sensitivityPStrat (version 1.0-6)

sensitivityJR: Principal stratification sensitivity analysis relaxing the monotonicity assumption.

Description

Principal stratification sensitivity analysis relaxing monotonicity as described by Jemiai and Rotnitzky (2005) and implemented by Shepherd, Redman, and Ankerst (2008).

Usage

sensitivityJR(z, s, y, beta0, beta1, phi, Pi, psi, selection, groupings, ci = 0.95, ci.method = c("analytic","bootstrap"), ci.type = "twoSided", custom.FUN=NULL, na.rm = FALSE, N.boot = 100, interval = c(-100, 100), upperTest = FALSE, lowerTest = FALSE, twoSidedTest = TRUE, verbose=getOption("verbose"), isSlaveMode = FALSE)

Arguments

z

vector; contains the grouping values (e.g., treatment assignment) for each record.

s

vector; indicates whether a record is selected.

y

vector; outcome values. Can be NA for unselected records.

beta0

vector; values of the sensitivity parameter $\beta$0 linking outcome in group g0 with selection if assigned group g1.

beta1

vector; values of the sensitivity parameter $\beta$1 linking outcome in group g1 with selection if assigned group g0.

phi, Pi, psi

vector; 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 ($Pr(S(\var{g0}) = 1|S(\var{g1}) = 1)$).

selection

The value of s indicating selection.

groupings

vector of two elements c(g0,g1); describes to possible group values. 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.

ci

numeric vector; confidence interval value. Defaults to 0.95

ci.method

character; method by which the confidence interval and variance are calculated. Can be “analytic” or “bootstrap”. Defaults to c("analytic","bootstrap")

ci.type

character vector; type of confidence interval that the corresponding ci element is referring to. Can be “upper”, “lower”, or “twoSided”. Defaults to "twoSided".

custom.FUN

function; function to calculate custom result. mu0, mu1, p0, p1 are available to be used as arguments in the custom function, where $\code{mu0} = E(Y(\var{g0})|S(\var{g0}) = S(\var{g1}) = selected)$, $\code{mu1} = E(Y(\var{g1})|S(\var{g0}) = S(\var{g1}) = selected)$, $\code{p0} = P(S(\var{g0}) = selected)$, and $\code{p1} = P(S(\var{g1}) = selected)$. The custom function must return a single value.

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 by optimize to estimate $\alpha$0 and $\alpha$1.

lowerTest

logical. Return the lower one sided p-value for the ACE. Defaults to FALSE

upperTest

logical. Return the upper one sided p-value for the ACE. Defaults to FALSE

twoSidedTest

logical. Return a two sided p-value for the ACE. Defaults to TRUE

verbose

logical; prints dots when bootstrapping to show that something is happening. Bootstrapping can take a long time.

isSlaveMode

logical. Internal Use only. Used in recursion.

Value

object of class sensitivity3d

ACE

array; estimated values of ACE for all combinations of beta0, beta1, and phi, Pi, psi. Array dimensions are length(beta0), length(beta1), length(psi).

ACE.ci

array; confidence interval determined by quantile if ci.method includes “bootstrap”. Otherwise calculated using analytic variance with large sample normal approximation. Array dimensions the same as ACE element.

ACE.var

array; estimated variance of ACE. Array dimensions the same as ACE element.

ACE.p

vector; estimated p-value of ACE.

beta0

vector; $\beta$ values used for the first group.

alphahat0

vector; estimated $\alpha$ values for the first group.

Fas0

function; estimator for the distribution function of y0 in the first group in the always selected stratum.

beta1

vector; $\beta$ values used for the second group.

alphahat1

vector; estimated $\alpha$ values for the second group.

Fas1

function; estimator for the distribution function of y1 in the second group in the always selected stratum.

phi

vector; $phi$ 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.

Details

Performs a sensitivity analysis estimating the average causal effect among those who would have been selected regardless of treatment assignment (ACE) without assuming monotonicity (i.e., that one of the principal strata is empty). The method assumes no interference (i.e., potential outcomes of all subjects are unaffected by treatment assignment of other subjects) and ignorable (i.e., random) treatment assignment. ACE 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). 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, psi 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.

References

Jemiai Y (2005), “Semiparametric Methods for Inferring Treatment Effects on Outcomes Defined Only if a Post-Randomization Event Occurs,” unpublished doctoral dissertation under the supervision of A. Rotnitzky, Harvard School of Public Health, Dept. of Biostatistics.

Shepherd BE, Redman MW, Ankerst DP (2008), “Does Finasteride affect the severity of prostate cancer? A causal sensitivity analysis,” Journal of the American Statistical Association 2008, 484, 1392-1404. 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.

See Also

sensitivityGBH, sensitivitySGD

Examples

data(vaccine.trial)
ansJR<-with(vaccine.trial,
          sensitivityJR(z=treatment,s=hiv.outcome,y=logVL,
                    beta0=c(-1,-.5,0,.5,1),
                    beta1=c(-1,-.5,0,.5,1),
                    phi=c(0.95,0.9), selection="infected",
                    groupings=c("placebo","vaccine"),
                    N.boot=100)
         )
ansJR

data(vaccine.trial)
ansJR<-with(vaccine.trial,
          sensitivityJR(z=treatment,s=hiv.outcome,y=logVL,
                    beta0=c(-1,-.5,0,.5,1),
                    beta1=c(-1,-.5,0,.5,1),
                    phi=c(0.95,0.9), selection="infected",
                    groupings=c("placebo","vaccine"),
                    custom.FUN=function(mu0, mu1, ...) mu1 - mu0,
                    upperTest=TRUE, lowerTest=TRUE, twoSidedTest=TRUE,
                    N.boot=100)
         )
ansJR