# Backwards Strategy

## Backwards Strategy for Potential Confounders

In the Backwards Strategy we initially evaluate all potential confounders together:
• Looking for joint confounding
This is conceptually preferred because in nature variables are all present and act together.

This is relevant not only for stratification, but also for when you do multivariable regression modeling.
• In fact, this gets at the heart of the most difficult aspect of multivariable modeling, that what is called model selection.

## Procedure for Backwards Strategy for Potential Confounders

Procedure: Consider all potential confounders by forming an adjusted estimate.
An example of these steps can be found in Kleinbaum's MRSA study report.

### First - Dropping Variables

THEN:
1. One variable can then be dropped and the adjusted estimate is re-calculated (adjusted for remaining variables)
2. If the dropping of the first variable results in a non-meaningful (eg <10%) change compared to the gold standard, it can be eliminated
3. The procedure continues until no more variables can be dropped (i.e. are remaining variables are relevant)

### Second - Checking for Meaningful Change

If the dropping of the variable results in no consequential change in the measure of association then it can be eliminated from further consideration.
• If dropping the variable does result in a meaningful change, then it cannot be dropped.
• Instead, another variable is dropped and you recalculate.
• The procedure continues until no more variables can be dropped

### Third - Improving Precision

Often the elimination of factors whose absence results in a non-meaningful change in the adjusted measure of association will result in a gain in precision.
• In other words, without that factor the confidence interval for the newly calculated adjusted measure of association will be narrower.

## Problem with Many Potential Confounders

Problem: With many potential confounders,
• cells become very sparse and some strata provide no information
The problem, however, with this is depending upon how many potential confounders there are and how many levels there are for each confounder the number of strata you’d need could be very large, and the cells in the strata very small rendering the weighting procedures unusable.