Compute redistribute-to-the-right weights

For many survival estimands, one approach is to redistribute each censored observation's weight to those other observations with a longer survival time (think of distributing an estate to the heirs). Then compute on the remaining, uncensored data.

Usage

rttright(formula, data, weights, subset, na.action, times, id, timefix = TRUE,
         renorm= TRUE)

Arguments

formula

a formula object, which must have a Surv object as the response on the left of the ~ operator and, if desired, terms separated by + operators on the right. Each unique combination of predictors will define a separate strata.

data

a data frame in which to interpret the variables named in the formula, subset and weights arguments.

weights

The weights must be nonnegative and it is strongly recommended that they be strictly positive, since zero weights are ambiguous, compared to use of the subset argument.

subset

expression saying that only a subset of the rows of the data should be used in the fit.

na.action

a missing-data filter function, applied to the model frame, after any subset argument has been used. Default is options()$na.action.

times

a vector of time points, for which to return updated weights. If missing, a time after the largest time in the data is assumed.

id

optional: if the data set has multiple rows per subject, a a variable containing the subect identifier of each row.

timefix

correct for possible round-off error

renorm

the resulting weights sum to 1 within each group

Details

The formula argument is treated exactly the same as in the survfit function.

Redistribution is recursive: redistribute the weight of the first censored observation to all those with longer time, which may include other censored observations. Then redistribute the next smallest and etc. up to the specified time value. After re-distributing the weight for a censored observation to other observations that are not censored, ordinary non-censored methods can often be applied. For example, redistribution of the weights, followed by computation of the weighted cumulative distribution function, reprises the Kaplan-Meier estimator.

A primary use of this routine is illustration of methods or exploration of new methods. Methods that use RTTR directly, such as the Brier score, will often do these compuations internally.

A covariate on the right hand side of the formula causes redistribution to occur within group; a censoring in group 1 redistributes weights to others in group 1, etc. This is appropriate when the censoring pattern depends upon group.

Value

a vector or matrix of weights, with one column for each requested time

See also

survfit

Examples

afit <- survfit(Surv(time, status) ~1, data=aml)
rwt  <- rttright(Surv(time, status) ~1, data=aml)

# Reproduce a Kaplan-Meier
index <- order(aml$time)
cdf <- cumsum(rwt[index])  # weighted CDF
cdf <- cdf[!duplicated(aml$time[index], fromLast=TRUE)]  # remove duplicate times
cbind(time=afit$time, KM= afit$surv, RTTR= 1-cdf)
#>       time         KM       RTTR
#>  [1,]    5 0.91304348 0.91304348
#>  [2,]    8 0.82608696 0.82608696
#>  [3,]    9 0.78260870 0.78260870
#>  [4,]   12 0.73913043 0.73913043
#>  [5,]   13 0.69565217 0.69565217
#>  [6,]   16 0.69565217 0.69565217
#>  [7,]   18 0.64596273 0.64596273
#>  [8,]   23 0.54658385 0.54658385
#>  [9,]   27 0.49689441 0.49689441
#> [10,]   28 0.49689441 0.49689441
#> [11,]   30 0.44168392 0.44168392
#> [12,]   31 0.38647343 0.38647343
#> [13,]   33 0.33126294 0.33126294
#> [14,]   34 0.27605245 0.27605245
#> [15,]   43 0.22084196 0.22084196
#> [16,]   45 0.16563147 0.16563147
#> [17,]   48 0.08281573 0.08281573
#> [18,]  161 0.08281573 0.08281573

# Hormonal patients have a diffent censoring pattern
wt2 <- rttright(Surv(dtime, death) ~ hormon, rotterdam, times= 365*c(3, 5))
dim(wt2)
#> [1] 2982    2