Probabilistic sensitivity analysis. — probsens • episensr

Probabilistic sensitivity analysis to correct for exposure misclassification or outcome misclassification and random error. Non-differential misclassification is assumed when only the two bias parameters seca.parms and spca.parms are provided. Adding the 2 parameters seexp.parms and spexp.parms (i.e. providing the 4 bias parameters) evaluates a differential misclassification.

Usage

probsens(
  case,
  exposed,
  type = c("exposure", "outcome"),
  reps = 1000,
  seca.parms = list(dist = c("constant", "uniform", "triangular", "trapezoidal",
    "logit-logistic", "logit-normal", "beta"), parms = NULL),
  seexp.parms = NULL,
  spca.parms = list(dist = c("constant", "uniform", "triangular", "trapezoidal",
    "logit-logistic", "logit-normal", "beta"), parms = NULL),
  spexp.parms = NULL,
  corr.se = NULL,
  corr.sp = NULL,
  discard = TRUE,
  alpha = 0.05
)

Arguments

case

Outcome variable. If a variable, this variable is tabulated against.

exposed

Exposure variable.

type

Choice of correction for exposure or outcome misclassification.

reps

Number of replications to run.

seca.parms

List defining:

The sensitivity of exposure classification among those with the outcome (when type = "exposure"), or
The sensitivity of outcome classification among those with the exposure (when type = "outcome").

The first argument provides the probability distribution function (constant, uniform, triangular, trapezoidal, logit-logistic, logit-normal, or beta) and the second its parameters as a vector. Logit-logistic and logit-normal distributions can be shifted by providing lower and upper bounds. Avoid providing these values if a non-shifted distribution is desired.

constant: constant value,
uniform: min, max,
triangular: lower limit, upper limit, mode,
trapezoidal: min, lower mode, upper mode, max,
logit-logistic: location, scale, lower bound shift, upper bound shift,
logit-normal: location, scale, lower bound shift, upper bound shift.
beta: alpha, beta.

seexp.parms

List defining:

The sensitivity of exposure classification among those without the outcome (when type = "exposure"), or
The sensitivity of outcome classification among those without the exposure (when type = "outcome").

spca.parms

List as above for seca.parms but for specificity.

spexp.parms

List as above for seexp.parms but for specificity.

corr.se

Correlation between case and non-case sensitivities.

corr.sp

Correlation between case and non-case specificities.

discard

A logical scalar. In case of negative adjusted count, should the draws be discarded? If set to FALSE, negative counts are set to zero.

alpha

Significance level.

Value

A list with elements:

obs.data: The analyzed 2 x 2 table from the observed data.
obs.measures: A table of observed relative risk and odds ratio with confidence intervals.
adj.measures: A table of corrected relative risks and odds ratios.
sim.df: Data frame of random parameters and computed values.
reps: Number of replications.

References

Lash, T.L., Fox, M.P, Fink, A.K., 2009 Applying Quantitative Bias Analysis to Epidemiologic Data, pp.117--150, Springer.

Examples

# The data for this example come from:
# Greenland S., Salvan A., Wegman D.H., Hallock M.F., Smith T.J.
# A case-control study of cancer mortality at a transformer-assembly facility.
# Int Arch Occup Environ Health 1994; 66(1):49-54.
set.seed(123)
# Exposure misclassification, non-differential
probsens(matrix(c(45, 94, 257, 945),
dimnames = list(c("BC+", "BC-"), c("Smoke+", "Smoke-")), nrow = 2, byrow = TRUE),
type = "exposure",
reps = 20000,
seca.parms = list("trapezoidal", c(.75, .85, .95, 1)),
spca.parms = list("trapezoidal", c(.75, .85, .95, 1)))
#> Chosen prior Se/Sp distributions lead to 784 negative adjusted counts which were discarded.
#> --Observed data-- 
#>          Outcome: BC+ 
#>        Comparing: Smoke+ vs. Smoke- 
#> 
#>     Smoke+ Smoke-
#> BC+     45     94
#> BC-    257    945
#> 
#>                                       2.5%    97.5%
#>  Observed Relative Risk: 1.646999 1.182429 2.294094
#>     Observed Odds Ratio: 1.760286 1.202457 2.576898
#> ---
#>                                                  Median 2.5th percentile
#>            Relative Risk -- systematic error:  2.189053         1.738635
#>               Odds Ratio -- systematic error:  2.472228         1.872992
#> Relative Risk -- systematic and random error:  2.256939         1.422139
#>    Odds Ratio -- systematic and random error:  2.566966         1.492794
#>                                               97.5th percentile
#>            Relative Risk -- systematic error:          6.655220
#>               Odds Ratio -- systematic error:         14.674038
#> Relative Risk -- systematic and random error:          6.735689
#>    Odds Ratio -- systematic and random error:         14.740262

