We have previously described methods of identifying injured workers and assessing mortality follow-up, which we explain here in brief. The State of New Mexico provided workers’ compensation data, including worker, employer, injury, and benefit characteristics. Our study population consisted of people who received workers’ compensation benefits for injuries occurring from 1994 through 2000.

Among injured workers, those who received cash benefits as a result of losing more than 7 days from work or were deemed to have a permanent injury-related disability serve as our exposed group, which we refer to as the “lost-time” injured. The comparison group was “medical-only” injured workers who experienced 7 or fewer days lost from work. Workers with medical-only injuries received benefits for medical expenses but no benefits to cover lost earnings. For workers with more than one lost-time injury in the study period, we chose the first lost-time injury as the index injury. For workers with only medical-only injuries, we chose the first as the index injury. For workers with both kinds of injury, the first lost-time injury was the index injury. We excluded workers with a lost-time injury in 1992 or 1993 because they had a lost-time injury before the study period. We restricted the data to workers aged 15 to 80.

We linked the workers’ compensation data to Social Security earnings and mortality data based on name, date of birth, sex, and Social Security Number, successfully linking more than 95% of cases. In addition, we used the Social Security Administration’s (SSA’s) Numerical Identification System and Vital Status System to categorize vital status as dead, alive, and unknown and to determine date of death. We validated the SSA’s vital status determination by linking random samples stratified by SSA vital status, lost-time vs. medical-only, and sex with the National Death Index (NDI). We previously reported high concordance between the SSA and NDI vital status (over 99%), and as a result, we used the New Mexico data with mortality determined by SSA as our primary data.

Our primary analysis used Cox proportional hazards separately for men and women, adjusting the association between lost-time injuries and mortality for age, pre-injury earnings, and industry. However, as noted, we did not have data on two key confounders, smoking and obesity, for which we conducted a quantitative bias analysis. For both this hazard analysis and the QBA, we used StataMP© Version 16.

The Institutional Review Board at Boston University approved this study. It waived informed consent based on the criteria under 45 CFR 46.116(d). We signed confidentiality agreements with the State of New Mexico for use of the workers’ compensation data, and the SSA signed a confidentiality agreement with the National Center for Health Statistics for use of the NDI data.

For the QBA we simulated smoking as a three-level variable (never, former, or current) and obesity as a dichotomous variable where those with a body mass index (BMI) greater than or equal to 30 kg/m² are considered obese. We provide details of the method we used to conduct the QBA in the online appendix at https://www.bu.edu/sph/files/2021/08/QBA_Methodology-Injury-and-Mortality.pdf. We provide an intuitive overview next, along with a flowchart (Fig. 1).

To simulate the missing covariates, we needed to estimate bias parameters. These included data on the probability of being in each of the 6 categories of smoking-obesity among those with and without lost-time injury. We also needed information on the strength of the effect of each category of the smoking-obesity variable on the outcome (mortality). Estimating the parameters required two steps. First, we determined the likely joint distribution of pre-injury smoking and obesity status for those with and without lost-time injury using secondary data from the Panel Study of Income Dynamics (PSID) [26]. We used this information to simulate imputed smoking and obesity categories for our primary data.

The PSID is a publicly available longitudinal interview study of a stratified random sample of U.S. individuals and their families designed to be representative of the population as a whole [26]. It focuses on economic behavior, but includes measures of health status and health behaviors. Beginning with the 1999 wave, the PSID has consistently obtained wave-to-wave response rates of 95%–97% and has averaged about 17,000 sample persons since the 1999 wave. In the PSID, we know the temporality of the relationship between lost-time work injury and potential confounders. This is an important advantage, as we are interested in the values of these potential confounders before injury.

From the PSID waves in 2003–2010, we obtained the national distribution of BMI and smoking categories for two groups of employed individuals: those who received workers’ compensation cash benefits (lost-time) and those who did not. For each lost-time worker, we selected 20 randomly sampled workers from the group without workers’ compensation cash benefits. This latter group is primarily uninjured workers, who we use as a stand-in for workers with medical-only injuries.

