sensitivityGBH: Principal stratification sensitivity analysis.

In sensitivityPStrat: Principal Stratification Sensitivity Analysis Functions

Description

Performs a sensitivity analysis using the method described in Gilbert, Bosch, and Hudgens (2003).

Usage

sensitivityGBH(z, s, y, beta, selection, groupings,
               empty.principal.stratum, ci = 0.95,
               ci.method = c("analytic", "bootstrap"), na.rm = FALSE,
               N.boot = 100, interval = c(-100, 100),
               oneSidedTest = FALSE, twoSidedTest = TRUE,
               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	outcome vector. Can be NA for unselected records.
beta	vector; values of the sensitivity parameter. Inf and -Inf are acceptable.
selection	The value of s indicating selection.
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).
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”. Defaults to c("analytic","bootstrap")
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 ACE. Defaults to FALSE
twoSidedTest	logical. Return a two sided confidence interval for ACE. Defaults to TRUE
isSlaveMode	logical. Internal Use only. Used in recursion.

Details

Performs a sensitivity analysis estimating the average causal effect among those who would have been selected regardless of treatment assignment (ACE). 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 monotonicity (i.e., one of the principal strata is empty). ACE is identified by assuming a value of the sensitivity parameter beta, where exp(beta) has an odds ratio interpretation:

If empty.principal.stratum=c(S(g0)==not selected, S(g1)==selected) then given selected if assigned g0, the odds of being selected if assigned g1 multiplicatively increase exp(beta) for every 1-unit increase in Y(g0).

If empty.principal.stratum=c(S(g0)==selected, S(g1)==not selected) then given selected if assigned g1, the odds of being selected if assigned g0 multiplicatively increase exp(beta) for every 1-unit increase in Y(g1).

Specifying beta=-Inf or beta=Inf calls sensitivityHHS.

Value

an object of class sensitivity2d.

ACE	ACE=E(Y(g1)-Y(g0)|S(g1)==S(g0)==selection). Vector of the estimated ACE values for specified beta values.
ACE.ci	vector; confidence interval of ACE determined by quantiles of bootstrap if ci.method includes “bootstrap”. Otherwise calculated using analytic variance with large sample normal approximation.
ACE.var	vector; estimated variance of ACE.
beta	vector of user-specified beta values
alphahat	vector of estimated values of alpha
y0	vector of unique y values 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 y values 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)

Author(s)

Bryan E. Shepherd
Department of Biostatistics
Vanderbilt University

Charles Dupont
Department of Biostatistics
Vanderbilt University

References

Gilbert PB, Bosch RJ, and Hudgens MG (2003), "Sensitivity Analysis for the Assessment of Causal Vaccine Effects of Viral Load in HIV Vaccine Trials," Biometrics 59, 531-541.

See Also

sensitivityHHS, sensitivityJR, sensitivitySGL

Examples

data(vaccine.trial)
ans<-with(vaccine.trial,
          sensitivityGBH(z=treatment,s=hiv.outcome,y=logVL,
                    beta=c(0,.25,.5,.75,1,1.25,1.5),
                    selection="infected",
                    groupings=c("placebo","vaccine"),
                    empty.principal.stratum=c("not infected","infected"),
                    N.boot=100)
         )
ans

ans<-with(vaccine.trial,
          sensitivityGBH(z=treatment,s=hiv.outcome,y=logVL,
                    beta=c(-Inf,-1,-0.75,-0.5,-0.25,0,.25,.5,.75,1,Inf),
                    selection="infected",
                    groupings=c("placebo","vaccine"),
                    empty.principal.stratum=c("not infected","infected"),
                    ci.method="bootstrap",
                    N.boot=100)
         )
ans

Example output

Empty Principle Stratum:  S(placebo) = not infected, S(vaccine) = infected 
ACE:	 E(Y(vaccine) - Y(placebo) | S(placebo) = S(vaccine) = infected) 
     0.00      0.25      0.50      0.75      1.00      1.25      1.50 
0.4422777 0.3896437 0.3389877 0.2919282 0.2493324 0.2114175 0.1780977 

ACE confidence interval:
By analytic method
      ci.probs
              2.5%     97.5%
  0.00  0.22740332 0.6571521
  0.25  0.17241550 0.6068720
  0.50  0.11720238 0.5607729
  0.75  0.06416697 0.5196894
  1.00  0.01504383 0.4836210
  1.25 -0.02928454 0.4521196
  1.50 -0.06850629 0.4247017

By bootstrap method, N = 100
      ci.probs
               2.5%     97.5%
  0.00  0.250821082 0.6172243
  0.25  0.189741494 0.5668285
  0.50  0.125558150 0.5240571
  0.75  0.079299414 0.4843677
  1.00  0.037595396 0.4521137
  1.25 -0.005602387 0.4195092
  1.50 -0.047606241 0.3864527
Empty Principle Stratum:  S(placebo) = not infected, S(vaccine) = infected 
ACE:	 E(Y(vaccine) - Y(placebo) | S(placebo) = S(vaccine) = infected) 
       -Inf       -1.00       -0.75       -0.50       -0.25        0.00 
 0.94628842  0.63668723  0.59372114  0.54619861  0.49519461  0.44227773 
       0.25        0.50        0.75        1.00         Inf 
 0.38964373  0.33898766  0.29192820  0.24933240 -0.06428061 

ACE confidence interval:
By bootstrap method, N = 100
       ci.probs
               2.5%     97.5%
  -Inf   0.66892011 1.1879175
  -1.00  0.42081536 0.8422593
  -0.75  0.38637224 0.8032633
  -0.50  0.35146686 0.7613387
  -0.25  0.31266476 0.7156311
  0.00   0.25632322 0.6661761
  0.25   0.18871312 0.6195716
  0.50   0.13541496 0.5773782
  0.75   0.08637259 0.5395157
  1.00   0.04181278 0.5014318
  Inf   -0.34237071 0.1972803

sensitivityPStrat documentation built on May 2, 2019, 5:14 p.m.