sensitivitySGL: principal stratification sensitivity analysis with time to...
In sensitivityPStrat: Principal Stratification Sensitivity Analysis Functions

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

Principal stratification sensitivity analysis with time to event data using the method described by Shepherd, Gilbert, and Lumley (2007).

sensitivitySGL(z, s, d, y, v, beta, tau, time.points, selection, trigger,
               groupings, empty.principal.stratum, followup.time,
               ci=0.95, ci.method = c("analytic", "bootstrap"),
               custom.FUN = NULL, na.rm = FALSE,
               N.boot = 100L, interval = c(-100, 100),
               oneSidedTest = FALSE, twoSidedTest = TRUE,
               verbose = getOption("verbose"), isSlaveMode = FALSE)

`z`	vector; contains the grouping values (e.g., treatment assignment) for each record.
`s`	vector; indicates whether a record is selected.
`d`	vector; indicates whether a post-selection event has occurred. Can be `NA` for unselected records.
`y`	vector; the length of time from selection until event (`d`) or censoring. Can be `NA` for unselected records.
`v`	numeric vector; the length of time from randomization until selection or censoring.
`beta`	vector; values of the sensitivity parameter. `Inf` and `-Inf` are acceptable.
`tau`	maximum observed follow-up time after selection. Selection weights are constant for t>`tau`.
`time.points`	vector; time points, t, at which SCE(t) will be estimated.
`selection`	The value of `s` indicating selection.
`trigger`	logical; the value of `d` that denotes the post-selection event.
`groupings`	Vector of two elements `c(g0,g1)`, the first element `g0` being the value of `z` the delineates the first group, the last element `g1` being the value of `z` which delineates the second group.
`empty.principal.stratum`	vector of two elements `c(s0,s1)`; describes the `s` values that select the empty principal stratum. If `empty.principal.stratum=c(s0,s1)`, then stratum defined by S(g0)==s0 and S(g1)==s1 is the empty stratum. In this example s0 and s1 refer to the two possible values of s. (Note: method only works if s0 != s1).
`followup.time`	numeric value; cut-off point for `v` after which records are lost to censoring.
`ci`	numeric vector; confidence interval level, defaults to 0.95.
`ci.method`	character; method by which the confidence interval and variance are calculated. Can be “analytic” or “bootstrap”.
`custom.FUN`	function; function to calculate custom result. `Fas0`, `Fas1`, `time.points`, `p0`, `p1` are available to be used as arguments in the custom function. The custom function must return a vector of elements that is the same length as `time.points`.
`na.rm`	logical; indicates whether records that are invalid due to `NA` values should be removed from the data set.
`N.boot`	integer; number of bootstrap repetitions that will be run when `ci.method` includes “bootstrap”.
`interval`	numeric vector of length 2. Controls the range limits used to by optimise to estimate alphahat.
`oneSidedTest`	logical. Return a one sided confidence interval for SCE(t). Defaults to `FALSE`.
`twoSidedTest`	logical. Return a two sided confidence interval for SCE(t). Defaults to `TRUE`.
`verbose`	logical; prints dots when bootstrapping to show that something is happening.
`isSlaveMode`	logical. Internal Use only. Used in recursion.

Performs a sensitivity analysis estimating the “survival causal effect” among those who would have been selected regardless of treatment assignment (SCE). The method assumes no interference (i.e., potential outcomes of all subjects are unaffected by treatment assignment of other subjects), ignorable (i.e., random) treatment assignment, monotonicity (i.e., one of the principal strata is empty), and independent censoring (i.e., time from selection to event is independent of time from selection until censoring). SCE is then identified by assuming a value of the sensitivity parameter beta, where exp(beta) has an odds ratio interpretation (see help for sensitivityGBH). Given selection in one treatment arm, the probability of selection if in the other treatment arm is assumed to be constant for for T(z)>tau.

SCE is computed at user specified time points. Specifying beta=-Inf or beta=Inf estimates the bounds for SCE.

object of class sensitivity2d

`SCE`	SCE(t)=Pr(T(g0)<=t\|S(g0)=S(g1)=selection) - Pr(T(g1)<=t\|S(g0)=S(g1)=selection). Array of the estimated SCE at all `time.points` for specified beta values. Array dimensions are `length(time.points)` by `length(beta)`.
`SCE.ci`	array; confidence interval of SCE determined by `quantile` if using `ci.method` “bootstrap”. Otherwise calculated using analytic variance with large sample normal approximation. Array dimentions the same as element `SCE`.
`SCE.var`	array; estimated variance of SCE. Array dimentions the same as element `SCE`.
`beta`	vector of user-specified beta values
`alphahat`	vector of estimated values of alpha
`y0`	vector of unique event times in the first group.
`Fas0`	matrix of estimated empirical distribution function values for `y0` in the first group in the always selected principal stratum. Pr(Y(g0) <= y0\|S(g0)=S(g1)=selection; beta)
`y1`	vector of unique event times in the second group.
`Fas1`	matrix of estimated empirical distribution function values for `y1` in the second group in the always selected principal stratum. Pr(Y(g1) <= y1\|S(g0)=S(g1)=selection; beta)

Bryan E. Shepherd
Department of Biostatistics
Vanderbilt University

Charles Dupont
Department of Biostatistics
Vanderbilt University

Shepherd BE, Gilbert PB, Lumley T (2007), "Sensitivity analyses comparing time-to-event outcomes existing only in a subset selected postrandomization," Journal of the American Statistical Association 102, 573-582.

sensitivityGBH, sensitivityHHS, sensitivitySGD, Surv

data(vaccine.trial)
sens.time<-with(vaccine.trial,
                sensitivitySGL(z=treatment, s=hiv.outcome, y=followup.yearsART,
                          d=ARTinitiation, beta=c(.25, 0,-.25,-.5), tau=3,
                          time.points=c(2,3), selection="infected",
                          trigger="initiated ART", groupings=c("placebo","vaccine"),
                          empty.principal.stratum=c("not infected","infected"),
                          N.boot=100, interval=c(-200,200))
               )
sens.time

sens.time2<-with(vaccine.trial,
                sensitivitySGL(z=treatment, s=hiv.outcome, y=followup.yearsART,
                          d=ARTinitiation, beta=c(.25, 0,-.25,-.5), tau=3,
                          time.points=c(2,3), selection="infected",
                          trigger="initiated ART", groupings=c("placebo","vaccine"),
                          empty.principal.stratum=c("not infected","infected"),
                          custom.FUN=function(Fas0,Fas1,time.points,
                ...) { Fas0(time.points) - Fas1(time.points) },
                          N.boot=100, interval=c(-200,200))
               )
sens.time2