confounders: Uncontrolled confounding

In episensr: Basic Sensitivity Analysis of Epidemiological Results

Uncontrolled confounding

Description

confounders() and probsens_conf() allow to provide adjusted measures of association corrected for unknown or unmeasured confounding without effect modification.

Usage

confounders(
  case,
  exposed,
  type = c("RR", "OR", "RD"),
  bias_parms = NULL,
  alpha = 0.05
)

confounders.emm(
  case,
  exposed,
  type = c("RR", "OR", "RD"),
  bias_parms = NULL,
  alpha = 0.05
)

confounders.poly(
  case,
  exposed,
  type = c("RR", "OR", "RD"),
  bias_parms = NULL,
  alpha = 0.05
)

probsens_conf(
  case,
  exposed,
  reps = 1000,
  prev_exp = list(dist = c("constant", "uniform", "triangular", "trapezoidal", "normal",
    "beta"), parms = NULL),
  prev_nexp = list(dist = c("constant", "uniform", "triangular", "trapezoidal", "normal",
    "beta"), parms = NULL),
  risk = list(dist = c("constant", "uniform", "triangular", "trapezoidal",
    "log-logistic", "log-normal"), parms = NULL),
  corr_p = NULL,
  alpha = 0.05
)

Arguments

case	Outcome variable. If a variable, this variable is tabulated against.
exposed	Exposure variable.
type	Choice of implementation, with no effect measure modification for ratio measures (relative risk – RR; odds ratio – OR) or difference measures (risk difference – RD).
bias_parms	Numeric vector defining the 3, 4, or 6 necessary bias parameters. This vector has 3 elements for the confounders() function, in the following order: the association between the confounder and the outcome among those who were not exposed (RR, OR, or RD according to choice of implementation), the prevalence of the confounder among the exposed (between 0 and 1), and the prevalence of the confounder among the unexposed (between 0 and 1). This vector has 4 elements for the confounders.emm() function, in the following order: the association between the confounder and the outcome among those who were exposed, the association between the confounder and the outcome among those who were not exposed, the prevalence of the confounder among the exposed (between 0 and 1), and the prevalence of the confounder among the unexposed (between 0 and 1). This vector has 6 elements for the confounders.poly() function, in the following order: the association between the highest level confounder and the outcome, the association between the mid-level confounder and the outcome, the prevalence of the highest level confounder among the exposed (between 0 and 1), the prevalence of the highest level confounder among the unexposed (between 0 and 1), the prevalence of the mid-level confounder among the exposed (between 0 and 1), and the prevalence of the mid-level confounder among the unexposed (between 0 and 1).
alpha	Significance level.
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, truncated normal, or beta) and the second its parameters as a vector. Lower bound of the truncated normal cannot be less than zero. Upper bound is Inf by default. constant: constant value, uniform: min, max, triangular: lower limit, upper limit, mode, trapezoidal: min, lower mode, upper mode, max. normal: lower bound, upper bound, mean, sd. 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: 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.

Details

confounders.emm() allows to provide for adjusted measures of association corrected for unknown or unmeasured confounding in the presence of effect modification.

confounders.poly() allows to provide for adjusted measures of association corrected for unknown or unmeasured polychotomous (3-level) confounding without effect modification.

Value

A list with elements:

obs_data	The analyzed 2 x 2 table from the observed data.
cfder_data	The same table for Confounder +.
cfder1.data	The same table for Mid-level Confounder + (for confounders.poly()).
cfder2.data	The same table for Highest-level Confounder + (for confounders.poly()).
nocfder_data	The same table for Confounder -.
obs_measures	A table of relative risk with confidence intervals; for Total, Confounder +, and Confounder -.
adj_measures	A table of Standardized Morbidity Ratio and Mantel-Haenszel estimates.
bias_parms	Input bias parameters.

A list with elements (for probsens_conf()):

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.

Simple bias analysis with confounders()

confounders() allows you to run a simple sensitivity analysis to correct for unknown or unmeasured confounding without effect modification. Implementation for ratio measures (relative risk – RR, or odds ratio – OR) and difference measures (risk difference – RD).

