E-value for meta-analysis with multiple biases

Usage

multibias_evalue(
  yi,
  vi,
  sei,
  cluster = 1:length(yi),
  biased = TRUE,
  selection_ratio,
  q = 0,
  favor_positive = TRUE,
  alpha_select = 0.05,
  ci_level = 0.95,
  small = TRUE,
  bias_max = 20,
  assumed_bias_type = NULL
)

Arguments

yi: A vector of point estimates to be meta-analyzed.
vi: A vector of estimated variances (i.e., squared standard errors) for the point estimates.
sei: A vector of estimated standard errors for the point estimates. (Only one of vi or sei needs to be specified).
cluster: Vector of the same length as the number of rows in the data, indicating which cluster each study should be considered part of (defaults to treating studies as independent; i.e., each study is in its own cluster).
biased: Boolean indicating whether each study is considered internally biased; either single value used for all studies or a vector the same length as the number of rows in the data (defaults to all studies).
selection_ratio: Ratio by which publication bias favors affirmative studies (i.e., studies with p-values less than alpha_select and estimates in the direction indicated by favor_positive).
q: The attenuated value to which to shift the point estimate or CI. Should be specified on the same scale as yi (e.g., if yi is on the log-RR scale, then q should be as well).
favor_positive: TRUE if publication bias are assumed to favor significant positive estimates; FALSE if assumed to favor significant negative estimates.
alpha_select: Alpha level at which an estimate's probability of being favored by publication bias is assumed to change (i.e., the threshold at which study investigators, journal editors, etc., consider an estimate to be significant).
ci_level: Confidence interval level (as proportion) for the corrected point estimate. (The alpha level for inference on the corrected point estimate will be calculated from ci_level.)
small: Should inference allow for a small meta-analysis? We recommend always using TRUE.
bias_max: The largest value of bias, on the additive scale, that should be included in the grid search. The bias has the same units as yi.
assumed_bias_type: List of biases to consider for computing evalues (objects of bias as returned by EValue::confounding(), EValue::selection(), EValue::misclassification()) (defaults to NULL, i.e. agnostic as to the nature of the internal bias). If not NULL, the yi argument must be on the log-RR scale (if yi is not already on that scale, use EValue::convert_measures() to make it so).

Value

An object of class metabias::metabias(), a list containing:

data: A tibble with one row per study and the columns yi, vi, sei, cluster, biased.
values: A list with the elements selection_ratio, q, favor_positive, alpha_select, ci_level, small, bias_max.
stats: A tibble with the columns bias_est, bias_ci, evalue_est, evalue_ci.

Details

For more on the functions passed as assumed_bias_type, see the EValue package multiple-bias vignette: vignette("multiple-bias", package = "EValue")

References

Mathur MB (2022). “Sensitivity analysis for the interactive effects of internal bias and publication bias in meta-analyses.” doi:10.31219/osf.io/u7vcb .

Ding P, VanderWeele TJ (2016). “Sensitivity analysis without assumptions.” Epidemiology (Cambridge, Mass.), 27(3), 368.

Smith LH, VanderWeele TJ (2019). “Bounding bias due to selection.” Epidemiology (Cambridge, Mass.), 30(4), 509.

VanderWeele TJ, Li Y (2019). “Simple sensitivity analysis for differential measurement error.” American journal of epidemiology, 188(10), 1823--1829.

Examples

# \donttest{
  # specify confounding as internal bias
  evalues <- multibias_evalue(yi = meta_meat$yi,
                              vi = meta_meat$vi,
                              biased = !meta_meat$randomized,
                              selection_ratio = 4)
  evalues$stats
#> # A tibble: 1 × 2
#>   bias_est bias_ci
#>      <dbl>   <dbl>
#> 1    0.539   0.270

  # specify confounding as internal bias
  evalues_confounding <- multibias_evalue(yi = meta_meat$yi,
                                          vi = meta_meat$vi,
                                          biased = !meta_meat$randomized,
                                          selection_ratio = 4,
                                          assumed_bias_type = list(EValue::confounding()))
  evalues_confounding$stats
#> # A tibble: 1 × 4
#>   bias_est bias_ci evalue_est evalue_ci
#>      <dbl>   <dbl>      <dbl>     <dbl>
#> 1    0.539   0.270       2.82      1.95
# }