# Exposure misclassification, differential
probsens(matrix(c(45, 94, 257, 945),
dimnames = list(c("BC+", "BC-"), c("Smoke+", "Smoke-")), nrow = 2, byrow = TRUE),
type = "exposure",
reps = 20000,
seca.parms = list("trapezoidal", c(.75, .85, .95, 1)),
seexp.parms = list("trapezoidal", c(.7, .8, .9, .95)),
spca.parms = list("trapezoidal", c(.75, .85, .95, 1)),
spexp.parms = list("trapezoidal", c(.7, .8, .9, .95)),
corr.se = .8,
corr.sp = .8)
#> Chosen prior Se/Sp distributions lead to 4290 negative adjusted counts which were discarded.
#> --Observed data-- 
#>          Outcome: BC+ 
#>        Comparing: Smoke+ vs. Smoke- 
#> 
#>     Smoke+ Smoke-
#> BC+     45     94
#> BC-    257    945
#> 
#>                                       2.5%    97.5%
#>  Observed Relative Risk: 1.646999 1.182429 2.294094
#>     Observed Odds Ratio: 1.760286 1.202457 2.576898
#> ---
#>                                                  Median 2.5th percentile
#>            Relative Risk -- systematic error:  2.915912         1.683775
#>               Odds Ratio -- systematic error:  3.531380         1.809583
#> Relative Risk -- systematic and random error:  2.995075         1.516361
#>    Odds Ratio -- systematic and random error:  3.650628         1.607822
#>                                               97.5th percentile
#>            Relative Risk -- systematic error:         10.165878
#>               Odds Ratio -- systematic error:         49.256329
#> Relative Risk -- systematic and random error:         10.523872
#>    Odds Ratio -- systematic and random error:         51.193712

probsens(matrix(c(45, 94, 257, 945),
dimnames = list(c("BC+", "BC-"), c("Smoke+", "Smoke-")), nrow = 2, byrow = TRUE),
type = "exposure",
reps = 20000,
seca.parms = list("beta", c(908, 16)),
seexp.parms = list("beta", c(156, 56)),
spca.parms = list("beta", c(153, 6)),
spexp.parms = list("beta", c(205, 18)),
corr.se = .8,
corr.sp = .8)
#> --Observed data-- 
#>          Outcome: BC+ 
#>        Comparing: Smoke+ vs. Smoke- 
#> 
#>     Smoke+ Smoke-
#> BC+     45     94
#> BC-    257    945
#> 
#>                                       2.5%    97.5%
#>  Observed Relative Risk: 1.646999 1.182429 2.294094
#>     Observed Odds Ratio: 1.760286 1.202457 2.576898
#> ---
#>                                                 Median 2.5th percentile
#>            Relative Risk -- systematic error: 1.608690         1.474532
#>               Odds Ratio -- systematic error: 1.714321         1.550609
#> Relative Risk -- systematic and random error: 1.627964         1.150670
#>    Odds Ratio -- systematic and random error: 1.738616         1.165817
#>                                               97.5th percentile
#>            Relative Risk -- systematic error:          1.940020
#>               Odds Ratio -- systematic error:          2.136385
#> Relative Risk -- systematic and random error:          2.343554
#>    Odds Ratio -- systematic and random error:          2.647539

probsens(matrix(c(338, 490, 17984, 32024),
dimnames = list(c("BC+", "BC-"), c("Smoke+", "Smoke-")), nrow = 2, byrow = TRUE),
type = "exposure",
reps = 1000,
seca.parms = list("trapezoidal", c(.8, .9, .9, 1)),
spca.parms = list("trapezoidal", c(.8, .9, .9, 1)))
#> --Observed data-- 
#>          Outcome: BC+ 
#>        Comparing: Smoke+ vs. Smoke- 
#> 
#>     Smoke+ Smoke-
#> BC+    338    490
#> BC-  17984  32024
#> 
#>                                       2.5%    97.5%
#>  Observed Relative Risk: 1.224104 1.066961 1.404390
#>     Observed Odds Ratio: 1.228315 1.068081 1.412589
#> ---
#>                                                 Median 2.5th percentile
#>            Relative Risk -- systematic error: 1.298245         1.246925
#>               Odds Ratio -- systematic error: 1.304096         1.251625
#> Relative Risk -- systematic and random error: 1.295969         1.122475
#>    Odds Ratio -- systematic and random error: 1.301775         1.124729
#>                                               97.5th percentile
#>            Relative Risk -- systematic error:          1.382128
#>               Odds Ratio -- systematic error:          1.390072
#> Relative Risk -- systematic and random error:          1.508913
#>    Odds Ratio -- systematic and random error:          1.519908