The analytic approach uses the "relative risk due to confounding" as defined by Miettinen (1972), i.e. RR_{adj} = \frac{RR_{crude}}{RR_{conf}} where RR_{adj} is the standardized (adjusted) risk ratio, RR_{crude} is the crude risk ratio, and RR_{conf} is the relative risk component attributable to confounding by the stratification factors. The output provides both RR_{adj} (SMR or Mantel-Haenszel) and the RR_{conf} (i.e., RR, OR or RD due to confounding from the unmeasured confounder).

Probabilistic sensitivity analysis with probsens_conf()

probsens_conf() performs a summary-level probabilistic sensitivity analysis to correct for unknown or unmeasured confounding and random error simultaneously. It returns the Mantel-Haenszel risk ratio.

Correlations between prevalences of exposure classification among cases and controls can be specified and use the NORmal To Anything (NORTA) transformation (Li & Hammond, 1975).

Simple bias analysis with confounders.emm()

confounders.emm() allows you to run a simple sensitivity analysis to correct for unknown or unmeasured confounding in the presence of effect modification. Implementation for ratio measures (relative risk – RR, or odds ratio – OR) and difference measures (risk difference – RD).

Simple bias analysis with confounders.poly()

confounders.poly() allows you to run a simple sensitivity analysis to correct for unknown or unmeasured polychotomous (3-level) confounding without effect modification. Implementation for ratio measures (relative risk – RR, or odds ratio – OR) and difference measures (risk difference – RD).

Updated calculations

episensr 2.0.0 introduced updated calculations of probabilistic bias analyses by (1) using the NORTA transformation to define a correlation between distributions, and (2) sampling true prevalences and then sampling the adjusted cell counts rather than just using the expected cell counts from a simple quantitative bias analysis. This updated version should be preferred but if you need to run an old analysis, you can easily revert to the computation using probsens.conf_legacy() as follows:

library(episensr)
probsens.conf <- probsens.conf_legacy

References

Fox, M.P, MacLehose, R.F., Lash, T.L., 2021 Applying Quantitative Bias Analysis to Epidemiologic Data, pp.105–140, 256–262, Springer.

Miettinen, 1971. Components of the Crude Risk Ratio. Am J Epidemiol 96(2):168-172.

Li, S.T., Hammond, J.L., 1975. Generation of Pseudorandom Numbers with Specified Univariate Distributions and Correlation Coefficients. IEEE Trans Syst Man Cybern 5:557-561.

See Also

Other confounding: confounders.array(), confounders.evalue(), confounders.ext(), confounders.limit(), probsens.irr.conf()

Examples

# The data for this example come from:
# Tyndall M.W., Ronald A.R., Agoki E., Malisa W., Bwayo J.J., Ndinya-Achola J.O.
# et al.
# Increased risk of infection with human immunodeficiency virus type 1 among
# uncircumcised men presenting with genital ulcer disease in Kenya.
# Clin Infect Dis 1996;23:449-53.
confounders(matrix(c(105, 85, 527, 93),
dimnames = list(c("HIV+", "HIV-"), c("Circ+", "Circ-")),
nrow = 2, byrow = TRUE),
type = "RR",
bias_parms = c(.63, .8, .05))

confounders(matrix(c(105, 85, 527, 93),
dimnames = list(c("HIV+", "HIV-"), c("Circ+", "Circ-")),
nrow = 2, byrow = TRUE),
type = "OR",
bias_parms = c(.63, .8, .05))

confounders(matrix(c(105, 85, 527, 93),
dimnames = list(c("HIV+", "HIV-"), c("Circ+", "Circ-")),
nrow = 2, byrow = TRUE),
type = "RD",
bias_parms = c(-.37, .8, .05))
#
confounders.emm(matrix(c(105, 85, 527, 93),
dimnames = list(c("HIV+", "HIV-"), c("Circ+", "Circ-")),
nrow = 2, byrow = TRUE),
type = "RR",
bias_parms = c(.4, .7, .8, .05))

