Probabilistic sensitivity analysis for unmeasured confounding of person-time data and random error.

Probabilistic sensitivity analysis to correct for unmeasured confounding when person-time data has been collected.

Usage

probsens.irr.conf(
  counts,
  pt = NULL,
  reps = 1000,
  prev.exp = list(dist = c("constant", "uniform", "triangular", "trapezoidal",
    "logit-logistic", "logit-normal", "beta"), parms = NULL),
  prev.nexp = list(dist = c("constant", "uniform", "triangular", "trapezoidal",
    "logit-logistic", "logit-normal", "beta"), parms = NULL),
  risk = list(dist = c("constant", "uniform", "triangular", "trapezoidal",
    "log-logistic", "log-normal"), parms = NULL),
  corr.p = NULL,
  discard = TRUE,
  alpha = 0.05
)

Arguments

counts

A table or matrix where first row contains disease counts and second row contains person-time at risk, and first and second columns are exposed and unexposed observations, as:

	Exposed	Unexposed
Cases	a	b
Person-time	N1	N0

pt

A numeric vector of person-time at risk. If provided, counts must be a numeric vector of disease counts.

reps

Number of replications to run.

prev.exp

List defining the prevalence of exposure among the exposed. 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; 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.

prev.nexp

List defining the prevalence of exposure among the unexposed.

risk

List defining the confounder-disease relative risk or the confounder-exposure odds ratio. The first argument provides the probability distribution function (constant,uniform, triangular, trapezoidal, log-logistic, or log-normal) and the second its parameters as a vector:

constant: value,
uniform: min, max,
triangular: lower limit, upper limit, mode,
trapezoidal: min, lower mode, upper mode, max.
log-logistic: shape, rate. Must be strictly positive,
log-normal: meanlog, sdlog. This is the mean and standard deviation on the log scale.

corr.p

Correlation between the exposure-specific confounder prevalences.

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 incidence rate ratio with exact confidence interval.
adj.measures: A table of corrected incidence rate ratios.
sim.df: Data frame of random parameters and computed values.

References

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

Examples

set.seed(123)
# Unmeasured confounding
probsens.irr.conf(matrix(c(77, 10000, 87, 10000),
dimnames = list(c("D+", "Person-time"), c("E+", "E-")), ncol = 2),
reps = 20000,
prev.exp = list("trapezoidal", c(.01, .2, .3, .51)),
prev.nexp = list("trapezoidal", c(.09, .27, .35, .59)),
risk = list("trapezoidal", c(2, 2.5, 3.5, 4.5)),
corr.p = .8)
#> --Observed data-- 
#>          Outcome: D+ 
#>        Comparing: E+ vs. E- 
#> 
#>                E+    E-
#> D+             77    87
#> Person-time 10000 10000
#> 
#>                                                2.5%     97.5%
#>  Observed Incidence Rate ratio: 0.8850575 0.6427270 1.2167540
#> ---
#>                                                         Median 2.5th percentile
#>            Incidence Rate Ratio -- systematic error: 0.9653268        0.7620055
#> Incidence Rate Ratio -- systematic and random error: 0.9708964        0.6592832
#>                                                      97.5th percentile
#>            Incidence Rate Ratio -- systematic error:         1.2655813
#> Incidence Rate Ratio -- systematic and random error:         1.4505021