Responder proportions from continuous arm summaries — responder

Estimates, for each study arm, the probability that a patient's change score crosses the minimal important difference (MID) threshold under a parametric model for the change scores, together with a delta-method (sampling) variance for that probability.

Usage

responder_proportions(
  change,
  sd,
  n,
  mid,
  direction = c("higher", "lower"),
  dist = c("normal", "lognormal", "t"),
  df = NULL
)

Arguments

change: Numeric vector of mean change scores.
sd: Numeric vector of standard deviations (> 0).
n: Numeric vector of sample sizes (>= 2).
mid: Single finite number: the minimal important difference threshold.
direction: "higher" (a larger change indicates response) or "lower".
dist: Change-score distribution: "normal" (default), "lognormal" or "t".
df: Degrees of freedom when dist = "t" (a single number greater than 2).

Value

A data frame with one row per input element and columns p (responder probability) and var_p (delta-method variance).

Details

The probability is computed from the requested tail on the log scale, so very small probabilities keep full relative precision. The variance propagates the sampling uncertainty of the arm mean and SD, using the third and fourth moments of the chosen distribution (for the Normal model this is phi(a)^2 (1/n + a^2 / (2 (n - 1))) with a = (mu - mid) / sigma).

References

Thorlund K, Walter SD, Johnston BC, Furukawa TA, Guyatt GH (2011). Pooling health-related quality of life outcomes in meta-analysis: a tutorial and review of methods for enhancing interpretability. Research Synthesis Methods, 2(3), 188 to 203. doi:10.1002/jrsm.46

Anzures-Cabrera J, Sarpatwari A, Higgins JPT (2011). Expressing findings from meta-analyses of continuous outcomes in terms of risks. Statistics in Medicine, 30(25), 2967 to 2985. doi:10.1002/sim.4298

Examples

responder_proportions(
  change = c(0.96, 0.79, 1.02), sd = c(1.26, 1.28, 1.34),
  n = c(43, 139, 156), mid = 1
)
#>           p       var_p
#> 1 0.4873373 0.003699457
#> 2 0.4348410 0.001129700
#> 3 0.5059541 0.001020111