sensitivitySGD: 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 relaxing monotonicity as described by Shepherd, Gilbert, and Dupont (in press).

sensitivitySGD(z, s, d, y, v, beta0, beta1, phi, Pi, psi, tau,
               time.points, selection, trigger, groupings,
               followup.time,
               ci=0.95, ci.method = c("bootstrap", "analytic"),
               ci.type="twoSided", custom.FUN = NULL, na.rm = FALSE,
               N.boot = 100L, N.events = NULL, interval = c(-100, 100),
               upperTest = FALSE, lowerTest = FALSE, twoSidedTest=TRUE,
               inCore = TRUE,verbose = getOption("verbose"),
               colsPerFile = 1000L, 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.
`beta0`	numeric vector; values of the sensitivity parameter β linking outcome in group `g0` with `selection` if assigned group `g1`.
`beta1`	numeric vector; values of the sensitivity parameter β linking outcome in group `g1` with `selection` if assigned group `g0`.
`phi, Pi, psi`	vectors; sensitivity parameters specifying the joint distribution of S(\var{g0}), S(\var{g1}). Only one of the three parameters should be specified. `psi` is the log-odds ratio of selection. `Pi` is the probability of being in the always selected principal stratum (Pr(S(\var{g0}) = S(\var{g1}) = selected)). `phi` is the probability of selection in group `g0` given selection in group `g1` (Pr(S(\var{g0}) = 1\|S(\var{g1}) = 1)).
`tau`	maximum observed follow-up time after selection. Selection weights are constant for \var{t}>\code{tau}.
`time.points`	vector; time points, `t`, at which SCE(\var{t}) will be estimated.
`selection`	The value of `s` indicating selection.
`trigger`	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.
`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”. Currently only works for “bootstrap”.
`ci.type`	character vector; type of confidence interval that the corresponding `ci` element is refering to. Can be “upper”, “lower”, or “twoSided”. Defaults to `"twoSided"`.
`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”.
`N.events`	integer; number of selection-events (S) for each bootstrap replication when doing selection-event based bootstrapping.
`interval`	numeric vector of length 2. Controls the range limits used to by `optimize` to estimate α.
`lowerTest`	logical. Return the lower one sided p-value for SCE. Defaults to `FALSE`
`upperTest`	logical. Return the upper one sided p-value for SCE. Defaults to `FALSE`
`twoSidedTest`	logical. Return a two sided p-value for SCE. Defaults to `TRUE`
`verbose`	logical; prints dots when bootstrapping to show that something is happening. Bootstrapping can take a long time.
`inCore`	logical; running in memory if `TRUE`, running with scratch files if `FALSE`. Default is `TRUE`. For large data analysis, the user may want to switch this to `FALSE` to allow for processing on data sets larger than can fit in memory.
`colsPerFile`	integer; number of columns of the scratch file to process in each pass (e.g., 100 columns).
`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) without assuming monotonicity (i.e., that one of the principal stratum is empty). 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, and independent censoring (i.e., time from selection to event is independent of time from selection until censoring). SCE is identified by assuming values for the sensitivity parameters beta0, beta1, and one of the parameters phi, psi, or Pi. The sensitivity parameters beta0 and beta1 have a log-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(\code{z})>\code{tau}.

Only one of the parameters phi, psi, or Pi should be specified as all depend on each other. psi is unrestrained taking any value on the real line. The other parameters, phi and Pi have constraints and there will be estimation problems if these parameters are set at values outside the of their range of acceptable values based on the observed data. See Shepherd, Gilbert, Dupont (in press) for more details.

object of class sensitivity3d

`SCE`	array; Calculated values of SCE for all combinations of the values from `beta0`, `beta1`, `phi`/`Pi`/`psi`, and `time.points`. Array dimensions are `length(time.points)`, `length(beta0)`, `length(beta1)`, `length(psi)`.
`SCE.ci`	array; Confidence interval of the SCE value. Confidence interval determined by `quantile` if using `ci.method` “bootstrap”. Otherwise calculated using analytic variance with large sample normal approximation. Array dimensions the same as element `SCE`.
`SCE.var`	array; estimated variance of SCE. Array dimensions the same as element `SCE`.
`beta0`	vector; β values used for first group.
`beta1`	vector; β values used for second group.
`psi`	vector; ψ values used.
`Pi`	vector; Pi values used.
`psi`	vector; psi values used.
`ci.map`	list; mapping of confidence interval to quantile probability. Use numbers contained within as indices to the `SCE.ci` element.

Bryan E. Shepherd
Department of Biostatistics
Vanderbilt University

Charles Dupont
Department of Biostatistics
Vanderbilt University

Shepherd BE, Gilbert PB, and Dupont CT, “Sensitivity analyses comparing time-to-event outcomes only existing in a subset selected postrandomization and relaxing monotonicity,” Biometrics, in press.

sensitivitySGL, sensitivityJR, Surv

data(vaccine.trial)
sens.analysis<-with(vaccine.trial,
                sensitivitySGD(z=treatment, s=hiv.outcome, y=followup.yearsART,
                          d=ARTinitiation, beta0=c(0,-.25,-.5),
                          beta1=c(0, -.25, -.5), phi=c(0.95, 0.90), tau=3,
                          time.points=c(2,3), selection="infected",
                          trigger="initiated ART",
                          groupings=c("placebo","vaccine"), ci=.95,
                          ci.method="bootstrap", N.boot=100)
               )
sens.analysis


sens.analysis2<-with(vaccine.trial,
                sensitivitySGD(z=treatment, s=hiv.outcome, y=followup.yearsART,
                          d=ARTinitiation, beta0=c(0,-.25,-.5),
                          beta1=c(0, -.25, -.5), phi=c(0.95, 0.90), tau=3,
                          time.points=c(2,3), selection="infected",
                          trigger="initiated ART",
                          groupings=c("placebo","vaccine"), ci=.95,
                          custom.FUN=function(Fas0,Fas1,...,time.points) {
                            Fas0(time.points) - Fas1(time.points)
                          },
                          ci.method="bootstrap", N.boot=100)
               )
sens.analysis2