Incarceration Effect on Mortality, PSID 2015 + Imputation Model + Weights

Similar exercise, this time using PSID weights. This is the procedure to define individual weights.

From around 70,000 individual records, I save longitudinal weights. I define our analytical sample and consider only the first weight (i.e., the one at the start of the period of observation for individual \(i\)). If the individual \(i\) doesn’t have any weight, I get weights from member of the family unit \(u\) at time \(t\), compute the average and use it for individual \(i\). Using this procedure I only lost 400 individuals.

It’s important to note that non-sample members (that is, all of the ones don’t have sampling weights) don’t have probability of selection.

I get estimates of the effect of incarceration on mortality, where incarceration is based on the non-response variable, and examine an initial imputation model.

The variables I consider are:

• Gender (I)
• Age (I)
• Race (I)
• Income (V)
• Education (V)
• Poor health (V)
• Incarceration / non-response (V)

knitr::opts_knit$set(root.dir = 'Users/sdaza/Google Drive/01Projects/01IncarcerationHealth/')

I consider records since 1968 and respondents 18 years old or more, that is, a sample of 53764. During that period 6584 people died. The median age of death was 71.

Differences by gender. The odds ratios are lower than 1, timing is important, not just proportions!

# explore differences by gender
x <- org[, .(male = max(male, na.rm = TRUE), 
             prison = max(nrprison, na.rm = TRUE), 
             death = max(died, na.rm = TRUE), 
             age = max(agei, na.rm = TRUE)), pid]
# these numbers are different because of age >= 18
table(x[, .(prison, death, male)]) # very small sample sizes for women

, , male = 0

      death
prison     0     1
     0 24130  3157
     1    62     2

, , male = 1

      death
prison     0     1
     0 22443  3375
     1   545    50

# odds ratio male
a <- table(x[male == 1, .(prison, death)])
(a[2,2]*a[1,1]) / (a[2,1]*a[1,2]) # it's not higher than 1, timing might be more important rather than dying or not

[1] 0.6100714

# odd ratios female
b <- table(x[male == 0, .(prison, death)]) 
(b[2,2]*b[1,1]) / (b[2,1]*b[1,2]) # even 

[1] 0.2465591

Just to get an idea of the missing data:

countmis(org)

 dghealth     eduic linc_adjc  nrprison     frace 
    0.369     0.131     0.080     0.072     0.001 

The highest proportion of missing cases is health and education. I defined imputation multivel models, where I use both time invariant and variant variables, age and year. Just to provide an example, the income imputation model is:

\[income = \alpha + year + age + edu + prison \\ + health + dropout + death + \delta_r + \epsilon_i \]

Death and dropout are time-invariant variables. For this exercise, I generated 20 imputations. Final versions of this exercise should use more iterations and imputations (e.g., 30 iterations, 60 imputations). Anyways mixing doesn’t look that bad. Increasing the number of imputations increases standard errors… so we have a trade-off here.

Then, I examine the distribution of the imputed variables by age and year. Weird pattern of the incarceration variable by year, still waiting the reply of the PSID staff. Health is also weird, I wouldn’t know what to do here.

Without Sampling Weights

Not including the health covariate.

Model 1: Standard Model

Multiple imputation results:
      MIcombine.default(models)
               results           se      (lower      upper) missInfo
prison      0.60915266 0.3145192800 -0.07236020  1.29066552     86 %
male        0.45427243 0.0257177752  0.40384519  0.50469968      6 %
agec        0.07523002 0.0009869461  0.07326874  0.07719130     33 %
fraceblack  0.34387285 0.0292159606  0.28653990  0.40120579     10 %
fraceother -0.42188168 0.0717197482 -0.56244995 -0.28131340      0 %
linc_adjc  -0.06616004 0.0241303745 -0.11791655 -0.01440353     83 %
eduic      -0.04884552 0.0043554316 -0.05744057 -0.04025047     23 %

Model 2: Marginal Structural Model

Multiple imputation results:
      MIcombine.default(modelsMSM)
               results          se      (lower      upper) missInfo
prison      0.57493475 0.398537745 -0.27904705  1.42891656     82 %
male        0.45366990 0.026405398  0.40190149  0.50543831      5 %
agec        0.07490819 0.001186132  0.07255196  0.07726443     33 %
fraceblack  0.33735188 0.033154171  0.27223666  0.40246709     13 %
fraceother -0.41658902 0.069003829 -0.55183745 -0.28134060      1 %
linc_adjc  -0.06349345 0.023671520 -0.11415777 -0.01282914     82 %
eduic      -0.04900787 0.004506372 -0.05791635 -0.04009940     26 %

With Sampling Weights

Model 3: Standard model

Multiple imputation results:
      MIcombine.default(models)
               results          se      (lower       upper) missInfo
prison      0.76868946 0.459993636 -0.22370545  1.761084377     85 %
male        0.45815774 0.032000960  0.39541498  0.520900504      5 %
agec        0.08265764 0.001593325  0.07951515  0.085800130     22 %
fraceblack  0.24856883 0.062828651  0.12537803  0.371759637      5 %
fraceother -0.51449164 0.088080277 -0.68712815 -0.341855122      1 %
linc_adjc  -0.07659407 0.036744885 -0.15676665  0.003578505     89 %
eduic      -0.05462636 0.005489502 -0.06546461 -0.043788116     24 %

Model 4: Marginal structural model

Multiple imputation results:
      MIcombine.default(modelsMSM)
               results          se      (lower       upper) missInfo
prison      0.74966358 0.529419122 -0.39304630  1.892373454     85 %
male        0.45729601 0.032235699  0.39409689  0.520495134      5 %
agec        0.08237502 0.001646513  0.07912000  0.085630040     26 %
fraceblack  0.23917647 0.064957423  0.11169873  0.366654215     10 %
fraceother -0.50479494 0.089058295 -0.67936840 -0.330221470      3 %
linc_adjc  -0.07317306 0.036410015 -0.15250006  0.006153939     88 %
eduic      -0.05479641 0.005566744 -0.06580398 -0.043788840     27 %