Wrapper function for the SCAS method. Score-based confidence intervals for the rate (or risk) difference ("RD") or ratio ("RR") for independent binomial or Poisson rates, or for odds ratio ("OR", binomial only), or the single rate ("p"). (This is the "GNbc" method from Laud & Dane, developed from Gart & Nam, and generalised as "SCAS" in Laud 2017) including optional continuity adjustment. This function is vectorised in x1, x2, n1, and n2. Vector inputs may also be combined into a single stratified analysis (e.g. meta-analysis). This method assumes the contrast is constant across strata (fixed effects). For a 'random-effects' method use tdasci (or scoreci with random = TRUE).
scasci(
x1,
n1,
x2 = NULL,
n2 = NULL,
distrib = "bin",
contrast = "RD",
level = 0.95,
cc = FALSE,
theta0 = NULL,
precis = 6,
plot = FALSE,
hetplot = FALSE,
xlim = NULL,
ylim = NULL,
plotmax = 100,
stratified = FALSE,
weighting = NULL,
mn_tol = 1e-08,
MNtol = NULL,
wt = NULL,
warn = TRUE,
...
)A list containing the following components:
a matrix containing estimates of the rates in each group and of the requested contrast, with its confidence interval
a matrix containing details of the corresponding 2-sided significance test against the null hypothesis that p_1 = p_2, and one-sided significance tests against the null hypothesis that theta >= or <= theta0
details of the function call
If stratified = TRUE, the following outputs are added:
a vector of values describing and testing heterogeneity
a string indicating the selected weighting method
a matrix containing stratum estimates and weights
Numeric vectors of numbers of events in group 1 & group 2 respectively.
Numeric vectors of sample sizes (for binomial rates) or exposure times (for Poisson rates) in each group.
Character string indicating distribution assumed for the input
data:
"bin" = binomial (default),
"poi" = Poisson.
Character string indicating the contrast of interest:
"RD" = rate difference (default);
"RR" = rate ratio;
"OR" = odds ratio;
"p" gives an interval for the single proportion or rate x1/n1.
Number specifying confidence level (between 0 and 1, default 0.95).
Number or logical (default FALSE) specifying (amount of) continuity
adjustment. Numeric value between 0 and 0.5 is taken as the gamma parameter
in Laud 2017, Appendix S2 (cc = TRUE translates to 0.5 for 'conventional'
Yates adjustment).
IMPORTANT NOTES:
This adjustment (conventionally but controversially termed 'continuity correction') is aimed at approximating strictly conservative coverage, NOT for dealing with zero cell counts. Such 'sparse data adjustments' are not needed in the score method, except to deal with double-zero cells for stratified RD (& double-100% cells for binomial RD & RR) with IVS/INV weights.
The continuity adjustments provided here have not been fully tested for
stratified methods, but are found to match the continuity-adjusted version
of the Mantel-Haenszel test, when cc = 0.5 for any of the binomial
contrasts. Flexibility is included for a less conservative adjustment, such
as cc = 0.25 suggested in Laud 2017 (see Appendix S3.4), or cc = 3/16 = 0.1875 in Mehrotra & Railkar (2000).
Number to be used in a one-sided significance test (e.g. non-inferiority margin). 1-sided p-value will be <0.025 iff 2-sided 95\ excludes theta0. By default, a two-sided test against theta0 = 0 (for RD) or 1 (for RR/OR) is also output.
Number (default 6) specifying precision (i.e. number of decimal places) to be used in optimisation subroutine for the confidence interval.
Logical (default FALSE) indicating whether to output plot of the score function
Logical (default FALSE) indicating whether to output plots for evaluating heterogeneity of stratified datasets.
pair of values indicating range of values to be plotted.
pair of values indicating range of values to be plotted.
Numeric value indicating maximum value to be displayed on x-axis of plots (useful for ratio contrasts which can be infinite).
Logical (default FALSE) indicating whether to combine
vector inputs into a single stratified analysis.
IMPORTANT NOTE: The mechanism for stratified calculations is enabled for
contrast = "p", but the performance of the resulting intervals has not
been fully evaluated.
String indicating which weighting method to use if
stratified = "TRUE":
"IVS" = Inverse Variance of Score (see Laud 2017 for details);
"INV" = Inverse Variance (bcf omitted, default for contrast = "OR" giving
CMH test);
"MH" = Mantel-Haenszel (n1j * n2j) / (n1j + n2j)
(default for contrast = "RD" or "RR" giving CMH test);
(= sample size for contrast = "p");
"MN" = Miettinen-Nurminen weights.
(similar to MH for contrast = "RD" or "RR",
similar to INV for contrast = "OR");
"Tang" = (n1j * n2j) / (n1j + n2j) / (1 - pj) from Tang 2020,
for an optimal test of RD if RRs are constant across strata.
(Included only for validation purposes. In general, such a test
would more logically use contrast = "RR" with weighting = "INV")
For CI consistent with a CMH test, select skew = FALSE, random = FALSE,
and use default MH weighting for RD/RR and INV for OR.
Weighting = "MN" also matches the CMH test.
For the Radhakrishna optimal (most powerful) test, select INV weighting.
Note: Alternative user-specified weighting may also be applied, via the
'wt' argument.
Numeric value indicating convergence tolerance to be used in iteration with weighting = "MN".
(deprecated: argument renamed to mn_tol)
Numeric vector containing (optional) user-specified weights.
Overrides weighting if non-empty.
Logical (default TRUE) giving the option to suppress warnings.
Other arguments.
Pete Laud, p.j.laud@sheffield.ac.uk
Laud PJ. Equal-tailed confidence intervals for comparison of rates. Pharmaceutical Statistics 2017; 16:334-348.
Laud PJ. Corrigendum: Equal-tailed confidence intervals for comparison of rates. Pharmaceutical Statistics 2018; 17:290-293.