Introduction
In epidemiologic research, reliable statistical analysis is critical for drawing high-quality conclusions. Often a false association is created between cause and effect, which has the potential to harm the national health care system. OR and RR tests are used to test association hypotheses between variables as options for examining the quantitative strength of associations between cause and effect. The present paper tests causality for diabetes and allergies as family history factors, using formulas (1) and (2) to test OR and RR, respectively.
OR = a*d / b*c (1)
RR = (a / a+b) / (c / (c+d)) (2)
Diabetes
One way in which a patient’s diabetes is thought to occur is through inherited mechanisms that result in mutations that disrupt natural pancreatic function. The current dataset allowed us to test the OR for the relationship between family history of diabetes (column L) and the presence of diabetes in a particular patient (column J): all variables were dichotomous and discrete and could take no values other than “yes” or “no.” The total number of values was thus 300. For OR, Ratio Table #1 was created to divide the entire sample into four groups at once using a 2-by-2 system (MedCalc, 2016). Then, using the formula to determine the OR, the specific result for this relationship was calculated as shown in equation (3).
Table 1. Relationships between family history of diabetes and the presence of diabetes in a patient.
OR = 89*168 / 20*23 = 14 952 / 460 = 32,5 (3)
Using the 95% confidence interval calculation, the correct entry for the result obtained is an expression (3). Such a wide interval is justified by the fact that the number of patients diagnosed without a family history is relatively small compared to patients with a family history.
OR = 32,5 ⌈95% CI: from 16.9 to 63.4⌉ (4)
Allergies
In addition, the presence of allergies can also be related to family history. Using the relative risk formula (2) allows for estimating this value for the data set. Table 2 follows the logic of Table 1 but now uses data not for diabetes but for the presence of allergies in the patient. Then, using formula (2), it became possible to determine the relative risk for this table, which is reflected in equation (5). The value obtained means that people with a family history of the disease and people without a family history had allergies at the same frequency. It is essential to say that the transposition of the table led to the same outcome, which means that the obtained conclusion is formulated correctly.
Table 2. Relationships between family history of allergies and the presence of allergies in the patient.
RR = (89 / 148) / (91 / 152) = 0.60 / 0.60 = 100 (5)
Discussion
Thus, summarizing the results leads to some interesting conclusions. First, the OR for diabetes turns out to be higher than 1, which means that the probability of the two events being related is high. In other words, having a family history of the disease, according to the criterion of effect severity, is related to diabetes. An additional RR check for Table 1 shows that the event is more frequent in the experimental group than in the group of patients without a family history of the disease (RR = 7.47). This is plausible because it is consistent with the scientific evidence (Franklin & Muthukumar, 2020). For allergic reactions, the RR level meant an equal risk of having allergies in both types of patients, and an additional OR check for these data (OR = 1.01, 95% CI: 0.64…1.61) confirms that having a family history does not affect the occurrence of allergies. It is essential to understand that OR and RR are not the same, which motivates additional examinations (Davies et al., 1998). The 95% confidence interval for the diabetes analysis proved the statistical significance of the result because it includes the OR. However, one cannot exclude the specificity criterion of the sample collected, resulting in a causality bias (Bradford Hill, 2020). In contrast, because the confidence interval for allergy studies included 1, the result was not statistically significant.
Conclusion
Epidemiological accuracy requires qualitative validation of data sets, and the OR and RR tests can be used for this purpose. The present work showed that diabetes does show a strong association with a family history of the disease, and the association is statistically significant. In contrast, the relationship between an individual’s allergies and family history was shown to be absent, with the result not being statistically significant. Thus, the main statistical patterns were identified, and relevant conclusions were formed, which can be used in practice.
References
Bradford Hill criteria of causality. (2020). Euro Surveillance.
Davies, H. T. O., Crombie, I. K., & Tavakoli, M. (1998). When can odds ratios mislead?The BMJ, 316(7136), 989-991.
Franklin, R. G., & Muthukumar, B. (2020). A prediction system for diagnosis of Diabetes Mellitus.Journal of Computational and Theoretical Nanoscience, 17(1), 6-9.
MedCalc. (2016). Relative risk, Risk difference and Odds ratio. MedCalc Software Ltd.