Meta-Regression of Pooled DLNM Estimates with City-Level Covariates

Extends two-stage multivariate meta-analysis (sus_mod_pool()) by including city-level covariates (e.g., mean temperature, poverty index, age structure) to explain between-city heterogeneity in climate-health associations. Covariates are automatically standardized to mean 0, SD 1 so the intercept represents the predicted association for an "average city". Returns covariate Wald tests, residual heterogeneity statistics, and BLUP predictions per city adjusted for covariate information.

Usage

sus_mod_metaregression(
  fits,
  covariates,
  covariate_cols = NULL,
  city_col = NULL,
  pred_at = c(0.75, 0.9, 0.95, 0.99),
  blup = TRUE,
  method = "reml",
  alpha = 0.05,
  lang = "pt",
  verbose = TRUE
)

Arguments

fits: A named list of climasus_dlnm objects, one per city or region. All fits must use the same climate_col, lag_max, argvar, and arglag. Produced by sus_mod_dlnm().
covariates: A data.frame with one row per city and city-level predictors. City names must be stored as row names (default) or in the column specified by city_col. Cities present in fits but absent in covariates are excluded from the meta-regression with a warning.
covariate_cols: Character vector of column names to use as meta-regression predictors. Default NULL uses all numeric columns in covariates (after removing the city identifier column if any).
city_col: Character. Name of the column in covariates that holds city identifiers. Default NULL uses row names of covariates.
pred_at: Numeric vector of quantile probabilities (0–1) for the exposure-response summary table. Default c(0.75, 0.90, 0.95, 0.99).
blup: Logical. Compute BLUP city-specific predictions? Default TRUE.
method: Character. mvmeta estimation method: "reml" (default), "ml", or "fixed".
alpha: Numeric. Significance level for confidence intervals. Default 0.05.
lang: Character. Language for messages: "pt" (default), "en", "es".
verbose: Logical. Print progress messages. Default TRUE.

Value

A climasus_metaregression list with:

$mvmeta_fit: The mvmeta model with covariates.
$null_fit: Intercept-only mvmeta model (for heterogeneity comparison).
$pooled_pred: dlnm::crosspred for the average city (all standardized covariates = 0, i.e., the intercept).
$blup_preds: Named list of per-city BLUP crosspred objects (when blup = TRUE).
$city_table: Tibble: one row per city with raw and BLUP RRs at the 75th percentile exposure.
$covariate_tests: Tibble: one row per covariate with Wald chi-square statistic (df = n_crossbasis_coef) and p-value.
$heterogeneity: Tibble comparing null and full-model heterogeneity: Cochran Q, df, p-value, I^2, and proportion of heterogeneity explained by covariates (R^2_het).
$cov_scales: Tibble with the mean and SD used to standardize each covariate (for back-transformation).
$meta: Metadata: climate_col, outcome_col, lag_max, n_cities, city_names, covariate_cols, method, alpha, call_time.

Statistical framework

Let $\boldsymbol{\theta}_i$ be the $p$-dimensional vector of cross-basis coefficients for city $i$, with variance-covariance matrix $S_i$. The meta-regression model is:

$$\boldsymbol{\theta}_i \sim N\!\left(\boldsymbol{B}_0 + \sum_{j=1}^{k} \boldsymbol{B}_j x_{ij}, S_i + \Psi\right)$$

where $\boldsymbol{B}_j$ is the $p$-vector of regression coefficients for covariate $j$ and $\Psi$ is the residual between-city covariance estimated by REML. Because covariates are standardized before fitting, $\boldsymbol{B}_0$ is the predicted association for a city with mean covariate values.

The significance of each covariate is assessed by a multivariate Wald test: $$W_j = \hat{\boldsymbol{B}}_j^{\top} \hat{V}_j^{-1} \hat{\boldsymbol{B}}_j \;\sim\; \chi^2_p$$

where $\hat{V}_j$ is the estimated covariance of $\hat{\boldsymbol{B}}_j$.

References

Gasparrini, A., et al. (2012). Multivariate meta-analysis for non-linear and other multi-parameter associations. Statistics in Medicine, 31(29), 3821-3839. doi:10.1002/sim.5471

Berkey, C.S., et al. (1998). Meta-analysis of multiple outcomes by regression with random effects. Statistics in Medicine, 17(22), 2537-2550.

Examples

if (FALSE) { # \dontrun{
# City-level covariates: mean annual temperature and poverty index
city_meta <- data.frame(
  mean_temp  = c(28.5, 22.1, 19.8),
  poverty_pct = c(42, 28, 15),
  row.names  = c("fortaleza", "belo_horizonte", "curitiba")
)

mr <- sus_mod_metaregression(fits, city_meta, lang = "en")
print(mr)
tidy(mr)
} # }