sen2sample: Treatment versus control sensitivity analysis without strata.

Description

Performs a two-sample, treated-versus-control sensitivity analysis without strata or matching. The method is described in Rosenbaum and Krieger (1990) and Rosenbaum (2002, Section 4.6). The example in those references is used below to illustrate use of the sen2sample() function.

Usage

sen2sample(sc, z, gamma = 1, alternative = "greater", method="BU")

Arguments

A vector of scored outcomes for one stratum. For instance, for Wilcoxon's rank sum test, these would be the ranks of the outcomes.

Treatment indicators, with length(z)=length(sc). Here, z[i]=1 if i is treated and z[i]=0 if i is control.

gamma

The sensitivity parameter \(\Gamma\), where \(\Gamma \ge 1\).

alternative

If alternative="greater", then the test rejects for large values of the test statistic. If alternative="less" then the test rejects for small values of the test statistic. In a sensitivity analysis, it is safe but somewhat conservative to perform a two-sided test at level \(\alpha\) by doing two one-sided tests each at level \(\alpha\)/2.

method

If method="RK" or if method="BU", exact expectations and variances are used in a large sample approximation. Methods "RK" and "BU" should give the same answer, but "RK" uses formulas from Rosenbaum and Krieger (1990), while "BU" obtains exact moments for the extended hypergeometric distribution using the BiasedUrn package and then applies Proposition 20, page 155, section 4.7.4 of Rosenbaum (2002). In contrast, method="LS" does not use exact expectations and variances, but rather uses the large sample approximations in section 4.6.4 of Rosenbaum (2002). Finally, method="AD" uses method="LS" for large strata and method="BU" for smaller strata.

Value

A vector of scored outcomes for one stratum. For instance, for Wilcoxon's rank sum test, these would be the ranks of the outcomes in the current stratum.

Treatment indicators, with length(z)=length(sc). Here, z[i]=1 if i is treated and z[i]=0 if i is control.

The sensitivity parameter \(\Gamma\), where \(\Gamma \ge 1\).

References

Rosenbaum, P. R. and Krieger, A. M. (1990). Sensitivity of two-sample permutation inferences in observational studies. Journal of the American Statistical Association, 85, 493-498.

Rosenbaum, P. R. (2002). Observational Studies (2nd edition). New York: Springer. Section 4.6.

Skerfving, S., Hansson, K., Mangs, C., Lindsten, J., & Ryman, N. (1974). Methylmercury-induced chromosome damage in man. Environmental Research, 7, 83-98.

Examples

Run this code

# NOT RUN {
mercury<-c(5.3, 15, 11, 5.8, 17, 7, 8.5, 9.4, 7.8, 12, 8.7, 4, 3, 12.2, 6.1, 10.2,
           100, 70, 196, 69, 370, 270, 150, 60, 330, 1100, 40, 100, 70,
           150, 200, 304, 236, 178, 41, 120, 330, 62, 12.8)
z<-c(rep(0,16),rep(1,23))
CuCells<-c(2.7, .5, 0, 0, 5, 0, 0, 1.3, 0, 1.8, 0, 0, 1.0, 1.8,
           0, 3.1, .7, 4.6, 0, 1.7, 5.2, 0, 5, 9.5, 2, 3, 1, 3.5,
           2, 5, 5.5, 2, 3, 4, 0, 2, 2.2, 0, 2)

#Reproduces Rosenbaum and Krieger (1990), page 497
sen2sample(rank(mercury),z,gamma=5)
#Reproduces Rosenbaum and Krieger (1990), page 497
sen2sample(rank(CuCells),z,gamma=2)
(551.500000-492.334479)/sqrt(1153.775252) #Computation of the deviate
#Intermediate calculations: expectation and variance are in row 21.
evall(rank(CuCells),z,2,method="RK")

#The following three examples, if run, reproduce the
#calculations in the final paragraph of page 145,
#Section 4.6.6 of Rosenbaum (2002) Observational Studies, 2nd Ed.
#The first calculation uses large sample approximations
#to expectations and variances.
sen2sample(rank(mercury),z,gamma=2,method="LS")
#The next two calculations use exact expectations and variances
sen2sample(rank(mercury),z,gamma=2,method="RK")
sen2sample(rank(mercury),z,gamma=2,method="BU")
# }