Distribution of risk of the outcome among scenarios for which the calculated odds ratio and confidence interval coincide with the published values.  

Distribution of risk of the outcome among scenarios for which the calculated odds ratio and confidence interval coincide with the published values.  

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In medical and epidemiological studies, the odds ratio is a commonly applied measure to approximate the relative risk or risk ratio in cohort studies. It is well known tha such an approximation is poor and can generate misleading conclusions, if the incidence rate of a study outcome is not rare. However, there are times when the incidence rate is n...

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... answer this question, we obtain the rounded odds ratio and confidence interval if they coincide with the published values, then plot the corresponding risk of the study outcome in the control and treatment groups, respectively. Figure 1 suggests that, although the incidence rate is unknown from the published data, there is a clear evidence that the incidence is high (>18%) in both the control and treatment groups. Consequently, the reported odds ratio in Table 2 can potentially overestimate the true risk ratio. ...

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... Specifically, it uses the OR as the primary epidemiological measure and aligns it with the commonly used BMD modeling framework for regulatory risk assessment. The objective of this study is to investigate and compare two approaches: the "effective count" based BMD modeling approach (Allen et al., 2020b), combined with the Wang algorithm (Wang, 2013), and the adjusted OR-based BMD analysis approach (Shao et al., 2021). ...
... Model epidemiological data as dichotomous data This model works in two steps. Initially, data are pre-treated to derive the "effective counts" based on an approach following Allen et al. (2020b) and the Wang algorithm (Wang, 2013), that is, the effective number of cases A and of controls B obtained as we consider the OR and the interval of its SEs both varying with respect to the different dose groups. Eventually, the effective counts are modeled as dichotomous data to calculate BMDs as outlined in Shao and Shapiro (2018). ...
... where W symbolizes the Wang algorithm, N is the total number of subjects counting for all dosage groups, the bar symbol operator represents the mean over all the odds ratios and their lower and upper bound of the confidence interval at the 95% level, and SS is a sum of squares as defined in Wang (2013). Eventually, we derive the full number of effective counts for the treatment groups (that is, for all remaining dosage groups) by exploiting the previously mentioned condition on the number of subjects and, similarly, an equivalence of ORs between ...
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Following a previous article that focused on integrating epidemiological data from prospective cohort studies into toxicological risk assessment, this paper shifts the focus to case‐control studies. Specifically, it utilizes the odds ratio (OR) as the main epidemiological measure, aligning it with the benchmark dose (BMD) methodology as the standard dose–response modeling approach to determine chemical toxicity values for regulatory risk assessment. A standardized BMD analysis framework has been established for toxicological data, including input data requirements, dose–response models, definitions of benchmark response, and consideration of model uncertainty. This framework has been enhanced by recent methods capable of handling both cohort and case‐control studies using summary data that have been adjusted for confounders. The present study aims to investigate and compare the “effective count” based BMD modeling approach, merged with an algorithm used for converting odds ratio to relative risk in cohort studies with partial data information (i.e., the Wang algorithm), with the adjusted OR‐based BMD analysis approach. The goal is to develop an adequate BMD modeling framework that can be generalized for analyzing published case‐control study data. As in the previous study, these methods were applied to a database examining the association between bladder and lung cancer and inorganic arsenic exposure. The results indicate that estimated BMDs and BMDLs are relatively consistent across both methods. However, modeling adjusted OR values as continuous data for BMD estimation aligns better with established practices in toxicological BMD analysis, making it a more generalizable approach.
... Also, to convert the results reported in RR to OR, the following conversion was used(25): ...
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... , where σ X is the standard deviation of the independent variable and σ Y is standard deviation of the dependent variable. When risk ratios (RRs) were reported, we transformed them into odds ratios (ORs) using the following formula (Wang, 2013): ...
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... We standardized each risk factor by log-transformation and unifying the direction of the predictors [15]. In studies that reported the measure of association as hazard ratio or risk ratio, we converted them to OR using the baseline risk reported in the studies [16,17]. We conducted a meta-analysis of associations using the generic inverse variance-based method to produce an overall measure of association. ...
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... We reported the adjusted relative risks (aRRs) with 95% confidence intervals (CIs) that were converted from odds ratios in an established method. [13,14] ...
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Background Our recent observational study showed that regular consumption of cow’s milk (CM) formula during early infancy (3–6 months old) was associated with a reduced risk of CM allergy (CMA) at 12 months old. However, the long-term association is unclear. The present study was aimed to examine how long this inverse association persists after 12 months old. Methods This study used the dataset of an ongoing nationwide prospective cohort, the Japan Environment and Children’s Study, in which participants were registered between January 2011 and March 2014. We analyzed 65,568 children followed-up until 36 months old. The exposure factors were the consumption statuses of formula milk from 0–3, 3–6, and 6–12 months old. The primary outcome was the prevalence of CMA at 6, 12, 18, 24 and 36 months old. CMA was defined as an allergic reaction and sensitization to CM protein in an individual with no or limited intake of this protein at the evaluation time, combined with physician-diagnosed food allergy. Multivariable regression models were used to estimate the association between the periods of formula consumption and the prevalence of CMA. Results The prevalence of CMA increased with a peak of 1.51% at 18 months old and then declined to 0.79% at 36 months old. Formula milk from 3–6 months old was associated with a reduced risk of CMA throughout the first 3 years of life, although the extent of the reduction was mitigated with age (adjusted relative risk: [95% confidence interval]: 0.19 [0.10–0.34] at 12 months old, 0.23 [0.16–0.33] at 18 months old, 0.41 [0.26–0.64] at 24 months old, and 0.47 [0.26–0.80] at 36 months old). The association between early formula and CMA were observed in both children with and without eczema, but more prominent and long-lasting in the former than the latter. Conclusions Regular exposure to CM protein during infancy was associated with a reduced prevalence of CMA during early childhood. At present, however, this observational study does not necessarily encourage formula feeding, and randomized controlled trials are warranted to confirm the findings and their significance.
... The log odds ratio output from the glm() was converted into a relative risk score and accompanying 95% confidence interval using the function odds_to_rr() from the sjstats package. This function uses the equation: Zhang and Yu (1998), Wang (2013) and Grant (2014). ...
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... Table 1 was later transformed to two by two simple contingency table, in which antenatal women that uptake partial and optimal IPTp SP were categorizes as exposed group, while those with 0-Dose were unexposed group. The odds ratio is the probability that an event will happened divided by the probability that an event will not happened [14]. This research intended to determine the odds that malaria in pregnancy will occur among women who were exposed to IPTp and the magnitude of the effect. ...