (i.e. start of year) populations in both scenarios is determined as follows: $$entry\_population_{year_1} = midyear\_population_{year_1} + \frac{deaths_{year_1}}{2}$$

Exposed scenario The survival probabilities in the exposed scenario from start of year i to start of year i+1 are calculated as follows: $$prob\_survival = \frac{midyear\_population_i - \frac{deaths_i}{2}}{midyear\_population_i + \frac{deaths_i}{2}}$$ Analogously, the probability of survival from start of year i to mid-year i: $$prob\_survival\_until\_midyear = 1 - \frac{1 - prob\_survival}{2}$$

Unexposed scenario The survival probabilities in the unexposed scenario are calculated as follows:

First, the age-group specific hazard rate in the exposed scenario is calculated using the inputted age-specific mid-year populations and deaths. $$hazard\_rate = \frac{deaths}{mid\_year\_population}$$ Second, the hazard rate is multiplied with the modification factor (\(= 1 - PAF\)) to obtain the age-specific hazard rate in the unexposed scenario. $$hazard\_rate\_mod = hazard\_rate \times modification\_factor$$ Third, the the age-specific survival probabilities (from the start until the end in a given age group) in the unexposed scenario are calculated as follows (cf. Miller & Hurley 2003): $$prob\_survival\_mod = \frac{2-hazard\_rate\_mod}{2+hazard\_rate\_mod}$$ Then the mid-year populations of the (first) year of analysis (year_1) in the unexposed scenario are determined as follows:

First, the survival probabilities from start of year i to mid-year i in the unexposed scenario is calculated as: $$prob\_survival\_until\_midyear\_{mod} = 1 - \frac{1 - prob\_survival\_mod}{2}$$ Second, the mid-year populations of the (first) year of analysis (year_1) in the unexposed scenario is calculated: $$midyear\_population\_unexposed_{year_1} = entry\_population_{year_1} \times prob\_survival\_until\_midyear_{mod}$$

Population projection

Using the age group-specific and scenario-specific survival probabilities calculated above, future populations of each age-group under each scenario are calculated.

Unexposed scenario The entry and mid-year population projections of in the exposed scenario is done as follows:

First, the entry population of year i+1 is calculated (which is the same as the end of year population of year i) by multiplying the entry population of year i and the modified survival probabilities. $$entry\_population_{i+1} = entry\_population_i \times prob\_survival\_mod$$ Second, the mid-year population of year i+1 is calculated. $$midyear\_population_{i+1} = entry\_population_{i+1} \times prob\_survival\_until\_midyear$$

Exposed scenario The population projections for the two possible options of approach_exposure ("single_year" and "constant") for the unexposed scenario are different. In the case of "single_year" exposure, the population projection for the years after the year of exposure is the same as in the unexposed scenario.

In the case of "constant" the population projection is done as follows:

First, the entry population of year i+1 is calculated (which is the same as the end of year population of year i) using the entry population of year i. $$entry\_population_{i+1} = entry\_population_i \times prob\_survival$$ Second, the mid-year population of year i+1 is calculated. $$midyear\_population_{i+1} = entry\_population_{i+1} \times prob\_survival\_until\_midyear$$

Conversion of alternative risk measures to relative risks

For conversion of hazard ratios and/or odds ratios to relative risks refer to https://doi.org/10.1111/biom.13197 and/or use the conversion tool for hazard ratios (https://ebm-helper.cn/en/Conv/HR_RR.html) and/or odds ratios (https://ebm-helper.cn/en/Conv/OR_RR.html).

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