Calculate attributable number and fractions from a Bayesian distributed-lag model (B-DLNM).

Compute attributable numbers (AN) and attributable fractions (AF) from a fitted Bayesian distributed lag non-linear model (bdlnm()). The function uses posterior predicted relative risks from bcrosspred() and applies a forward or backward lag algorithm to compute per-time and total attributable measures, optionally filtering the calculation to a subset of time points.

Usage

attributable(
  object,
  data,
  name_date = NULL,
  name_exposure,
  name_cases = NULL,
  name_filter = NULL,
  dir = "back",
  basis = NULL,
  cen,
  range = NULL,
  lag_average = TRUE
)

Arguments

object: A fitted "bdlnm" class object returned by bdlnm().
data: A data frame containing the temporal series needed to calculate attributable measures. It can include a date column (optional, see name_date), the exposure values (mandatory, see name_exposure), the number of cases (optional, see name_cases) and a binary (0/1) filter column (optional, see name_filter).
name_date: Optional single string with the name of the column in data containing the date. The column must be of class Date or POSIXt. When provided the function checks that the series is regularly spaced (see Details).
name_exposure: Single string with the name of the exposure column in data.
name_cases: Optional single string with the name of the cases column in data. If not provided, the function returns only attributable fractions (AF) per time point.
name_filter: Optional single string with the name of a binary (0/1) column in data. Only rows with value 1 are used to compute total AF and AN and per-time results are returned only for the filtered rows.
dir: Character; direction of the algorithm to calculate attributable measures. "back" (default) calculates AF and AN attributing current-time outcome to past exposures; "forw" calculates AF and AN attributing current-time exposure to future outcomes.
basis: If the bdlnm model has more than one basis, the name of the basis to use to compute predictions. It must be one of names(object$basis). If the model contains only one basis it is selected automatically.
cen: Numeric scalar; centering exposure value used to compute predictions. If missing the function will attempt to read it from the attributes of the specified basis. If no centering is available the function aborts.
range: Optional numeric vector of length 2 with the exposure range for which attributable measures will be calculated. Values outside range are coerced to cen before prediction.
lag_average: Logical (default TRUE). When TRUE use lag-averaged contributions to compute AN in the forward algorithm; when FALSE use the full lag-structured contributions instead.

Value

A list with components:

af: matrix (rows = time points, columns = posterior samples) with attributable fractions per time point.
an: matrix (rows = time points, columns = posterior samples) with attributable numbers per time point.
aftotal: numeric vector (length = number of posterior samples) with posterior samples of total AF across all the selected period.
antotal: numeric vector (length = number of posterior samples) with posterior samples of total AN across all the selected period.
af.summary: data.frame with summary statistics (mean, sd, quantiles, mode) for AF per time point.
an.summary: data.frame with summary statistics (mean, sd, quantiles, mode) for AN per time point.
aftotal.summary: data.frame with summary statistics (mean, sd, quantiles, mode) for total AF.
antotal.summary: data.frame with summary statistics (mean, sd, quantiles, mode) for total AN.

Details

The function first obtains posterior predicted effects at the observed exposure values by calling bcrosspred() with exp_at = data[[name_exposure]]. Predictions must include relative-risk scale predictions so the previously fitted "bdlnm" model must have a log or logit link; otherwise the function aborts. These predictions require a defined centering value (cen), as attributable measures are always computed with respect to a reference exposure. This reference exposure is usually an optimal exposure computed with the optimal_exposure() function, such as the Minimum Mortality Temperature (MMT).

Two different algorithms can be chosen to calculate attributable measures:

Backward (dir = "back"): for each time point, contributions from past exposures (over the lag window) are combined to calculate the daily AF/AN.
Forward (dir = "forw"): for each time point, the contribution of that time point exposure to future outcomes (over the lag window) is combined to calculate the daily AF/AN.

Both algorithms are fully described by Gasparrini and Leone (2014) doi:10.1186/1471-2288-14-55.

Required columns to calculate AF and AN are name_exposure and name_cases columns. If name_cases is not supplied only AF per time can be computed and the output will only contain two elements: $af and $af.summary. If name_date is provided the function checks that dates are equispaced (checks seconds, minutes, hours, days, weeks, months or years). Time series have to be equispaced because the algorithms used to calculate attributable measures rely on consecutive time points over the lag window,. For example, if you only have seasonal observations (e.g., summers) expand the data to the full sequence and insert NA for missing exposures/cases and use name_filter to compute measures only for the seasonal subset.

Only "bdlnm" objects fitted with a cross-basis are supported; models fitted with a one-basis (no lag) are not suitable for attributable calculations.

Note

This function is inspired by attrdl() developed by Gasparrini and Leone (2014) doi:10.1186/1471-2288-14-55. It has been adapted to work in a Bayesian framework within the bdlnm package.

References

Gasparrini A., Leone M. (2014). Attributable risk from distributed lag models. BMC Medical Research Methodology, 14, 55. doi:10.1186/1471-2288-14-55.

Quijal-Zamorano M., Martinez-Beneito M.A., Ballester J., Marí-Dell'Olmo M. (2024). Spatial Bayesian distributed lag non-linear models (SB-DLNM) for small-area exposure-lag-response epidemiological modelling. International Journal of Epidemiology, 53(3), dyae061. doi:10.1093/ije/dyae061.

Author

Pau Satorra, Marcos Quijal-Zamorano.

Examples


# Filter the dataset to reduce computational time:

# Exposure-response and lag-response spline parameters
dlnm_var <- list(
  var_prc = c(10, 75, 90),
  var_fun = "ns",
  lag_fun = "ns",
  max_lag = 21,
  lagnk = 3
)

# Cross-basis parameters
argvar <- list(fun = dlnm_var$var_fun,
               knots = stats::quantile(london$tmean,
                                dlnm_var$var_prc/100, na.rm = TRUE),
               Bound = range(london$tmean, na.rm = TRUE))

arglag <- list(fun = dlnm_var$lag_fun,
               knots = dlnm::logknots(dlnm_var$max_lag, nk = dlnm_var$lagnk))

# Create crossbasis
cb <- dlnm::crossbasis(london$tmean, lag = dlnm_var$max_lag, argvar, arglag)

# Seasonality of mortality time series
seas <- splines::ns(london$date, df = round(8 * length(london$date) / 365.25))

# Prediction values (equidistant points)
temp <- round(seq(min(london$tmean), max(london$tmean), by = 0.1), 1)

# Model

if (check_inla()) {
mod <- bdlnm(mort_75plus ~ cb + factor(dow) + seas,
             data = london,
             family = "poisson",
             sample.arg = list(seed = 432, seed = 1L))

# Predict
cpred <- bcrosspred(mod, exp_at = temp)

# compute centering (MMT) using optimal_exposure
mmt <- optimal_exposure(mod, exp_at = temp)
cen <- mmt$summary[["0.5quant"]]

# Attributable numbers and fractions (using the backwards algorithm):
attr <- attributable(mod, london, name_date = "date",
name_exposure = "tmean", name_cases = "mort_75plus", cen = cen, dir = "back")
}
#> Warning: Since 'seed!=0', parallel model is disabled and serial model is selected, num.threads='1:1'
#> Warning: Centering value unspecified (`cen`). Automatically set to: 12.85.
#> Registered S3 methods overwritten by 'crs':
#>   method         from
#>   print.crs      sf  
#>   predict.gsl.bs np