Table 1. Analysis Strategy and Expectations.
Expectation
If Combo Debits Warranted
If Combo Debits Not Warranted
Strategy Technique
Key Variable 4-Category
1
Cox Model
HR(both) > HR(smoker) x HR(diabetes)
HR(both) <= HR(smoker) x HR(diabetes)
2
Cox Model
Interaction Term
Interaction > 1 and significant RMR(sd:snd) > RMR(nsd:nsnd)
Interaction < 1 or not significant
3
Actuarial Model
Ratio of Mortality Ratios
RMR(sd:snd) <= RMR(nsd:nsnd)
Note : HR = hazard ratio, RMR = ratio of mortality ratios, sd = smoking diabetics, snd = smoking non-dia - betics, nsd = non-smoking diabetics, nsnd = non-smoking non-diabetics.
significantly smaller than 1 or if it is not statistically significant at all, it would suggest that combo debits are not warranted. The third method is more complex but also more grounded in the actuarial methods that are commonly used in life insurance. First, we need to recognize that the death assessment from the Social Security Death Master File is incomplete. So, when the observed mortality rate from the study is compared to the “ex - pected” rate from the 2015 valuation basic table (VBT, smoker-distinct), the mortality ratio (MR) will be artificially low. However, if we compare two groups by taking a ratio of MRs, we can, hopefully, remove this problem. For instance, the observed to expected ratio will be calculated for diabetic non-smokers to the VBT based on age, sex and smoking status - and the same will be done for non-smokers without diabetes. Both of these will be artificially low due to incomplete death assessment, but we assume that effect is similar between the two groups. When we take the ratio of the observed: expected ratio for the diabetic non-smokers to that of the non-diabetic non-smokers, we get a ratio of mortality ratios (RMR). What we expect here is that if combo debits are indeed warranted, then the RMR of smoking diabetics to smoking non-diabetics would be higher than the RMR for non-smoking dia - betics compared to non-smokers without diabetes.
Thus, we are measuring and comparing the effect of diabetes on non-smokers vs. smokers. The strate- gies and expectations are summarized in Table 1. Results For Strategy 1 (see Table 2), we see that for both men and women, the hazard ratio for smoking alone is about 3, while for diabetes alone, it is about 2. For the category of smoking diabetics, we see that the hazard ratio is smaller than the product of the other 2. For women, 3.0 times 2.08 is 6.24, which is higher than the 5.45 hazard ratio for the “both” category (see Table 2). For men, we see that the product of smoking (2.54) and diabetes (1.93) is 4.9 - quite a bit more than the 3.75 we see for smoking diabetics. For Strategy 2, we see that the interaction terms for both men and wom- en are less than 1 and are statistically significant. This implies that being a smoking diabetic is slightly better than what would be expected from the effects of each. Strategy 3 is, again, more complicated. In Table 3 (next page), it can be seen that the mortality ratio compared to the 2015 VBT matched for age, sex and smoking status is below 1 for all categories. This is, again, be- cause of the incomplete nature of the Social Security Death Master File. The mortality rates themselves are 10-year (geometric) averages. In the final calcula - tion, we compare how diabetes impacts mortality in
Table 2. Results of Strategy 1 and 2.
Hazard Ratios
Strategy 1
Hazard Ratios
Strategy 2
Smoking or Diabetes Women Men Neither 1(ref). 1(ref). Smoking Only 3.00 2.54 Diabetes Only 2.08 1.93 Both 5.45 3.75
Smoking or Diabetes Women Men Smoking 3.01 2.46 Diabetes 2.01 1.84 Interaction 0.87 0.78
Note : All results are statistically significant.
ON THE RISK vol.40 n.3 (2024)
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