Description Usage Arguments Details Value Note Author(s) References See Also Examples
Simultaneous confidence intervals for general contrasts (linear functions) of normal means (e.g., "Dunnett", "Tukey", "Williams" ect.), and for single or multiple endpoints (primary response variables) simultaneously. The procedure of Hasler and Hothorn (2011) <doi:10.2202/1557-4679.1258> is applied for differences of means of normally distributed data. The variances/ covariance matrices of the treatment groups (containing the covariances between the endpoints) may be assumed to be equal or possibly unequal for the different groups (Hasler, 2014 <doi:10.1515/ijb-2012-0015>). For the case of only a single endpoint and unequal covariance matrices (variances), the procedure coincides with the PI procedure of Hasler and Hothorn (2008) <doi:10.1002/bimj.200710466>.
1 2 3 4 5 6 |
data |
a data frame containing a grouping variable and the endpoints as columns |
grp |
a character string with the name of the grouping variable |
resp |
a vector of character strings with the names of the endpoints; if
|
formula |
a formula specifying a numerical response and a grouping factor (e.g. response ~ treatment) |
na.action |
a character string indicating what should happen when the data
contain |
type |
a character string, defining the type of contrast, with the following options:
note that |
base |
a single integer specifying the control group for Dunnett contrasts, ignored otherwise |
ContrastMat |
a contrast matrix, where columns correspond to groups and rows correspond to contrasts |
alternative |
a character string specifying the alternative hypothesis,
must be one of |
covar.equal |
a logical variable indicating whether to treat the variances/
covariance matrices of the treatment groups (containing the
covariances between the endpoints) as being equal;
if |
conf.level |
a numeric value defining the simultaneous confidence level |
CorrMatDat |
a correlation matrix of the endpoints, if |
... |
arguments to be passed to SimCiDiff.default |
The interest is in simultaneous confidence intervals for several linear combinations
(contrasts) of treatment means in a one-way ANOVA model, and for single or
multiple endpoints simultaneously. For example, corresponding intervals for the all-
pair comparison of Tukey (1953) and the many-to-one comparison of Dunnett (1955) are
implemented, but allowing for heteroscedasticity and multiple endpoints. The user is
also free to create other interesting problem-specific contrasts. Approximate
multivariate t-distributions are used to calculate lower and upper limits
(Hasler and Hothorn, 2011 <doi:10.2202/1557-4679.1258>). Simultaneous tests based on
these intervals control the familywise error rate in admissible ranges and in the
strong sense. The variances/ covariance matrices of the treatment groups (containing
the covariances between the endpoints) can be assumed to be equal
(covar.equal=TRUE
) or unequal (covar.equal=FALSE
). If being equal, the
pooled variance/ covariance matrix is used, otherwise approximations to the degrees
of freedom (Satterthwaite, 1946) are used (Hasler, 2014 <doi:10.1515/ijb-2012-0015>;
Hasler and Hothorn, 2008 <doi:10.1002/bimj.200710466>). Unequal covariance matrices
occure if variances or correlations of some endpoints differ depending on the
treatment groups.
An object of class SimCi containing:
estimate |
a matrix of estimated differences |
lower.raw |
a matrix of raw (unadjusted) lower limits |
upper.raw |
a matrix of raw (unadjusted) upper limits |
lower |
a matrix of lower limits adjusted for multiplicity |
upper |
a matrix of upper limits adjusted for multiplicity |
CorrMatDat |
if not prespecified by |
CorrMatComp |
the estimated correlation matrix of the comparisons |
degr.fr |
a matrix of degrees of freedom |
By default (na.action="na.error"
), the procedure stops if there are
missing values. A new experimental version for missing values is used if
na.action="multi.df"
. If covar.equal=TRUE
, the number of endpoints
must not be greater than the total sample size minus the number of treatment
groups. If covar.equal=FALSE
, the number of endpoints must not be greater
than the minimal sample size minus 1. Otherwise the procedure stops.
All intervals have the same direction for all comparisons and endpoints
(alternative="..."
). In case of doubt, use "two.sided"
.
Mario Hasler
Hasler, M. (2014): Multiple contrast tests for multiple endpoints in the presence of heteroscedasticity. The International Journal of Biostatistics 10, 17–28, <doi:10.1515/ijb-2012-0015>.
Hasler, M. and Hothorn, L.A. (2011): A Dunnett-type procedure for multiple endpoints. The International Journal of Biostatistics 7, Article 3, <doi:10.2202/1557-4679.1258>.
