survSpearman {survSpearman} | R Documentation |
Computes Spearman's Correlation for Bivariate Survival Data.
Description
Computes non-parametric estimates of Spearman's rank correlation for bivariate survival data. Two correlations are returned: a highest rank correlation that can be interpreted as Spearman's correlation after assigning a highest rank to observations beyond a specified region, and a restricted correlation that estimates Spearman's correlation within the specified region.
Usage
survSpearman(X = NULL, Y = NULL, deltaX = NULL, deltaY = NULL, data = NULL,
tauX = Inf, tauY = Inf, bivarSurf = NULL)
Arguments
X |
Time to event or censoring for variable |
Y |
Time to event or censoring for variable |
deltaX |
Event indicator for variable |
deltaY |
Event indicator for variable |
data |
Data frame containing variables (arguments) |
tauX |
The |
tauY |
The |
bivarSurf |
A matrix containing the marginal and joint survival probabilities. The first column is the marginal survival probability corresponding to variable |
Details
The function computes the highest rank and restricted Spearman's correlations with bivariate survival data. The data can be supplied in three ways: 1) as vectors X
, Y
, deltaX
, and deltaY
; 2) as data frame data
that contains the variables mentioned in 1); and 3) as matrix bivarSurf
containing marginal and joint survival probabilities. If bivarSurf
is not NULL
then 1) and 2) are ignored. If bivarSurf
is NULL
and data
is not then 2) is used. If bivarSurf
and data
are NULL
then 1) is used. The highest rank correlation is the Spearman's correlation that can be interpreted as Spearman's rank correlation computed after assigning the highest rank to the events outside of tauX
and tauY
. The restricted Spearman's correlation is Spearman's correlation computed within the restricted region defined by tauX
and tauY
. Note that given tauX
and tauY
the survival probability is estimated using the values that are just above the latest observed event times within that region, what we call an effective restricted region. This means that if, for example, tauX
is greater than the latest observed event time for X
variable and tauY
is greater than the latest observed event time for Y
variable, then tauX
and tauY
do not affect the correlation values since the effective restricted region remains the same (as defined by the maximum observed event or censoring event times). The method of Dabrowska can result in negative probability mass for some points. This may result in zero or negative probability of failure in the restricted region, in which case the restricted Spearman's correlation cannot be computed and NA value is returned. This only happens when the sample size is small and censoring is heavy.
Value
The function returns the following list of values. 'Restricted region set by user'
is a character vector of two user-specified restricted region values, tauX
and tauY
. 'Effective restricted region'
is character vector of two values that define the effective restricted region, the values that are just above the latest observed event times within the user-specified restricted region. 'Correlation'
is a numeric vector of two correlation values: the highest rank Spearman's correlation ('HighestRank'
) and the restricted region Spearman's correlation ('Restricted'
), where the restricted region is defined by the values in 'Effective restricted region'
.
Author(s)
Svetlana K Eden, svetlanaeden@gmail.com
References
Dabrowska, D. M. (1988) Kaplan–Meier estimate on the plane. The Annals of Statistics 16, 1475–1489.
Eden, S.K., Li, C., Shepherd B.E. (2021). Non-parametric Estimation of Spearman's Rank Correlation with Bivariate Survival Data. Biometrics (under revision).
Examples
### Compute correlation from data
X <- c(0.5, 0.6, 0.7, 0.8)
Y <- c(0.44, 0.77, 0.88, 0.99)
deltaX <- c(1, 0, 1, 1)
deltaY <- c(1, 1, 1, 1)
survSpearman(X, Y, deltaX, deltaY)
survSpearman(X, Y, deltaX, deltaY, tauX = 100, tauY = 100)
survSpearman(X, Y, deltaX, deltaY, tauX = 100, tauY = 0.99)
survSpearman(X, Y, deltaX, deltaY, tauX = 0.8, tauY = 0.99)
### Compute correlation from survival surface
someSurf <- survDabrowska(X, Y, deltaX, deltaY)$DabrowskaEst
survSpearman(tauY = 0.9, bivarSurf = someSurf)