Dif.Surv.Rec: This function computes statistical difference between two...
In TestSurvRec: Statistical tests to compare two survival curves with recurrent events

Description Usage Arguments Details Value Author(s) References See Also Examples

p-values of these tests are computed.

1	Dif.Surv.Rec(XX, type, alfa, beta,gamma,eta)

`XX`	Object type recurrent events data
`type`	"LRrec","Grec","TWrec","PPrec","PMrec","FHrec","CMrec","Mrec","all"
`alfa`	The appropriate choice, see w_{z}. Defect value is equal zero
`beta`	The appropriate choice, see w_{z}. Defect value is equal zero
`gamma`	The appropriate choice, see w_{z}. Defect value is equal zero
`eta`	The appropriate choice, see w_{z}. Defect value is equal zero

This function contains tests to compare survival curves with recurrent events. The curves are estimated using Pe<f1>a-Strawderman-Hollander estimator . Pe<f1>a et al. (2001) defined the estimator of the survival function to recurrent events or Kaplan-Meier estimator GPLE. They used two counting processes N and Y. The PSH estimator was defined as,

\hat{S}(z) =∏_{t≤q\,z}≤ft[1-\frac{Δ\,N≤ft(s,z\right)}{Y≤ft(s,z\right)}\right]

The authors considered two time scales: one related to calendar time (S) and other related to intercurrences time (T). So, the counting process N(s, z) represents the number of observed events in the calendar period [0,s] with t≤q\,z and Y(s, z) represents the number of observed events in the period [0,s] with t≥q\,z. The produc-limit estimator was developed by Pe<f1>a, Strawderman and Hollander,called PSH. This estimator is useful when the interoccurrence times are assumed to represents IID sample from some underlying distribution F. GPLE model The GPLE estimator is defined as: A fundamental assumption of this approach is that individuals have been previously and properly classified in groups according to a stratification variable denote by r. Thus, the estimator of the survival curve by each group is defined as,

\hat{S}_{r}(z) =∏_{t≤q\,z}≤ft[1-\frac{Δ\,N≤ft(s,z;r\right)}{Y≤ft(s,z;r\right)}\right]\!\nabla\:r\:=\!1,2.

# Dif.Surv.Rec(TBCplapyr,"all",0,0,0,0). Values returned

Nomb.Est	Chi.square	p.value
LRrec	0.3052411	0.5806152
Grec	1.4448446	0.2293570
TWrec	0.9551746	0.3284056
PPrec	1.1322772	0.2872901
PMrec	1.1430319	0.2850126
PPrrec	1.1834042	0.2766641
HFrec	0.3052411	0.5806152
CMrec	0.3052411	0.5806152
Mrec	1.5298763	0.2161310

Dr. Carlos Mart<ed>nez, <cmmm7031@gmail.com>

Mart<ed>nez C., Ram<ed>rez, G., V<e1>squez M. (2009).Pruebas no param<e9>tricas para comparar curvas de supervivencia de dos grupos que experimentan eventos recurrentes. Propuestas. Revista Ingenier<ed>a U.C.,Vol 16, 3, 45-55. Mart<ed>nez, C. (2009). Generalizaci<f3>n de algunas pruebas cl<e1>sicas de comparaci<f3>n de curvas de supervivencia al caso de eventos de naturaleza recurrente. Tesis doctoral. Universidad Central de Venezuela (UCV). Caracas-Venezuela. Pe<f1>a E., Strawderman R., Hollander, M. (2001). Nonparametric Estimation with Recurrent Event Data. J.A.S.A. 96, 1299-1315.

Plot.Event.Rec,Plot.Surv.Rec,Print.Summary

data(TBCplapyr)
 #Return the p-values of the all tests 
 Dif.Surv.Rec(TBCplapyr,"all",0,0,0,0)
 #Return the p-value of the LRrec test
 Dif.Surv.Rec(TBCplapyr)
 #Return the p-value of the Grec test
 Dif.Surv.Rec(TBCplapyr,"Grec")
 #Return the p-values of the CMrec tests 
 #The CMrec test with this parameters generates LRrec test
 Dif.Surv.Rec(TBCplapyr,"all",0,0,0,0)
 #The CMrec test with this parameters generates Grec test
 Dif.Surv.Rec(TBCplapyr,"all",0,0,1,0)
 #The CMrec test with this parameters generates TWrec test
 Dif.Surv.Rec(TBCplapyr,"all",0,0,0.5,0)
 #The CMrec test with this parameters generates PPrec test
 Dif.Surv.Rec(TBCplapyr,"all",1,0,0,0)
 #The CMrec test with this parameters generates HFrec test
 Dif.Surv.Rec(TBCplapyr,"all",1,1,0,0)