nnspat (version 0.1.2)

rnonRL: Non-Random Labeling of a Given Set of Points

Description

An object of class "SpatPatterns".

Given the set of \(n\) points, dat, in a region, this function assigns some of them as cases, and the rest as controls in a non-RL type=type fashion.

Type I nonRL pattern assigns \(n_1=\)round(n*prop,0) of the data points as cases, and the rest as controls with first selecting a point, \(Z_i\), as a case and assigning the label case to the remaining points with infection probabilities prob=c(prop+((1-prop)*rho)/(1:k)) where rho is a parameter adjusting the NN dependence of infection probabilities.

Type II nonRL pattern assigns \(n_1=\)round(n*ult.prop,0) of them as cases, and the rest as controls with first selecting \(k_0=\)round(n*init.prop,0) as cases initially, then selecting a contagious case and then assigning the label case to the remaining points with infection probabilities inversely proportional to their position in the kNNs.

Type III nonRL pattern assigns \(n_1=\)round(n*prop,0) of them as cases, and the rest as controls with first selecting a point, \(Z_i\), as a case and assigning the label case to the remaining points with infection probabilities \(prob=rho (1-d_{ij}/d_{\max})^{pow}\) where \(d_{ij}\) is the distance from \(Z_j\) to \(Z_i\) for \(j \ne i\), \(d_{\max}\) is the maximum of \(d_{ij}\) values, rho is a scaling parameter for the infection probabilities and pow is a parameter in the power adjusting the distance dependence.

Type IV nonRL pattern assigns \(n_1=\)round(n*ult.prop,0) of them as cases, and the rest as controls with first selecting \(k_0=\)round(n*init.prop,0) as cases initially and assigning the label case to the remaining points with infection probabilities equal to the scaled bivariate normal density values at those points.

The number of cases in Types I and III will be \(n_1\) on the average if the argument poisson=TRUE (i.e., \(n_1=\)rpois(1,round(n*prop,0)) ), otherwise \(n_1=\)round(n*prop,0). The initial and ultimate number of cases in Types II and IV will be \(k_0\) and \(n_1\) on the average if the argument poisson=TRUE (i.e., \(k_0=\)rpois(1,round(n*init.prop,0)) and \(n_1=\)rpois(1,round(n*ult.prop,0))), otherwise they will be exactly equal to \(n_1=\)round(n*ult.prop,0) and \(k_0=\)round(n*init.prop,0).

At each type, we stop when we first exceed \(n_1\) cases. That is, the procedure ends when number of cases \(n_c\) exceed \(n_1\), and \(n_c-n_1\) of the cases (other than the initial case(s)) are randomly selected and relabeled as controls, i.e., 0s, so that the number of cases is exactly \(n_1\).

In the output cases are labeled as 1 and controls as 0, and initial contagious case is marked with a red cross in the plot of the pattern.

See ceyhan:SiM-seg-ind2014;textualnnspat and the functions rnonRLI, rnonRLII, rnonRLIII, and rnonRLIV for more detail on each type of non-RL pattern.

Although the non-RL pattern is described for the case-control setting, it can be adapted for any two-class setting when it is appropriate to treat one of the classes as cases or one of the classes behave like cases and other class as controls.

The parameters of the non-RL patterns are specified in the argument par.vec, and the logical arguments rand.init and poisson pass on to the types where required. rand.init is not used in type I but used in all other types, poisson is used in all types, and init.from.cases is used in type I non-RL only.

