ccostr is an R package to calculate estimates of mean total cost incensored cost data. Censoring is a frequent obstacle when working withtime to event data, as e.g. not all patients in a medical study can beobserved until death. For estimating the distribution of time to eventthe Kaplan-Meier estimator is useful, but when estimating mean costs itis not, since costs, opposed to time, do typically not accumulate at aconstant rate. Often costs accumulate a at a higher rate at thebeginning (e.g. at diagnosis) and end (e.g. death).
Several methods for estimating mean costs when working with censoreddata have been developed. Of note is the work by(Lin et al,1997), who proposed three different estimators. Later(Bang andTsiatis, 2000) proposed another method based on inverse probabilityweighting, where complete (fully observed) cases are weighted with theprobability of being censored at their event time.(Zhao and Tian,2001) proposed an extension of the (BT) estimator, (ZT), whichincludes cost history from both censored and fully observed cases.
The primary function of ccostr is the implementation of the BT and ZTestimator
ccostr may be installed using the following command
devtools::install_github("HaemAalborg/ccostr")# Or including a vignette that demonstrates the bias and coverage of the estimatorsdevtools::install_github("HaemAalborg/ccostr",build =TRUE,build_opts =c("--no-resave-data","--no-manual"))The main function of ccostr is ccmean(), which implements 4estimators, these are:
The package calculates two naive estimates of the mean cost. Thefirst is the available sample (AS) estimator which divides total costsof all observations with the number of observations. This is correct ifthere is no censoring present. With censored data it is underestimatingthe real costs due to missing information. The second is the completecases (CC) estimator, here all incomplete cases is filtered out. Thiscreates a bias towards short cases as they have a greater chance of notbeing removed, and this would normally also give a downward bias.
The BT estimator(Bang and Tsiatis, 2000), weights the costfor the complete case with the probability of censoring at the eventtime.
If cost history is present, the above estimator may be improved byusing the ZT estimator(Zhao and Tian, 2001).
For all formulas above (n) is number of individuals, (M_i) and (_i)are the total cost and event indicator for individual (i), with (_i = 1)or (_i = 0) for respectively fully observed and censored cases. ((T_i))is the Kaplan-Meier estimator of the probability of censoring at time(T_i), i.e. the time of event for individual (i). () is the average ofcost until time (C_i) among individuals with event time later than(C_i), and ((C_i)) is the Kaplan-Meier estimator of the censoringprobability at the time (T_i).
The accepted data format for ccmean is a dataframe as shown belowwith observations in rows. Columns detail the id for the observation,start and stop time for a time interval, the cost for the interval, theoverall survival for the individual and a censoring indicator (1 = fullyobserved, 0 = censored). The dataset may contain multiple rows for thesame individual detailing a cost history. If cost history is available,including it may lead to better estimates.
df<-data.frame(id =c("A","A","A","B" ,"C","C","D"),start =c(1,30,88,18,1,67,43),stop =c(1,82,88,198,5,88,44),cost =c(550,1949,45,4245,23,567,300),delta =c(0,0,0,0,1,1,1),surv =c(343,343,343,903,445,445,652))kable(df)| id | start | stop | cost | delta | surv |
|---|---|---|---|---|---|
| A | 1 | 1 | 550 | 0 | 343 |
| A | 30 | 82 | 1949 | 0 | 343 |
| A | 88 | 88 | 45 | 0 | 343 |
| B | 18 | 198 | 4245 | 0 | 903 |
| C | 1 | 5 | 23 | 1 | 445 |
| C | 67 | 88 | 567 | 1 | 445 |
| D | 43 | 44 | 300 | 1 | 652 |
The estimated average cost for the dataset shown above, is nowcalculated using ccmean.
library(ccostr)ccmean(df,L =1000)#> ccostr - Estimates of mean cost with censored data#>#> Observations Induviduals FullyObserved Limits TotalTime MaxSurvival#> N 7 4 2 1000 2343 903#>#> Estimate Variance SE 0.95LCL 0.95UCL#> AS 1919.7500 849025.06 921.4256 113.75590 3725.744#> CC 445.0000 21025.00 145.0000 160.80000 729.200#> BT 296.6667 13618.21 116.6971 67.94038 525.393#> ZT 504.7500 283732.74 532.6657 -539.27475 1548.775#>#> Mean survival time: 666.67 With SE: 108.12ccostr also includes a function for simulating data in the correctformat based on the method from(Lin et al, 1997).
# With the uniform distribution the true mean is 40.000, see documentation for further details.sim<-simCostData(n =1000,dist ="unif",censor ="heavy",L =10)ccmean(sim$censoredCostHistory)#> ccostr - Estimates of mean cost with censored data#>#> Observations Induviduals FullyObserved Limits TotalTime MaxSurvival#> N 4164 1000 592 9.995016 3656.722 9.995016#>#> Estimate Variance SE 0.95LCL 0.95UCL#> AS 29438.20 191796.3 437.9455 28579.82 30296.57#> CC 38980.98 135293.6 367.8228 38260.05 39701.91#> BT 40914.39 136711.2 369.7447 40189.69 41639.09#> ZT 40925.29 140572.4 374.9299 40190.42 41660.15#>#> Mean survival time: 5.2 With SE: 0.11Lin, D. Y., E. J. Feuer, R. Etzioni, and Y. Wax. (1997)“Estimating Medical Costs from Incomplete Follow-Up Data”, Biometrics53:2, 419-34.
Bang, H., A.A. Tsiatis (2000) “Estimating medical costs withcensored data”, Biometrika 87:2, 329-43.
Zhao, H., and T. Lili. (2001) “On Estimating Medical Cost andIncremental Cost-Effectiveness Ratios with Censored Data”, Biometrics57:4, 1002-8.