The clinical and behavioral endpoint that mean differences hide: the
proportion of each group whose outcome reaches a meaningful threshold
(a minimal clinically important difference, a remission cut, a mastery
criterion). For each group the function reports the responder count and
proportion with a Wilson confidence interval; with exactly two groups it
adds the risk difference with the Newcombe (1998) score-based hybrid
interval and the number needed to treat; and across any number of
groups it reports the omnibus chi square test of equal responder
proportions. An optional sweep repeats the analysis over a grid
of thresholds, making explicit how conclusions depend on where the line
is drawn, disclosing the threshold dependence that any
single-threshold claim leaves implicit.
responder_analysis(
x,
group,
threshold,
direction = c("ge", "le"),
conf_level = 0.95,
sweep = NULL
)A tidy wide data.frame (class dmar_tbl). One row
per group with group, n, responders,
estimate (the proportion), lower_limit,
upper_limit; with two groups, a difference row
(second level minus first) and an nnt row; and a final
omnibus row carrying chi_square, df, and
p_value (columns that are NA on the other rows). When
sweep is supplied, the same table is stacked per threshold
with a leading threshold column.
Numeric vector of outcomes (for example, change scores).
Group labels, one per observation (coerced to factor; the first level is the reference for the two-group difference).
The cut defining response.
"ge" (default): a responder has
x >= threshold; "le": x <= threshold (for
outcomes where lower is better).
Confidence level for all intervals. Defaults to 0.95.
Optional numeric vector of additional thresholds; the
analysis is repeated at each and stacked with a leading
threshold column.
Ken Kelley [email protected]
Per-group intervals are Wilson score intervals
(ci_proportion). The two-group risk difference uses
Newcombe's method 10: the difference interval is assembled from the two
Wilson limits, which keeps it inside [-1, 1] and well behaved at
boundary counts. The number needed to treat is \(1/|\Delta|\), with
its interval from the inverted difference limits when the difference
interval excludes zero; when it includes zero the NNT interval is
reported as NA (the interval is disjoint and an interval on the
NNT scale would mislead; Altman, 1998). Dichotomizing throws away
information, so a responder analysis complements, never replaces, the
analysis of the continuous outcome (Maxwell, Delaney, & Kelley, 2027).
Altman, D. G. (1998). Confidence intervals for the number needed to treat. BMJ, 317(7168), 1309--1312. tools:::Rd_expr_doi("10.1136/bmj.317.7168.1309")
Newcombe, R. G. (1998). Interval estimation for the difference between independent proportions: Comparison of eleven methods. Statistics in Medicine, 17(8), 873--890. tools:::Rd_expr_doi("10.1002/(SICI)1097-0258(19980430)17:8<873::aid-sim779>3.0.CO;2-I")
Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge.
ci_proportion for the per-group interval;
nnt_from_smd for the model-based route to the number
needed to treat from a standardized mean difference;
cliff_delta and proportion_of_superiority
for dominance-style effect sizes on the continuous outcome.
Other effect size estimates:
cles(),
cliff_delta(),
correction_for_attenuation(),
eta_squared(),
eta_squared_generalized(),
eta_squared_partial(),
expected_partial_r(),
expected_r(),
expected_smd(),
nnt_from_smd(),
omega_squared(),
omega_squared_partial(),
probability_of_superiority_paired(),
proportion_of_superiority(),
smd_trimmed()
# A two-arm trial: change scores, response defined as a gain of 10+.
set.seed(113)
change <- c(rnorm(60, 8, 9), rnorm(60, 13, 9))
arm <- rep(c("control", "treatment"), each = 60)
responder_analysis(change, arm, threshold = 10)
# How threshold-dependent is that conclusion?
responder_analysis(change, arm, threshold = 10, sweep = c(5, 15))
Run the code above in your browser using DataLab