Hasler, M. and Hothorn, L.A. (2008): Multiple contrast tests in the presence of heteroscedasticity. Biometrical Journal 50, 793–800, <doi:10.1002/bimj.200710466>.
SimTestDiff
, SimTestRat
,
SimCiRat
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | # Example 1:
# Simultaneous confidence intervals related to a comparison of the groups
# B and H against the standard S, for endpoint Thromb.count, assuming unequal
# variances for the groups. This is an extension of the well-known Dunnett-
# intervals to the case of heteroscedasticity.
data(coagulation)
interv1 <- SimCiDiff(data=coagulation, grp="Group", resp="Thromb.count",
type="Dunnett", base=3, alternative="greater", covar.equal=FALSE)
interv1
plot(interv1)
# Example 2:
# Simultaneous confidence intervals related to a comparisons of the groups
# B and H against the standard S, simultaneously for all endpoints, assuming
# unequal covariance matrices for the groups. This is an extension of the well-
# known Dunnett-intervals to the case of heteroscedasticity and multiple
# endpoints.
data(coagulation)
interv2 <- SimCiDiff(data=coagulation, grp="Group", resp=c("Thromb.count","ADP","TRAP"),
type="Dunnett", base=3, alternative="greater", covar.equal=FALSE)
summary(interv2)
plot(interv2)
|
Simultaneous 95% confidence intervals for differences of means of multiple endpoints
Assumption: Heterogeneous covariance matrices for the groups
comparison endpoint estimate degr.fr lower.raw upper.raw lower
B - S B - S Thromb.count 0.1217 17.95 -0.0367 Inf -0.0681
H - S H - S Thromb.count 0.0435 17.67 -0.1344 Inf -0.1695
upper
B - S Inf
H - S Inf
Contrast matrix:
Multiple Comparisons of Means: Dunnett Contrasts
B H S
B - S 1 0 -1
H - S 0 1 -1
Estimated covariance matrices of the data:
$B
Thromb.count ADP TRAP
Thromb.count 0.0626 0.0565 -0.0102
ADP 0.0565 0.0638 0.0054
TRAP -0.0102 0.0054 0.0963
$H
Thromb.count ADP TRAP
Thromb.count 0.0943 0.0637 0.0663
ADP 0.0637 0.0518 0.0446
TRAP 0.0663 0.0446 0.1157
$S
Thromb.count ADP TRAP
Thromb.count 0.0318 0.0132 0.0598
ADP 0.0132 0.0079 0.0269
TRAP 0.0598 0.0269 0.1376
Estimated correlation matrices of the data:
$B
Thromb.count ADP TRAP
Thromb.count 1.0000 0.8937 -0.1314
ADP 0.8937 1.0000 0.0687
TRAP -0.1314 0.0687 1.0000
$H
Thromb.count ADP TRAP
Thromb.count 1.0000 0.9121 0.6348
ADP 0.9121 1.0000 0.5770
TRAP 0.6348 0.5770 1.0000
$S
Thromb.count ADP TRAP
Thromb.count 1.0000 0.8338 0.9033
ADP 0.8338 1.0000 0.8161
TRAP 0.9033 0.8161 1.0000
Estimated correlation matrix of the comparisons:
Thromb.count ADP TRAP Thromb.count ADP TRAP
Thromb.count 1.0000 0.8494 0.3122 0.2833 0.1708 0.3755
ADP 0.8494 1.0000 0.2387 0.1335 0.1158 0.1917
TRAP 0.3122 0.2387 1.0000 0.3417 0.2232 0.5550
Thromb.count 0.2833 0.1335 0.3417 1.0000 0.8869 0.7054
ADP 0.1708 0.1158 0.2232 0.8869 1.0000 0.5818
TRAP 0.3755 0.1917 0.5550 0.7054 0.5818 1.0000
comparison endpoint estimate degr.fr lower.raw upper.raw lower upper
1 B - S Thromb.count 0.1217 12.25 -0.0367 Inf -0.1118 Inf
2 B - S ADP 0.2121 12.25 0.0691 Inf 0.0069 Inf
3 B - S TRAP 0.1053 12.25 -0.1395 Inf -0.2585 Inf
4 H - S Thromb.count 0.0435 14.27 -0.1344 Inf -0.2138 Inf
5 H - S ADP 0.0842 14.27 -0.0398 Inf -0.0930 Inf
6 H - S TRAP 0.0711 14.27 -0.1784 Inf -0.2936 Inf
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