How does multibias fit into the causal inference
workflow?
If the causal analysis process involves the following general steps:
- Specify a causal question
- Graph the causal assumptions (via a DAG)
- Apply confounder balancing (matching, weighting, etc.)
- Assess confounder balance
- Estimate the causal effect
- Perform sensitivity analysis of the effect estimate
Then multibias plugs into the final step of running
sensitivity analyses. Traditionally, the sensitivity analyses involve
re-estimating results under different assumptions related to the
specified or unspecified confounders via technique such as E-values and
tipping point analyses. However, we know that confounding is just one of
several different types of biases that may impact causal estimates, and
multibias helps fill this void. It does so by allowing for
the simultaneous adjustment of a variety of biases: uncontrolled
confounding, exposure misclassification, outcome misclassification, and
selection bias. This allows for a more transparent and complete
understanding of how all potential sources of
systematic error may be impacting the analysis.
My causal analysis leveraged propensity scores - how does that fit into a multibias analysis?
While propensity score methods are valuable for handling confounding by measured variables, they don’t address all potential sources of bias. This is where multibias analysis becomes a crucial next step.
A limitation of propensity scores is that they can only balance covariates that were actually measured and included in the propensity score model. A multibias analysis allows you to quantitatively assess the potential impact of such unmeasured confounding on top of the propensity score-adjusted analysis. In addition, propensity scores are designed specifically for confounding control. They do not inherently address other types of systematic error, such as selection bias and misclassification.
In practice, you would first conduct your primary analysis using
propensity scores to control for measured confounders.
You would then use multibias to perform a sensitivity
analysis for unmeasured confounders and other potential
sources of bias.
What is bootstrapping and how is it relevant here?
Bootstrapping is a statistical technique used to estimate the
uncertainty around an estimate. Instead of analyzing your study data
once, bootstrapping involves repeatedly drawing random samples with
replacement from your original data. Each of these samples is the same
size as the original data. For each bootstrap sample, you then calculate
the statistic of interest - a bias-adjusted estimate in the context of
multibias. By repeating this resampling, you end up with a
distribution of the statistic. From this distribution you can derive the
confidence interval and standard error.
When multibias adjusts the data’s exposure-outcome
effect for potential biases, the adjusted estimate has uncertainty. This
uncertainty comes not only from the original random (sampling) error in
the data, but also from the uncertainty in the bias parameters
(systematic error). Bootstrapping is particularly important for
multibias because it allows for confidence intervals that
incorporate two sources of uncertainty: uncertainty due to random error
and uncertainty due to systematic error.
This exercise of performing bias analysis with uncertainty in the
bias parameters is called probabilistic bias analysis. When running
multibias_adjust() with validation data (a
data_validation object) across bootstrap samples, the
function automatically resamples from the Normal distribution bias
parameters (estimate and standard error) inferred from the validation
data. When running multibias_adjust() with specified bias
parameters (a bias_params object) across bootstrap samples,
you must input the parameter values as statistical distributions (e.g.,
by using the rnorm() or runif() function).
How do I cite multibias?
To get the most up-to-date citation information, please use the
built-in citation() command in R.
citation("multibias")## To cite package 'multibias' in publications use:
##
## Brendel P (2025). _multibias: Multiple Bias Analysis in Causal
## Inference_. R package version 1.7.2,
## <https://github.com/pcbrendel/multibias>.
##
## A BibTeX entry for LaTeX users is
##
## @Manual{,
## title = {multibias: Multiple Bias Analysis in Causal Inference},
## author = {Paul Brendel},
## year = {2025},
## note = {R package version 1.7.2},
## url = {https://github.com/pcbrendel/multibias},
## }