Incarceration and Mortality

Sebastian Daza



About Me

  • PhD Sociology/Demography at UW-Madison
  • Consultancy within and outside the academia
  • Data Science projects


PhD Journey!

Consultancy & PhD

Consultancy & PhD

Data Science

Incarceration and Mortality

American exceptionalism


Expansion of Punishment

US Health Disadvantage


Research Questions

  • What is the long-term association between imprisonment and mortality in the US?
  • How much of the gap in mortality between the US and the UK can be attributed to different incarceration regimes?




  • Panel Study of Income Dynamic (PSID)

    • Since 1968, the survey has followed the same families

    • The first wave included roughly 5,000 families (18,000 individuals)

    • Recent waves have about 9,000 families (22,000 individuals)

  • National Longitudinal Survey of Youth 1979 (NLSY)

    • 12,686 respondents ages 14-22 when first interviewed in 1979


  • Mortality

    • Year of death, National Death Index (NDI) and non-response records

    • 6,457 deaths

  • Incarceration

    • Reports of whether a member of a household was incarcerated (n=630)

    • 1995 wave: have ever served time in jail or prison (n=836)

  • Incarceration PSID
  • Covariates

    • Age, gender, race, education attainment, household income, and health

Statistical Model

  • Survival Parametric Models (Gompertz)
    • Validate set up of the data using the underlying US population
  • Survival Semi-parametric Models (Cox)

    • Heterogeneity (gamma, family identifier)

    • Non-proportional hazard adjustments

    • Marginal Structural Models (MSM)

      • Attrition (non-independent censoring)
      • Time-varying confounders

Sensitivity Analysis

  • Specifications
  • Missing data
    • Last observation carried forward (LOCF) and backwards
    • Multiple imputation (100)
  • Sampling weights


How much of the gap in mortality between the US and the UK can be attributable to differential imprisonment experiences?

$$ D_{(x)} = MU_{(x)} - mu_{(x)} $$

$$ MU_{(x)} = MUo_{(x)} \times (P_{(x)} \times (E-1) + 1) = MUo_{(x)} \times H_{(x)}$$

$$ mu_{(x)} = muo_{(x)} \times (p_{(x)} \times(E-1) + 1) = muo_{(x)} \times h_{(x)}$$


$$D_{(x)} = A_{(x)} +B_{(x)}$$

  • $A_{(x)}$ is the contribution of the population who has not experienced prison
  • $B_(x)$, is the contribution of the population who has been in prison
  • $\frac{B_{(x)}}{D_{x}}$ is the fraction of the difference attributable to imprisonment



Incidence Mortality

Mortality Gap US - UK


  • Incarceration is associated with a moderate risk of mortality

    • Losses of life expectancy at age 50 of about 4 years or 12% of current U.S. life expectancy
  • The fraction of the mortality gap between the US and the UK that can be attributed to imprisonment experience ranges from 2% to 10%



  • Heterogeneity / Interactions / Sample size
  • Causality
  • Bayesian approach

    • Previous knowledge (priors)

    • Model Uncertainty: BMA or stacking


  • Measurement of incarceration

    • Underestimation?

    • Clear treatment

  • The UK better data