funsExpTk {nnspat}

Expected Value for Cuzick and Edwards T_k Test statistic

Description

Two functions: EV.Tk and EV.Tkaij.

Both functions compute the expected value of Cuzick and Edwards T_k test statistic based on the number of cases within kNNs of the cases in the data under RL or CSR independence.

The number of cases are denoted as n_1 (denoted as n1 as an argument) for both functions and number of controls as n_0 (denoted as n0 as an argument) in EV.Tk, to match the case-control class labeling, which is just the reverse of the labeling in Cuzick and Edwards (1990).

The function EV.Tkaij uses Toshiro Tango's moments formulas based on the A=(a_{ij}) matrix (and is equivalent to the function EV.Tk, see Tango (2007), where a_{ij}(k) = 1 if z_j is among the kNNs of z_i and 0 otherwise.

See also (Ceyhan (2014)).

Usage

EV.Tk(k, n1, n0)

EV.Tkaij(k, n1, a)

Arguments

k

Integer specifying the number of NNs (of subject i).

n1, n0

The number of cases and controls, n_1 used for both functions, and n_0 used in EV.Tk only.

a

The A=(a_{ij}) matrix

Value

The expected value of Cuzick and Edwards T_k test statistic for disease clustering

Author(s)

Elvan Ceyhan

References

Ceyhan E (2014). “Segregation indices for disease clustering.” Statistics in Medicine, 33(10), 1662-1684.

Cuzick J, Edwards R (1990). “Spatial clustering for inhomogeneous populations (with discussion).” Journal of the Royal Statistical Society, Series B, 52, 73-104.

Tango T (2007). “A class of multiplicity adjusted tests for spatial clustering based on case-control point data.” Biometrics, 63, 119-127.

See Also

ceTk and EV.Tcomb

Examples

n1<-20
n0<-25
k<-1 #try also 3, 5, sample(1:5,1)

EV.Tk(k,n1,n0)

###
n<-20  #or try sample(1:20,1)
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(0:1,n,replace = TRUE)
n1<-sum(cls==1)
n0<-sum(cls==0)
a<-aij.mat(Y,k)

EV.Tk(k,n1,n0)
EV.Tkaij(k,n1,a)