Lecture Notes on Inverse Probability Weighting

Introduction to Inverse Probability Weighting

• Last approach for adjustment: inverse probability weighting (IPW)
• Advantage: Retain data instead of throwing it away (e.g., 600 rows eliminated in matching)
• Goal: Weight observations to account for unusual cases

Steps to Implement Inverse Probability Weighting

1. Generate Propensity Scores

   • Model predicted probabilities for each observation
   • Use confounders from DAG (Directed Acyclic Graph) including:
     • Nighttime temperature
     • Income
     • Health
   • Use logistic regression to build a model to predict net usage.

2. Logistic Regression Model

   • Use the glm function (Generalized Linear Model) to predict net usage: model_net <- glm(net ~ income + temperature + health, data = data, family = binomial(link = "logit"))
   • Extract results with tidy(model_net) for log odds
   • Exponentiate coefficients to interpret as odds ratios.
   • Example observations:
     • Temperature increase: 6% less likely to use a net
     • Income increase: 0.2% more likely to use a net

3. Generating Propensity Scores

   • Create a new dataset with predicted probabilities: nets_ipw <- augment(model_net)
   • Keep necessary columns without losing data using augment_columns.
   • Convert predictions to propensities (0 to 1 probability scale).

4. Creating Inverse Probability Weights

   • Add a new column for weights (IPW): nets_ipw <- nets_ipw %>% mutate(ipw = net_num / propensity + (1 - net_num) / (1 - propensity))
   • Sorting helps identify outliers with high inverse probability weights.

Estimation of Effects

• Create a new section called find_effect for modeling with IPW: model_ipw <- lm(malaria_risk ~ net, data = nets_ipw, weights = ipw)
• Use tidy(model_ipw) to view results of causal effect:
  • Causal effect estimated at negative 10, improved accuracy compared to previous models.

Comparing All Models

• Use model_summary package to compare all models:
  • Combine models into a list:
  all_models <- list(naive = model_wrong, matched = model_matched, matched_weights = model_matched_weights, ipw = model_ipw)
• Results display each model’s coefficients, standard errors, and causal effects.

Conclusion

• Importance of making causal adjustments based on a DAG:
  • Results indicate the effectiveness of mosquito nets in reducing malaria risk through observational data.
  • Final report can be generated in R Markdown for sharing findings.