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What types of techniques can I use to address informative censoring when following a cohort of Medicaid recipients?

How do you know it is informative censoring? What is the outcome/target variable in this scenario?

If you think you have all the variables collected that are risk factors for mortality that also predict censoring, you can use inverse probability of censoring weights (see Robins & Finklestein, Biometrics 2000). IPCW are handy in that they can be used quite flexibly (e.g., in Cox models to get hazard ratios and to generate weighted survival or risk curves and report risk differences or risk ratios). (You can also use joint models - but I am admittedly less familiar with this approach to direct you to the best resources.)