# Inverse Probability Weighting

 Overview Software Description Websites Readings Courses

## Overview

If one is interested in estimating a casual effect, there are several analysis options to remove confounding. These options are restriction, matching, adjustment and weighting. One approach to remove confounding using weights is Inverse probability weighting. Inverse probability weighting relies on building a logistic regression model to estimate the probability of the exposure observed for a particular person, and using the predicted probability as a weight in subsequent analyses.

## Description

The problem of identifying causal effects of interest

Although we are generally interested in making causal conclusions based on our research, there is more than one way to specify what we mean by a causal effect. Some key distinctions are whether we want to estimate the causal effect on the exposed or on the entire population, and whether we want to estimate the “etiologic” effect of exposure on disease occurrence at the moment it was observed versus the “excess” effect of exposure on disease occurrence over a study period (keep in mind the latter distinction when we consider case-crossover designs in a few weeks).

The notation used to specify the causal effects of interest, and the assumptions that we need in order to estimate these effects from observed data, build on what was presented in Epi 5.

In some circumstances, the crude association can provide an adequate estimate of the causal effect we seek. In the simplified scenario of a single dichotomous exposure of interest and a dichotomous disease outcome, we can specify the required assumptions in terms of causal types (assuming for simplicity that people are either doomed, causal, or immune, and that exposure will cause disease for the causal type but not prevent disease for anyone). For a valid estimation of the effect of exposure on the exposed, we need to assume that the exposed and unexposed groups have an equal proportion of doomed individuals. For a valid estimation of the effect of exposure on the entire population, we need to assume that the exposed and unexposed groups have both equal proportions of doomed individuals and equal proportions of immune individuals.

In reality, we often think that these assumptions are not plausible, and we want to account for potential confounders including common prior causes of exposure and disease. There are several options to condition on such potential confounders.

Options for conditioning on potential confounders

1. Restriction – restrict the population to a single stratum of the potential confounder
2. Matching – enforce by design similar levels of the confounder between exposed and unexposed, or between diseased and nondiseased
3. Adjustment – commonly used in regression modeling to statistically “hold constant” the level of the confounder while looking at another association
4. Weighting – use weighting schemes such as standardization or inverse probability weighting

Settings for implementing inverse probability weighting

At a basic level, inverse probability weighting relies on building a logistic regression model to estimate the probability of the exposure observed for a particular person, and using the predicted probability as a weight in our subsequent analyses. This can be used for confounder control (the focus of example in class) or to account for loss-to-follow-up (selection bias) to estimate causal effects from marginal structural models.

### Methodological Articles

Author(s): MA Hernán, B Brumback, JM Robins
Journal: Epidemiology
Year published: 2000

Estimating causal effects from epidemiological data

Author(s): MA Hernán, JM Robins
Journal: Journal of Epidemiology and Community Health
Year published: 2006

Marginal structural models and causal inference in epidemiology

Author(s): JM Robins, MA Hernán, B Brumback
Journal: Epidemiology
Year published: 2000

### Application Articles

Author(s): SR Cole, MA Hernán, JM Robins, K Anastos, et al.
Journal: American Journal of Epidemiology
Year published: 2003

## Software

Causal Inference
Description: Program code to implement inverse probability weighting for SAS, Stata and R is available as a companion to chapter 12 of “Causal Inference” by Hernán and Robins.

## Websites

Causal Inference
Website overview: Author(s): MA Hernán, JM Robins
This book, scheduled to be in print in 2015, is available online for free as a PDF. Chapter 12 in Part II covers inverse probability weighting.