Sensitivity analysis for unmeasured confounders based on confounding imbalance among exposed and unexposed

Sensitivity analysis to explore effect of residual confounding using simple algebraic transformation (array approach). It indicates the strength of an unmeasured confounder and the necessary imbalance among exposure categories to affect the observed (crude) relative risk.

Usage

confounders.array(
  crude.risk,
  type = c("binary", "continuous", "RD"),
  bias_parms = NULL
)

Arguments

crude.risk

Crude (apparent or observed) relative risk between the exposure and the outcome. If type `RD`, this is the crude (observed) risk difference.

type

Choice of implementation, for binary covariates, continuous covariates, or on risk difference scale.

bias_parms

Numeric vector defining the necessary bias parameters. This vector has 3 elements, in the following order:

1. the association between the confounder and the outcome (RR, relative risk),

2. the prevalence of the confounder among the exposed (between 0 and 1, if type `binary`), or mean value of the confounder among the exposed (if type `continuous` or `RD`), and

3. the prevalence of the confounder among the unexposed (between 0 and 1, if type `binary`), or mean value of the confounder among the unexposed (if type `continuous` or `RD`).

Value

A list with elements:

model

Bias analysis performed.

bias.parms

Input bias parameters.

adj.measures

Output results, with bias as a percentage: (crude.RR - risk_adj)/risk_adj * 100.

References

Schneeweiss, S., 2006. Sensitivity analysis and external adjustment for unmeasured confounders in epidemiologic database studies of therapeutics. Pharmacoepidemiol Drug Safety 15: 291-303.

Examples

# Example from Schneeweiss, S. Sensitivity analysis and external adjustment for
# unmeasured confounders in epidemiologic database studies of therapeutics.
# Pharmacoepidemiol Drug Safety 2006; 15: 291-303.
confounders.array(crude.risk = 1.5, type = "binary",
bias_parms = c(5.5, 0.5, 0.1))
#> --Input bias parameters--
#>                              
#> RR(Confounder-Disease):   5.5
#> p(Confounder+|Exposure+): 0.5
#> p(Confounder+|Exposure-): 0.1
#> ---
#> 
#>                         
#> Adjusted RR    0.6692308
#> Percent bias 124.1379310
# Examples from Patorno E., Gopalakrishnan, C., Franklin, J.M., Brodovicz, K.G.,
# Masso-Gonzalez, E., Bartels, D.B., Liu, J., and Schneeweiss, S. Claims-based
# studies of oral glucose-lowering medications can achieve balance in critical
# clinical variables only observed in electronic health records 2017; 20(4): 974-
# 984.
confounders.array(crude.risk = 1.5, type = "binary",
bias_parms = c(3.25, 0.333, 0.384))
#> --Input bias parameters--
#>                                
#> RR(Confounder-Disease):   3.250
#> p(Confounder+|Exposure+): 0.333
#> p(Confounder+|Exposure-): 0.384
#> ---
#> 
#>                       
#> Adjusted RR   1.598399
#> Percent bias -6.156116
confounders.array(crude.risk = 1.5, type = "continuous",
bias_parms = c(1.009, 7.8, 7.9))
#> --Input bias parameters--
#>                                
#> RR(Confounder-Disease):   1.009
#> p(Confounder+|Exposure+): 7.800
#> p(Confounder+|Exposure-): 7.900
#> ---
#> 
#>                         
#> Adjusted RR   1.50134456
#> Percent bias -0.08955729
confounders.array(crude.risk = 0.05, type = "RD", bias_parms = c(0.009, 8.5, 8))
#> --Input bias parameters--
#>                                   
#> RR(Confounder-Disease):      0.009
#> mean(Confounder+|Exposure+): 8.500
#> mean(Confounder+|Exposure-): 8.000
#> ---
#> 
#>                     
#> Adjusted RD  0.04550
#> Percent bias 9.89011