Package NPHMC. R topics documented: February 19, Type Package

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1 Type Pacage Pacage NPHMC February 19, 2015 Tile Sample Size Calculaion for he Proporional Hazards Mixure Cure Model Version 2.2 Dae Auhor Chao Cai, Songfeng Wang, Wenbin Lu, Jiajia Zhang Mainainer Chao Cai An R-pacage for calculaing sample size of a survival rial wih or wihou cure fracions Depends survival, smcure License GPL-2 LazyLoad yes NeedsCompilaion no Reposiory CRAN Dae/Publicaion :45:18 R opics documened: NPHMC-pacage e1684szdaa f f f f H m NPHMC S Sc Index 11 1

2 2 e1684szdaa NPHMC-pacage An R-pacage for Esimaing Sample Size of Proporional Hazards Mixure Cure Model Esimaing sample size for survival rial wih or wihou cure fracions Deails Pacage: NPHMC Type: Pacage Version: 2.2 Dae: License: GPL-2 LazyLoad: yes Auhor(s) Chao Cai, Songfeng Wang, Wenbin Lu, Jiajia Zhang Mainainer: Chao Cai References S. Wang, J. Zhang, and W. Lu. Sample size calculaion for he proporional hazards cure model. Saisics in medicine, 31: , 2012 C. Cai, e al., smcure: An R-Pacage for esimaing semiparameric mixure cure models. Compuer Mehods and Programs in Biomedicine, 108(3): , 2012 See Also smcure e1684szdaa Easern Cooperaive Oncology Group (ECOG) Daa Example daa of nonparameric esimaion approach wih reamen as only covariae

3 f1 3 daa(e1684szdaa) Forma A daa frame wih 285 observaions on he following 3 variables: Time observed relapse-free ime Saus censoring indicaor (1 = even of ineres happens, and 0 = censoring) X arm indicaor (1 = reamen and 0 = conrol) Examples daa(e1684szdaa) f1 Funcion One The firs inegrae funcion f1(,,, ) survival disribuion of uncured paiens. I can be "exp" or "weib". if = "weib", he shape parameer needs o be specified. By defaul he scale parameer of exponenial disribuion or Weibull disribuion for survival imes of uncured paiens in he conrol arm.

4 4 f3 f2 Funcion Two The second inegrae funcion f2(, accrualime, followupime, accrualdis,,, ) accrualime followupime accrualdis lengh of accrual period. lengh of follow-up ime. accrual paern. I can be "uniform", "increasing" or "decreasing". survival disribuion of uncured paiens. I can be "exp" or "weib". if = "weib", he shape parameer needs o be specified. By defaul he scale parameer of exponenial disribuion or Weibull disribuion for survival imes of uncured paiens in he conrol arm. f3 Funcion Three The hird inegrae funcion f3(, bea0, gamma0, pi0,,, )

5 f4 5 bea0 gamma0 log hazard raio of uncured paiens log odds raio of cure raes beween wo arms pi0 cure rae for he conrol arm, which is beween 0 and 1. survival disribuion of uncured paiens. I can be "exp" or "weib". if = "weib", he shape parameer needs o be specified. By defaul he scale parameer of exponenial disribuion or Weibull disribuion for survival imes of uncured paiens in he conrol arm. f4 Funcion Four The fourh inegrae funcion f4(, accrualime, followupime, accrualdis, bea0, gamma0, pi0,,, ) accrualime followupime accrualdis bea0 gamma0 lengh of accrual period. lengh of follow-up ime. accrual paern. I can be "uniform", "increasing" or "decreasing". log hazard raio of uncured paiens log odds raio of cure raes beween he wo arms pi0 cure rae for he conrol arm, which is beween 0 and 1. survival disribuion of uncured paiens. I can be "exp" or "weib". if = "weib", he shape parameer needs o be specified. By defaul

6 6 H0 he scale parameer of exponenial disribuion or Weibull disribuion for survival imes of uncured paiens in he conrol arm. H0 Cumulaive hazard funcion Cumulaive Hazard Funcion for Exponenial and Weibull Disribuions H0(,,, ) survival disribuion of uncured paiens. I can be "exp" or "weib". if = "weib", he shape parameer needs o be specified. By defaul he scale parameer of exponenial disribuion or Weibull disribuion for survival imes of uncured paiens in he conrol arm.

