Topic 12 Applied Analysis: Inverse Probability Weighting

Pre-class work

Required reading

  • WHATIF: 12.1, 12.2, 12.4

Checkpoint





Learning Goals

  • IPTW1: Conduct and interpret results from an appropriate IPW analysis to estimate causal effects and effect modification of causal effects.
Navigate to PollEverywhere for some warm-up exercises.





Analysis

You can download a template RMarkdown file to start from here.

We’ll be looking at the dataset explored in our WHATIF book to answer the question:

How does smoking cessation affect weight gain?

The data are available in the cidata package. Install this package (you may need to install the remotes package first):

remotes::install_github("malcolmbarrett/cidata")

Our data come from the National Health and Nutrition Examination Survey Data I Epidemiologic Follow-up Study (NHEFS).

We will use the nhefs_complete dataset which has removed cases with missing data for some key variables. More information is available via ?nhefs_complete. The variable codebook is available as nhefs_codebook.

library(survey) # You may need to install the survey package
library(dplyr)
library(ggplot2)
library(splines)
library(cidata)

data(nhefs_complete) # Load the data
View(nhefs_codebook) # Look at the variable codebook


Part 1: Causal graph analysis

Use the causal graph below as a starting point for the analysis. The selection node S indicates those for whom we have complete data. The treatment variable is qsmk, and the outcome variable is wt82_71.

  • If this is the true causal graph underlying the data, can we achieve conditional exchangeability? Show your work fully.



Part 2: Propensity score modeling

  • Based on your causal graph analysis, fit an appropriate propensity score model. Use visualizations to inform the construction of your model. Accompany each visualization with a brief description of what it helps you decide.

  • Use your model to compute appropriate weights, and add these weights to the dataset.

  • Use “before and after” visualizations to compare balance of key variables before and after weighting. Write a few sentences summarizing your conclusions from this stage.


The code below adds logistic regression smoothing lines to ggplot2 figures:

ggplot(data, aes(x = X, y = y)) +
    geom_point() +
    geom_smooth(se = FALSE, color = "blue") +
    geom_smooth(formula = y~ns(x,2), method = "glm",
        method.args = list(family="binomial"),
        se = FALSE, color = "red"
    )


The (incomplete) code below is useful for computing appropriate weights:

your_data <- your_data %>%
    mutate(
        ps = predict(ps_mod, newdata = your_data, type = "response"),
        ip_weight = case_when(
            A==1 ~ ???,
            A==0 ~ ???
        )
    )


You can incorporate weights into most ggplot2 figures by adding weight to the aesthetics:

aes(..., weight = ip_weight)



Part 3: Modeling with IP weights

Assuming that you have added the ip_weight variable to the nhefs_complete dataset, the code below fits the model

\[ E[Y^a] = \beta_0 + \beta_1a \]

(As discussed in 12.4 of WHATIF, this model is called a marginal structural model (MSM).)

# Set up information about weights
design <- svydesign(ids = ~0, weights = nhefs_complete$ip_weight, data = nhefs_complete)

msm_fit <- svyglm(
    wt82_71 ~ qsmk,
    data = data,
    design = design
)
summary(msm_fit)
confint(msm_fit)

  • Fit a marginal structural model to estimate the overall average causal effect.

  • Construct a visualization to explore if the causal effect of smoking cessation might differ by prior smoking intensity (smokeintensity). Briefly interpret your visualization.

  • Fit a model to estimate how the average causal effect differs across smoking intensity. (Adapt the svyglm() formula in the same way you would for lm().)

  • Using both the confidence intervals and effect magnitudes, discuss the results of your analysis in a contextually meaningful way.