Build a Mediation Design From the WHO Health-Expenditure Data

Assembles the exposure, outcome, mediator, and confounder matrices for one of the analyses in Yu and Kelley (in press) from WHO_health_mediation, ready to pass to pe_mediation(). The exposure is GDP per capita growth, the mediators are the 57 health-expenditure indicators, and the outcome is the chosen health indicator. Optionally restrict to a WHO region and/or a World Bank income group, as in the article's region-specific, income-specific, and region-by-income models.

Usage

WHO_mediation_design(
  outcome = c("imr", "u5mr", "leb", "lbw", "pou"),
  region = NULL,
  income = NULL,
  data = WHO_health_mediation
)

Arguments

outcome: Which health outcome to use as $Y$: "imr" (infant mortality rate), "u5mr" (under-five mortality rate), "leb" (life expectancy at birth), "lbw" (prevalence of low birthweight), or "pou" (prevalence of undernourishment).
region: Optional character vector of WHO regions to keep ("AFR", "AMR", "EMR", "EUR", "SEAR", "WPR"). Default NULL keeps all regions.
income: Optional character vector of income groups to keep ("Low", "Lower-middle", "Upper-middle", "High"). Default NULL keeps all groups.
data: The source data frame, in the shape of WHO_health_mediation: the columns code, region, income, year, gdp_growth, and the chosen outcome, plus at least two indicator columns. Every column other than the key, exposure, and outcome columns of WHO_health_mediation is treated as a candidate mediator, so the year, the exposure, the outcome, and every indicator column must be numeric; region and income may be character or factor. Every row the design uses needs its country code and year, and its region and income wherever those vary among the rows kept (that is, wherever they enter the confounders); a row missing one of them stops the design with a message naming the country. Rows outside the requested region or income group, or dropped for a missing outcome or exposure, are not checked. A data that breaks these rules stops with a message naming the column. Defaults to WHO_health_mediation.

Value

A list with X (exposure, $n \times 1$), Y (outcome vector), M (the $n \times 57$ mediator matrix), Z (the confounder matrix: the region and income indicators that still vary after subsetting, and the year), and the metadata outcome, n (country-year observations), n_countries (unique countries), indicators, region, and income.

Details

Rows with a missing outcome or missing exposure are dropped (the article handles each outcome's coverage separately, which is why the low-birthweight and undernourishment outcomes have fewer observations). The confounder matrix $Z$ contains the WHO region and income group (as indicator variables) and the year (numeric), the covariate set of the article. The region and income indicators enter only while they still vary after subsetting: a region-specific model drops the (now constant) region, and unused factor levels are dropped so no all-zero indicator columns remain. The year always enters, so a subset must span at least two years; a single-year subset leaves a constant year column, which pe_mediation() rejects.

The indicator columns are passed through as they are. A missing value in one of them makes pe_mediation() stop, since the method has no missing-data mechanism; WHO_mediation_analysis() instead drops such an indicator within the affected group and names it in a message.

To fit with the preprocessing of the analysis behind the article's tables, standardize the exposure and mediators and center the outcome while leaving the confounders (the region and income indicators and the year) unscaled. The article's text says that covariates are standardized; the unscaled confounders are a choice of that analysis. The grid below, seq(0.1, 2, length.out = 100), is the grid behind the article's Tables 1, 2, and S.8 to S.12 and the default of WHO_mediation_analysis(); the call gives the first row of Table 1 (benchmark p-value 0.0644, gge_gdp identified as active):


  des <- WHO_mediation_design("imr")
  pe_mediation(scale(des$X), des$Y - mean(des$Y), scale(des$M),
               Z = des$Z, outcome = "continuous", scale = FALSE,
               lambda_grid = seq(0.1, 2, length.out = 100))

HBIC chooses 0.1, the smallest value of that grid, for this fit, as it does in about half of the article's cells, so the fit warns (class poemed_grid_boundary); WHO_mediation_analysis() keeps the article's grid and does not raise the warning (see its Details).

The simpler call pe_mediation(des$X, des$Y, des$M, des$Z, outcome = "continuous") standardizes $X$, $M$, and $Z$ and centers $Y$, and so fits a different model: scaling the confounder columns changes both the benchmark Wald test and the penalized selection, so its p-values and its identified active set can differ from those of the call above. WHO_mediation_analysis() applies the preprocessing and the grid of the article's analysis for you.

References

Yu, X., & Kelley, K. (in press). Power Enhancement in High-Dimensional Heterogeneous Mediation Analysis. Journal of the American Statistical Association.

Author

Xiufan Yu and Ken Kelley

Examples

# Global infant-mortality model: GDP growth -> health spending -> IMR,
# with the preprocessing and the grid of the article's Table 1; the screen
# identifies gge_gdp. HBIC chooses 0.1, the smallest value of that grid, so
# the fit warns (class poemed_grid_boundary); WHO_mediation_analysis()
# keeps the article's grid and does not raise the warning.
des <- WHO_mediation_design("imr")
c(n = des$n, mediators = ncol(des$M))
#>         n mediators 
#>      2002        57 
fit <- pe_mediation(scale(des$X), des$Y - mean(des$Y), scale(des$M),
  Z = des$Z, outcome = "continuous", scale = FALSE,
  lambda_grid = seq(0.1, 2, length.out = 100))
#> Warning: HBIC selected lambda = 0.1, the smallest value of `lambda_grid`, for the full model and the reduced model of the benchmark test. The criterion is minimized over the grid alone, so its minimum may lie beyond that end or between the end and its neighbor. Consider extending the grid past it and using a finer partition (more values), and compare the active mediators identified and the p-values across grids.
fit
#>  term                  value   
#>  stat_hdmm             3.421   
#>  pval_hdmm             0.0644  
#>  stat_pe               145     
#>  j_pe                  141.6   
#>  pval_pe               < 0.0001
#>  total_indirect_effect 0.372   
#>  n_active_mediators    1       
#>  df                    1       
#>  n_candidate_mediators 57      
#>  n_observations        2002    
#> 
#> Outcome model: continuous (linear)
#> Active mediators identified (1): gge_gdp
#> Tuning parameter (HBIC): lambda = 0.1 from 100 values in [0.1, 2] (the grid's lower end)
# The identified mediator's full name:
WHO_indicator_codebook$description[
  match(des$indicators[attr(fit, "active_mediators")],
        WHO_indicator_codebook$indicator)]
#> [1] "General Government Expenditure (GGE) as % of GDP"

# A region-specific model (Europe).
des_eur <- WHO_mediation_design("imr", region = "EUR")