We drew this 20:1 matched sample of uninjured workers from the PSID, stratifying by sex, age group (less than 25, 25–34, 35–44, 45–54, 55–64, 65+ years), race/ethnicity (non-Hispanic White, non-Hispanic Black, Hispanic, Other), and education (less than high school, high school graduate, college graduate). For men and women separately, we calculated percentages in the six joint smoking and obesity categories reported in the wave of the PSID survey before the injury (for lost-time injured: survey wave before injury; for the sampled uninjured, survey wave before the injury of the matched injured worker). We weighted all measures derived from the PSID by sample weights provided by the PSID. A limitation of the PSID is the small number of lost-time injured workers surveyed in this period (131 men and 117 women). Although the PSID is a national sample and our sample is from New Mexico, the distributions of smoking and BMI categories for all New Mexico adults and U.S. adults were similar. Using the Behavioral Risk Factor Surveillance System (BRFSS) for the year 2000, we used the median percentage of characteristic across states. The median percent across states of current smokers (23.2%) and percent obese (20.1%) were within 1 percentage point of New Mexico’s (23.6% and 19.3% respectively). The smoking percentages remained close for other study years, although obesity was less prevalent in New Mexico. For example, for 1996, the median state’s percent of current smokers was 23.4% and in New Mexico 22.8%. For obesity, these numbers were 16.8% and 14.1% [27]. This suggests the PSID data can be used to approximate the distribution of smoking and obesity in our study population.

The PSID had virtually no deaths among injured workers. Therefore, we turned to the National Health and Nutrition Examination Survey (NHANES) to estimate mortality for BMI-smoking categories. We drew a sample from NHANES III (1988 – 1994) and Continuous NHANES waves (1999 – 2014), including people ages 35–79 at the time of the survey and employed in the private sector or state and local government. We did not include self-employed individuals or Federal workers, as the New Mexico and other state workers’ compensation systems do not cover them.

To derive the association of each smoking-obesity category with mortality, we applied Cox proportional hazards regressions with age as the underlying timescale to the NHANES data [28]. We constructed independent variables to account for 6 joint categories of smoking and obesity at survey. We adjusted for sex, race/ethnicity (non-Hispanic White, non-Hispanic Black, Hispanic, other), and educational attainment (less than high school, high school or equivalent, some college or greater).

Next, we applied methods described by Lash, Fink and Fox [24] to estimate what the strength of the relationship between mortality and lost-time injury would have been in the New Mexico data if we had data on smoking and obesity. We first used the unconditional relationships between lost-time injury and mortality in the New Mexico data together with the estimated hazard ratios from the NHANES regressions to estimate mortality probabilities for PSID observations based on their injury, obesity, and smoking status, controlling for sex, race, and education. This in turn yielded a probability distribution of smoking and obesity status for each sex-injury-mortality group. To account for uncertainty from the NHANES regression estimation, we sampled 100 iterations of random smoking/obesity effects on mortality from normal distributions around the regression coefficients using the standard errors from the regressions.

We then used the PSID probability distributions for smoking and obesity, stratified by sex, injury and mortality status, to simulate smoking and obesity values for observations in the primary New Mexico dataset. For each person in the New Mexico data, we imputed a value for them of being in 1 of the 6 smoking/obesity categories using the values derived above. We used the imputed value in the proportional hazards regression of the association between lost-time injury and mortality, adjusted for this new covariate (and other measured covariates). Because the proportions in the six categories are themselves estimates, subject to uncertainty, we repeated this process such that in each iteration a person could change their value of the smoking/obesity variable, and therefore each time leading to a different result from the proportional hazards regression.

Because these probability distributions are also estimated with uncertainty about the relationship between lost-time injury and smoking/obesity in the PSID dataset (separate from the uncertainty in the relationship between smoking/obesity and mortality in the NHANES dataset), we sampled 100 iterations of smoking/obesity values from normal distributions around the logit transformations for each of the 100 iterations of probability distributions calculated in the previous step. Thus, we had 100 × 100 = 10,000 simulations of smoking and obesity values. We used each probabilistic simulation of the confounders in the Cox proportional hazards regressions of worker mortality on lost-time injury, also controlling for age, pre-injury earnings and industry. We then added random error to each adjusted estimate by sampling from a standard random normal distribution, multiplying by the estimated standard error, and subtracting the result from the estimate adjusted for the systematic error. The betas from each model represent a single possible corrected result, which we then summarized using the median of the distribution as a point estimate and the 2.5th to the 97.5th percentile of the distribution as an interval accounting for systematic error. We compared this to the conventional analysis to see the impact of the bias on the magnitude, direction and uncertainty of the results due to the unmeasured confounding.