Usage

rnonRL(
  dat,
  par.vec,
  type,
  rand.init = TRUE,
  poisson = FALSE,
  init.from.cases = TRUE
)

Value

A list with the elements

pat.type

="cc" for the case-control patterns for RL or non-RL of the given data points, dat

type

The type of the point pattern

parameters

par.vec, the parameters required for each type of non-RL pattern. See the description in the parameter list.

lab

The labels of the points as 1 for cases and 0 for controls after the nonRL procedure is applied to the data set, dat. Cases are denoted as red dots and controls as black circles in the plot.

init.cases

The initial cases in the data set, dat. Marked with red crosses in the plot of the points.

cont.cases

The contagious cases in the data set, dat in type II non-RL pattern. Denoted as blue points in the plot of the points.

gen.points,ref.points

Both are NULL for this function, as initial set of points, dat, are provided for all of the non-RL procedures.

desc.pat

Description of the point pattern

mtitle

The "main" title for the plot of the point pattern

num.points

The vector of two numbers, which are the number of cases and controls.

xlimit,ylimit

The possible ranges of the \(x\)- and \(y\)-coordinates of the generated and the reference points

Arguments

dat

A set of points the non-RL procedure is applied to obtain cases and controls randomly in the type=type fashion (see the description).

par.vec

The parameter vector. It is c(prop,k,rho) for type I, c(k,rho,pow,init.prop,ult.prop) for type II, c(prop,rho,pow) for type III, and c(init.prop,ult.prop,s1,s2,rho) for type IV non-RL patterns. The parameters must be entered in this order in par.vec as a vector. See the respective functions for more detail on the parameters.

type

The type of the non-RL pattern. Takes on values "I"-"IV" for types I-IV non-RL patterns (see the description above).

rand.init

A logical argument (default is TRUE) to determine the choice of the initial case(s) in the data set, dat for types II-IV non-RL pattern. If rand.init=TRUE then the initial case(s) is (are) selected randomly from the data points, and if rand.init=FALSE, the first one is labeled as a case for type III and the first init.prop*n entries in the data set, dat, are labeled as the cases types II and IV.

poisson

A logical argument (default is FALSE) to determine whether the number of cases is random or fixed. In types II and IV initial and ultimate number of cases, \(k_0\) and \(n_1\), will be random if poisson=TRUE and fixed otherwise. In types I and III the number of cases, \(n_1\), will be random if poisson=TRUEURE and fixed otherwise. See the description.

init.from.cases

A logical argument (default is TRUE) to determine whether the initial cases at each round will be take from cases or controls in type I non-RL pattern. The initial cases are taken from cases if init.from.cases=TRUE, and from controls otherwise. See the function rnonRLI.

Author

Elvan Ceyhan

References

See Also

rnonRLI, rnonRLII, rnonRLIII, and rnonRLIV

Examples

#data generation
n<-40;  #try also n<-20; n<-100;
dat<-cbind(runif(n,0,1),runif(n,0,1))

#Type I non-RL pattern
#c(prop,k,rho) for type I
prop<-.5; knn<-3; rho<- .3
prv<-c(prop,knn,rho)

Xdat<-rnonRL(dat,type="I",prv) #labeled data 
# or try Xdat<-rnonRL(dat,type="I",prv) for type I non-RL
Xdat

table(Xdat$lab)

summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)

#Type II non-RL pattern
#c(k,rho,pow,init.prop,ult.prop) for type II
rho<-.8; pow<-2; knn<-5; ip<-.3; up<-.5
prv<-c(knn,rho,pow,ip,up)

Xdat<-rnonRL(dat,type="II",prv) #labeled data 
# or try Xdat<-rnonRL(dat,type="I",prv) for type I non-RL
Xdat

table(Xdat$lab)

summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)

#Type III non-RL pattern
#c(prop,rho,pow) for type III
prop<- .5; rho<-.8; pow<-2
prv<-c(prop,rho,pow)

Xdat<-rnonRL(dat,type="III",prv) #labeled data 
# or try Xdat<-rnonRL(dat,type="I",prv) for type I non-RL
Xdat

table(Xdat$lab)

summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)

#Type IV non-RL pattern
#c(init.prop,ult.prop,s1,s2,rho) for type IV
ult<-.5; int<- .1; s1<-s2<-.4; rho<- .1
prv<-c(int,ult,s1,s2,rho)

Xdat<-rnonRL(dat,type="IV",prv) #labeled data 
# or try Xdat<-rnonRL(dat,type="I",prv) for type I non-RL
Xdat

table(Xdat$lab)

summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)