# Disease misclassification
probsens(matrix(c(173, 602, 134, 663),
dimnames = list(c("BC+", "BC-"), c("Smoke+", "Smoke-")), nrow = 2, byrow = TRUE),
type = "outcome",
reps = 20000,
seca.parms = list("uniform", c(.8, 1)),
spca.parms = list("uniform", c(.8, 1)))
#> --Observed data-- 
#>          Outcome: BC+ 
#>        Comparing: Smoke+ vs. Smoke- 
#> 
#>     Smoke+ Smoke-
#> BC+    173    602
#> BC-    134    663
#> 
#>                                       2.5%    97.5%
#>  Observed Relative Risk: 1.184136 1.056368 1.327359
#>     Observed Odds Ratio: 1.421865 1.106140 1.827708
#> ---
#>                                                 Median 2.5th percentile
#>            Relative Risk -- systematic error: 1.232598         1.186130
#>               Odds Ratio -- systematic error: 1.566440         1.446098
#> Relative Risk -- systematic and random error: 1.237320         1.090023
#>    Odds Ratio -- systematic and random error: 1.570343         1.203445
#>                                               97.5th percentile
#>            Relative Risk -- systematic error:          1.311775
#>               Odds Ratio -- systematic error:          1.735362
#> Relative Risk -- systematic and random error:          1.410672
#>    Odds Ratio -- systematic and random error:          2.060658

probsens(matrix(c(338, 490, 17984, 32024),
dimnames = list(c("BC+", "BC-"), c("Smoke+", "Smoke-")), nrow = 2, byrow = TRUE),
type = "outcome",
reps = 20000,
seca.parms = list("uniform", c(.2, .6)),
seexp.parms = list("uniform", c(.1, .5)),
spca.parms = list("uniform", c(.99, 1)),
spexp.parms = list("uniform", c(.99, 1)),
corr.se = .8,
corr.sp = .8)
#> --Observed data-- 
#>          Outcome: BC+ 
#>        Comparing: Smoke+ vs. Smoke- 
#> 
#>     Smoke+ Smoke-
#> BC+    338    490
#> BC-  17984  32024
#> 
#>                                       2.5%    97.5%
#>  Observed Relative Risk: 1.224104 1.066961 1.404390
#>     Observed Odds Ratio: 1.228315 1.068081 1.412589
#> ---
#>                                                  Median 2.5th percentile
#>            Relative Risk -- systematic error: 0.9859093        0.4831291
#>               Odds Ratio -- systematic error: 0.9853800        0.4626676
#> Relative Risk -- systematic and random error: 0.9838802        0.4758175
#>    Odds Ratio -- systematic and random error: 0.9832842        0.4575911
#>                                               97.5th percentile
#>            Relative Risk -- systematic error:         1.8899501
#>               Odds Ratio -- systematic error:         1.9287984
#> Relative Risk -- systematic and random error:         1.9211116
#>    Odds Ratio -- systematic and random error:         1.9592833

probsens(matrix(c(173, 602, 134, 663),
dimnames = list(c("BC+", "BC-"), c("Smoke+", "Smoke-")), nrow = 2, byrow = TRUE),
type = "outcome",
reps = 20000,
seca.parms = list("beta", c(100, 5)),
seexp.parms = list("beta", c(110, 10)),
spca.parms = list("beta", c(120, 15)),
spexp.parms = list("beta", c(130, 30)),
corr.se = .8,
corr.sp = .8)
#> --Observed data-- 
#>          Outcome: BC+ 
#>        Comparing: Smoke+ vs. Smoke- 
#> 
#>     Smoke+ Smoke-
#> BC+    173    602
#> BC-    134    663
#> 
#>                                       2.5%    97.5%
#>  Observed Relative Risk: 1.184136 1.056368 1.327359
#>     Observed Odds Ratio: 1.421865 1.106140 1.827708
#> ---
#>                                                 Median 2.5th percentile
#>            Relative Risk -- systematic error: 1.373792         1.313693
#>               Odds Ratio -- systematic error: 1.810032         1.679607
#> Relative Risk -- systematic and random error: 1.382525         1.217798
#>    Odds Ratio -- systematic and random error: 1.826700         1.398461
#>                                               97.5th percentile
#>            Relative Risk -- systematic error:          1.513627
#>               Odds Ratio -- systematic error:          2.080689
#> Relative Risk -- systematic and random error:          1.591369
#>    Odds Ratio -- systematic and random error:          2.411097