maxstat.test {maxstat}

Maximally Selected Rank and Statistics

Description

Performs a test of independence of a response and one or more covariables using maximally selected rank statistics.

Usage

## S3 method for class 'data.frame'
maxstat.test(formula, data, subset, na.action, ...)
maxstat(y, x=NULL, weights = NULL, smethod=c("Wilcoxon", "Median",
            "NormalQuantil","LogRank", "Data"), pmethod=c("none", "Lau92",
            "Lau94", "exactGauss", "HL", "condMC", "min"), iscores=(pmethod=="HL"),
            minprop = 0.1, maxprop=0.9, alpha = NULL, keepxy=TRUE, ...)

Arguments

y

numeric vector of data values, dependent variable.

x

numeric vector of data values, independent variable.

weights

an optional numeric vector of non-negative weights, summing to the number of observations.

smethod

kind of statistic to be computed, i.e. defines the scores to be used for computing the statistic.

pmethod

kind of p-value approximation to be used.

iscores

logical: should the scores be mapped into integers 1:length(x)? This is TRUE by default for pmethod=="HL" and FALSE otherwise.

minprop

at least minprop*100% of the observations in the first group.

maxprop

not more than minprop*100% of the observations in the first group.

alpha

significance niveau, the appropriate quantile is computed if alpha is specified. Used for plotting within plot.maxtest.

keepxy

logical: return y and x as elements of the maxtest object.

formula

a formula describing the model to be tested of the form lhs ~ rhs where lhs is the response variable. For survival problems, i.e. using the log-rank statistic, the formula is of the form Surv(time, event) ~ rhs, see above.

data

an data frame containing the variables in the model formula. data is required.

subset

an optional vector specifying a subset of observations to be used.

na.action

a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action").

...

additional parameters to be passed to pmvnorm or B, an integer defining the number of Monte-Carlo replications.

Details

The assessment of the predictive power of a variable x for a dependent variable y can be determined by a maximally selected rank statistic.

smethod determines the kind of statistic to be used. Wilcoxon and Median denote maximally selected Wilcoxon and Median statistics. NormalQuantile and LogRank denote v.d. Waerden and log-rank scores.

pmethod specifies which kind of approximation of the p-value should be used. Lau92 is the limiting distribution by a Brownian bridge (see Lausen and Schumacher, 1992, and pLausen92), Lau94 the approximation based on an improved Bonferroni inequality (see Lausen, Sauerbrei and Schumacher, 1994, and pLausen94).

exactGauss returns the exact p-value for a maximally selected Gauss statistic, see Hothorn and Lausen (2003).

HL is a small sample approximation based on the Streitberg-R\"ohmel algorithm (see pperm) introduced by Hothorn and Lausen (2003). This requires integer valued scores. For v. d. Waerden and Log-rank scores we try to find integer valued scores having the same shape. This results in slightly different scores (and a different test), the procedure is described in Hothorn (2001) and Hothorn and Lausen (2003).

All the approximations are known to be conservative, so min gives the minimum p-value of all procedures.

condMC simulates the distribution via conditional Monte-Carlo.

For survival problems, i.e. using a maximally selected log-rank statistic, the interface is similar to survfit. The depended variable is a survival object Surv(time, event). The argument event may be a numeric vector of 0 (alive) and 1 (dead) or a vector of logicals with TRUE indicating death.

If more than one covariable is specified in the right hand side of formula (or if x is a matrix or data frame), the variable with smallest p-value is selected and the p-value for the global test problem of independence of y and every variable on the right hand side is returned (see Lausen et al., 2002).

Value

An object of class maxtest or mmaxtest (if more than one covariable was specified) containing the following components is returned:

statistic

the value of the test statistic.

p.value

the p-value for the test.

smethod

the type of test applied.

pmethod

the type of p-value approximation applied.

estimate

the estimated cutpoint (of x) which separates y best. For numeric data, the groups are defined by x less or equal to estimate and x greater estimate.

maxstats

a list of maxtest objects, one for each covariable.

whichmin

an integer specifying the element of maxstats with smallest p-value.

p.value

the p-value of the global test.

univp.values

the p-values for each of the variables under test.

cm

the correlation matrix the p-value is based on.

plot.maxtest and print.maxtest can be used for plotting and printing. If keepxy = TRUE, there are elements y and x giving the response and independent variable.

References

Hothorn, T. and Lausen, B. (2003). On the Exact Distribution of Maximally Selected Rank Statistics. Computational Statistics & Data Analysis, 43, 121–137.

Lausen, B. and Schumacher, M. (1992). Maximally Selected Rank Statistics. Biometrics, 48, 73–85

Lausen, B., Sauerbrei, W. and Schumacher, M. (1994). Classification and Regression Trees (CART) used for the exploration of prognostic factors measured on different scales. in: P. Dirschedl and R. Ostermann (Eds), Computational Statistics, Heidelberg, Physica-Verlag, 483–496

Hothorn, T. (2001). On Exact Rank Tests in R. R News, 1, 11–12

Lausen, B., Hothorn, T., Bretz, F. and Schmacher, M. (2004). Assessment of Optimally Selected Prognostic Factors. Biometrical Journal, 46(3), 364–374.

Examples

set.seed(29)

x <- sort(runif(20))
y <- c(rnorm(10), rnorm(10, 2))
mydata <- data.frame(cbind(x,y))

mod <- maxstat.test(y ~ x, data=mydata, smethod="Wilcoxon", pmethod="HL",
                    minprop=0.25, maxprop=0.75, alpha=0.05)
print(mod)
plot(mod)

# adjusted for more than one prognostic factor.
library("survival")
mstat <- maxstat.test(Surv(time, cens) ~ IPI + MGE, data=DLBCL, 
                      smethod="LogRank", pmethod="exactGauss", 
                      abseps=0.01)
plot(mstat)

### sphase
set.seed(29)
data("sphase", package = "TH.data")

maxstat.test(Surv(RFS, event) ~ SPF, data=sphase, smethod="LogRank",
             pmethod="Lau94")

maxstat.test(Surv(RFS, event) ~ SPF, data=sphase, smethod="LogRank",
             pmethod="Lau94", iscores=TRUE)

maxstat.test(Surv(RFS, event) ~ SPF, data=sphase, smethod="LogRank",
             pmethod="HL")

maxstat.test(Surv(RFS, event) ~ SPF, data=sphase, smethod="LogRank",
             pmethod="condMC", B = 9999)

plot(maxstat.test(Surv(RFS, event) ~ SPF, data=sphase, smethod="LogRank"))