7 m 7 m M Funcion M inegrae funcion m(, bea0, gamma0, pi0,,, ) bea0 gamma0 log hazard raio of uncured paiens log odds raio of cure raes beween wo arms pi0 cure rae for he conrol arm, which is beween 0 and 1. survival disribuion of uncured paiens. I can be "exp" or "weib". if = "weib", he shape parameer needs o be specified. By defaul he scale parameer of exponenial disribuion or Weibull disribuion for survival imes of uncured paiens in he conrol arm. NPHMC An R-pacage for Esimaing Sample Size and Power of Proporional Hazards Mixure Cure Model Esimaing sample size and power of survival rial based on PH mixure cure model and sandard PH model NPHMC(n=NULL, power = 0.8, alpha = 0.05, accrualime = NULL, followupime = NULL, p = 0.5, accrualdis = c("uniform", "increasing", "decreasing"), hazardraio = NULL, oddsraio = NULL, pi0 = NULL, = c("exp", "weib"), = 1, = NULL, daa = NULL)

8 8 NPHMC n he sample size needed for he power calculaion. power he power needed for sample size calculaion. The defaul power is 80%. alpha he level of significance of he saisical es. The defaul alpha is accrualime followupime he lengh of accrual period. he lengh of follow-up ime. p he proporion of subjecs in he reamen arm. The defaul p is 0.5. accrualdis he accrual paern. I can be "uniform", "increasing" or "decreasing". hazardraio he hazard raio of uncured paiens beween wo arms, which is defined as e β0 = λ 1 ()/λ 0 (). The value mus be greaer han 0 bu canno be 1 because β 0 is he denominaor of he sample size formula. oddsraio he odds raio of cure raes beween wo arms, which is equivalen o e γ0 = π 1 1 π 1 / π0 1 π 0. The value should be greaer han 0 if here is cured fracion. When i is 0, he model is reduced o he sandard proporional hazards model, which means here is no cure rae. pi0 he cure rae for he conrol arm, which is beween 0 and 1. he survival disribuion of uncured paiens. I can be "exp" or "weib". if = "weib", he shape parameer needs o be specified. By defaul he scale parameer of exponenial disribuion or Weibull disribuion for survival imes of uncured paiens in he conrol arm. daa if observed/hisorical daa is avaialble, he sample size can be calculaed based on he nonparameric esimaors from he proporional hazards mixure model by smcure pacage in R. The daa mus conain hree columns wih order of "Time","Saus" and "X" where "Time" refers o ime o even of ineres, "Saus" refers o censoring indicaor (1=even of ineres happens, and 0=censoring) and "X" refers o arm indicaor (1=reamen and 0=conrol). By defaul, daa=null. Value when daa is no specified, he pacage can reurn he following esimaed sample size (power) values: nsize nsizeph esimaed sample size based on he PH mixure cure model esimaed sample size based on he sandard PH model

9 S0 9 pw pwph esimaed power based on he PH mixure cure model esimaed power based on he sandard PH model when daa is specified, he pacage will display he esimaors from he "smcure" pacage in R and he reurned values lis as follows: f nonpar nonparph nonparpw nonparpwph a lis of esimaors from he smcure pacage esimaed nonparameric sample size esimaion based on he PH mixure cure model and observed daa esimaed nonparameric sample size esimaion based on he sandard PH model and observed daa esimaed nonparameric power esimaion based on he PH mixure cure model and observed daa esimaed nonparameric power esimaion based on he sandard PH model and observed daa Examples # parameric sample size calculaion NPHMC(power=0.90,alpha=0.05,accrualime=3,followupime=4,p=0.5,accrualdis="uniform", hazardraio=2/2.5,oddsraio=2.25,pi0=0.1,="exp",=1,=0.5) # nonparameric sample size calculaion daa(e1684szdaa) NPHMC(power=0.80,alpha=0.05,accrualime=4,followupime=3,p=0.5,accrualdis="uniform", daa=e1684szdaa) # parameric power calculaion n=seq(100, 500, by=50) NPHMC(n=n, alpha=0.05,accrualime=3,followupime=4,p=0.5, accrualdis="uniform", hazardraio=2/2.5,oddsraio=2.25,pi0=0.1,="exp", =1,=0.5) # nonparameric power calculaion n=seq(100, 500, by=50) NPHMC(n=n,alpha=0.05,accrualime=4,followupime=3,p=0.5, accrualdis="uniform",daa=e1684szdaa) S0 S0 Funcion Baseline survival funcion for mixure cure model S0(, pi0,,, )

10 10 Sc pi0 cure rae for he conrol arm, which is beween 0 and 1. survival disribuion of uncured paiens. I can be "exp" or "weib". if = "weib", he shape parameer needs o be specified. By defaul scale parameer of exponenial disribuion or Weibull disribuion for survival imes of uncured paiens in he conrol arm. Sc Sc Funcion Survival disribuion of censoring imes Sc(, accrualime, followupime, accrualdis) accrualime followupime accrualdis lengh of accrual period. lengh of follow-up ime. accrual paern. I can be "uniform", "increasing" or "decreasing".

11 Index Topic PH mixure cure model NPHMC, 7 Topic daases e1684szdaa, 2 Topic power NPHMC, 7 Topic sample size NPHMC, 7 e1684szdaa, 2 f1, 3 f2, 4 f3, 4 f4, 5 H0, 6 m, 7 NPHMC, 7 NPHMC-pacage, 2 S0, 9 Sc, 10 smcure, 2 11

Data Mining Anomaly Detection. Lecture Notes for Chapter 10. Introduction to Data Mining

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