confounders.emm(matrix(c(105, 85, 527, 93),
dimnames = list(c("HIV+", "HIV-"), c("Circ+", "Circ-")),
nrow = 2, byrow = TRUE),
type = "OR",
bias_parms = c(.4, .7, .8, .05))

confounders.emm(matrix(c(105, 85, 527, 93),
dimnames = list(c("HIV+", "HIV-"), c("Circ+", "Circ-")),
nrow = 2, byrow = TRUE),
type = "RD",
bias_parms = c(-.6, -.3, .8, .05))
#
# The data for this example come from:
# Tyndall M.W., Ronald A.R., Agoki E., Malisa W., Bwayo J.J., Ndinya-Achola J.O.
# et al.
# Increased risk of infection with human immunodeficiency virus type 1 among
# uncircumcised men presenting with genital ulcer disease in Kenya.
# Clin Infect Dis 1996;23:449-53.
confounders.poly(matrix(c(105, 85, 527, 93),
dimnames = list(c("HIV+", "HIV-"), c("Circ+", "Circ-")),
nrow = 2, byrow = TRUE),
type = "RR",
bias_parms = c(.4, .8, .6, .05, .2, .2))

confounders.poly(matrix(c(105, 85, 527, 93),
dimnames = list(c("HIV+", "HIV-"), c("Circ+", "Circ-")),
nrow = 2, byrow = TRUE),
type = "OR",
bias_parms = c(.4, .8, .6, .05, .2, .2))

confounders.poly(matrix(c(105, 85, 527, 93),
dimnames = list(c("HIV+", "HIV-"), c("Circ+", "Circ-")),
nrow = 2, byrow = TRUE),
type = "RD",
bias_parms = c(-.4, -.2, .6, .05, .2, .2))
#
# The data for this example come from:
# Tyndall M.W., Ronald A.R., Agoki E., Malisa W., Bwayo J.J., Ndinya-Achola J.O. et al.
# Increased risk of infection with human immunodeficiency virus type 1 among
# uncircumcised men presenting with genital ulcer disease in Kenya.
# Clin Infect Dis 1996;23:449-53.
tyndall <- matrix(c(105, 85, 527, 93),
dimnames = list(c("HIV+", "HIV-"), c("Circ+", "Circ-")), nrow = 2, byrow = TRUE)
set.seed(1234)
probsens_conf(tyndall, reps = 100000,
prev_exp = list("trapezoidal", c(.7, .75, .85, .9)),
prev_nexp = list("trapezoidal", c(.03, .04, .07, .1)),
risk = list("trapezoidal", c(.5, .6, .7, .8)))

set.seed(123)
probsens_conf(tyndall, reps = 20000,
prev_exp = list("beta", c(200, 56)),
prev_nexp = list("beta", c(10, 16)),
risk = list("triangular", c(.6, .7, .63)),
corr_p = .8)

set.seed(123)
probsens_conf(tyndall, reps = 20000,
prev_exp = list("normal", c(.01, .12, 0.03, 0.005)),
prev_nexp = list("normal", c(0, Inf, 0.01, 0.0001)),
risk = list("triangular", c(.6, .7, .63)), corr_p = .8)

# Fox M.P., MacLehose R.F., Lash T.L.
# SAS and R code for probabilistic quantitative bias analysis for
# misclassified binary variables and binary unmeasured confounders
# Int J Epidemiol 2023:1624-1633.
fox <- matrix(c(40, 20, 60, 80),
dimnames = list(c("Diseased", "Non-diseased"), c("Exposed", "Unexposed")),
nrow = 2, byrow = TRUE)
set.seed(1234)
probsens_conf(fox, reps = 10^5,
prev_exp = list("beta", c(10, 20)),
prev_nexp = list("beta", c(5, 20)),
risk = list("trapezoidal", c(1.5, 1.7, 2.3, 2.5)))

set.seed(1234)
probsens_conf(fox, reps = 20000,
prev_exp = list("beta", c(10, 20)),
prev_nexp = list("beta", c(5, 20)),
risk = list("log-normal", c(log(2), .23)))

episensr documentation built on June 8, 2025, 10:34 a.m.