ml_sens: Time-Varying Sensitivity Analysis via Longitudinal ITCV
In metaLong: Longitudinal Meta-Analysis with Robust Variance Estimation and Sensitivity Analysis

ml_sens

R Documentation

Time-Varying Sensitivity Analysis via Longitudinal ITCV

Description

Computes the Impact Threshold for a Confounding Variable (ITCV) at each follow-up time point using the pooled estimates and robust inference from ml_meta(). Two versions are returned: the raw ITCV (threshold to nullify the pooled effect) and the significance-adjusted ITCV_alpha (threshold to render the result non-significant under small-sample-corrected inference).

Usage

ml_sens(data, meta_obj, yi, vi, study, time, alpha = NULL, delta = 0.15)

Arguments

`data`	A `data.frame` in long format (same as passed to `ml_meta()`).
`meta_obj`	Output from `ml_meta()`.
`yi`, `vi`, `study`, `time`	Column names (same meaning as in `ml_meta()`).
`alpha`	Significance level. Defaults to the value stored in `meta_obj` (or `0.05` if absent).
`delta`	Numeric. User-defined practical fragility benchmark: time points with `ITCV_alpha(t) < delta` are flagged as "practically fragile". Default `0.15`.

Value

An object of class ml_sens (a data.frame) with columns:

time: Follow-up time.
theta, se, df: Copied from meta_obj.
sy: Weighted SD of observed effect sizes.
r_effect: Pooled effect on correlation scale.
itcv: Raw ITCV: confounding needed to nullify the estimate.
itcv_alpha: Significance-adjusted ITCV: confounding needed to make the result non-significant.
fragile: Logical; TRUE when itcv_alpha < delta.

Attributes include trajectory summaries (itcv_min, itcv_mean, fragile_prop) and a "fragile_times" character vector.

Mathematical background

At each time t, let \hat\theta_t be the pooled effect, s_{y,t}^2 the weighted variance of observed effect sizes, and c_t = t_{1-\alpha/2,\nu_t} \cdot \widehat{SE}(\hat\theta_t) the minimum effect still deemed significant. The correlation-scale pooled effect is

r_t = \hat\theta_t / \sqrt{\hat\theta_t^2 + s_{y,t}^2}

and the raw ITCV is \sqrt{|r_t|}. The significance-adjusted version replaces \hat\theta_t with |\hat\theta_t| - c_t.

References

Frank, K. A. (2000). Impact of a confounding variable on a regression coefficient. Sociological Methods & Research, 29(2), 147-194.

Examples

dat  <- sim_longitudinal_meta(k = 10, times = c(0, 6, 12), seed = 1)
meta <- ml_meta(dat, yi = "yi", vi = "vi", study = "study", time = "time")
sens <- ml_sens(dat, meta, yi = "yi", vi = "vi", study = "study", time = "time")
print(sens)
plot(sens)

metaLong documentation built on March 31, 2026, 1:07 a.m.