psws.qmd

# Weighting in Surveys {.unnumbered}

::: {.callout-note}
This section contains advanced materials for those who are interested (optional).
:::

## Video content

::: {style="position: relative; padding-bottom: 56.25%; height: 0; overflow: hidden;"}
<iframe src="https://www.youtube.com/embed/T7M4r3htN2w" style="position: absolute; top: 0; left: 0; width: 100%; height: 100%; border:0;" allowfullscreen>

</iframe>
:::


## Slides

[Download](https://github.com/ehsanx/PS-survey/raw/main/slides/5PropensityScoreweightingwithincomplexsurvey.pdf)

## Summary of topics discussed 

### Tabular summary

| Step | Basic IPW Process | IPW in Complex Survey |
|------|-----------------------------|---------------------------------|
| 1    | Fit PS model (A~L)          | Fit PS model (A~L) with survey-weights as design variable (as in Austin et al. (2018))/covariate (as in DuGoff et al. (2014)) |
| 2    | Convert PS to IPW(ATE)      | Convert PS to IPW(ATE)          |
|      | $IPW = 1/PS$, if $A = 1$         | $IPW = 1/PS$, if $A = 1$            |
|      | $IPW = 1/(1-PS)$, if $A = 0$     | $IPW = 1/(1-PS)$, if $A = 0$        |
| 3    | Check balance using SMD in IPW-weighted data | Check balance using SMD in data weighted by w = IPW * survey-weights |
| 4    | Apply outcome model with weight = IPW | Apply outcome model with weight = IPW * survey-weights |

If ATT is the target parameter, then use

$IPW(ATT) = 1$, if $A = 1$

$IPW(ATT) = PS/(1-PS)$, if $A = 0$

### Reference (Optional)

1. Ridgeway, G., Kovalchik, S. A., Griffin, B. A., & Kabeto, M. U. (2015). [Propensity score analysis with survey weighted data](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5802372/). Journal of causal inference, 3(2), 237-249.
2. Austin, Peter C., and Elizabeth A. Stuart. 2015. [Moving Towards Best Practice When Using Inverse Probability of Treatment Weighting (IPTW) Using the Propensity Score to Estimate Causal Treatment Effects in Observational Studies](https://doi.org/10.1002/sim.6607). Statistics in Medicine 34 (28): 3661–79.