# Odds Ratio OR and Relative Risk RR

Odds Ratio OR and Relative Risk RR Order Instructions:  MHS506 Biostatistics
Module 4 – SLP
ODDS RATIO, RELATIVE RISK, AND ANOVA
Calculate the OR and the RR from the data provided. Calculate the OR for diabetes (outcome) with a family history of diabetes (exposure).

Calculate the RR for allergies (outcome) with a family history of allergies (exposure). Write up the sentences to interpret the OR and RR that is calculated. Show your calculations and discuss the significance of each, OR and RR. Make sure to include Hill’s Criteria in discussions of potential causality. Given the 95% Confidence Interval, can you determine if the result is statistically significant?
Odds Ratio and 95% CI Calculator
http://easycalculation.com/statistics/odds-ratio.php
Relative Risk Calculator
http://easycalculation.com/statistics/relative-risk.php
SLP Assignment Expectations
Length: SLP assignments should be at least 2 pages (500 words) in length.
References: At least two references must be included from academic sources (e.g. peer-reviewed journal articles). Required readings are included. Quoted material should not exceed 10% of the total paper (since the focus of these assignments is critical thinking). Use your own words and build on the ideas of others. When the material is copied verbatim from external sources, it MUST be enclosed in quotes. The references should be cited within the text and also listed at the end of the assignment in the References section (APA format recommended).
Organization: Subheadings should be used to organize your paper according to question
Format: APA format is recommended for this assignment. See Syllabus page for more information on APA format.
Grammar and Spelling: While no points are deducted for minor errors, assignments are expected to adhere to standards guidelines of grammar, spelling, punctuation, and sentence syntax. Points may be deducted if grammar and spelling impact clarity.
The following items will be assessed in particular:
• Achievement of learning outcomes for SLP assignment.
• Relevance—all content is connected to the question.
• Precision—specific question is addressed; statements, facts, and statistics are specific and accurate.
• The depth of discussion—points that lead to deeper issues is presented and integrated.
• Breadth—multiple perspectives and references, multiple issues/factors considered/
• Evidence—points are well-supported with facts, statistics, and references.
• Logic—presented discussion makes sense; conclusions are logically supported by premises, statements, or factual information.
• Clarity—writing is concise, understandable, and contains sufficient detail or examples.
• Objectivity—use of the first person and subjective bias are avoided.

# Odds Ratio OR and Relative Risk RR Sample Answer

Introduction

Odds Ratio (OR) and Relative Risk (RR) are widely used in medical sciences to determine whether A’s presence or absence (exposure) has an association with presence or absence of B, and subsequently help quantify the association in terms of causality or causal effect (Viera, 2008).

Calculation Results

1. Odds Ratio

Table 1: Odds Ratio for Diabetes Data Summary

 Risk Disease Status Present Absent Total Family history of diabetes present (exposure) 89 (a) 23 (b) 112 Family history of diabetes absent 20 (c) 168 (d) 188 Total 109 191 300

Where, a&b = Positive Test Values c&d = Negative Test Values

Calculated Odds Ratio (OR) using the easy calculation Odds Ratio Calculator = 32.5043; and 95% Confidence Interval = from 16.9344 to 62.3896

The calculated OR result of 32.5043 (OR>1) shows that exposure is associated with higher odds of the outcome, which in this case indicates that there is an association between a person who has been exposed (i.e. presence of family history of diabetes) and diabetes (outcome).

1. Relative Risk

Table 2: Relative Risk for Allergies Data Summary

 Risk Disease Status Present Absent Total Family history of allergies present (exposure) 89 (a) 59 (b) 148 Family history of allergies absent 91  (c) 61 (d) 152 Total 180 120 300

Where; a = Exposed Group Positive Outcome, b = Exposed Group Negative Outcome, c = Control Group Positive Outcome, d = Control Group Negative Outcome

Calculated Relative Risk (RR) using the EasyCaculation Relative Risk Calculator = 1.0045

The calculated RR of 1.0045 shows that, a person with family history of allergies (exposure) would be 1.0045 times as likely to have allergies (outcome) as persons without family history of allergies presence. This means the relative risk of person has been exposed (i.e. presence of family history of allergies) to develop allergies is comparable to that of a person who has not been exposed.

## Odds Ratio OR and Relative Risk RR Discussion

Given the 95% Confidence Interval, it is possible to determine whether the result is statistically significant. This is because, when OR<1, it means that exposure is associated with lower odds of outcome; whereas when OR>1, it means that exposure is associated with higher odds of outcome (Bailey, 2008). However, when R=1 it means that exposure does not affect odds of outcome; hence, the null hypothesis for OR is that, when OR is greater that 1, then presence of condition A is regarded to have causal effect on condition B in a manner that having condition B raises (relatively to not having B) the odds of having condition A (Viera, 2008). Using this information, the calculated OR (32.5043) and 95% Confidence Interval (16.9344 to 62.3896), the result can be stated to be statistically significant. This means that, the causal effect between a people who have been exposed (i.e. presence of family history of diabetes) and diabetes (outcome) is statistically significant. As a result, based on Hill’s criteria of causality (plausibility) the association is aligned with currently accepted pathological process understanding because diabetes may be hereditary meaning genetic predisposition (exposure due to family diabetes history) is likely to cause diabetes (Höfler, 2005).

The RR calculation result of 1.0045 times, this means the relative risk of person has who has been exposed (i.e. presence of family history of allergies) to develop allergies is comparable to that of a person who has not been exposed. As a result, based on Hill’s criteria of causality (strength or effect size) presence of a small association does not rule out a causal effect, even though when the association is larger it means that there is more likely that it is causal and vice versa (Robbins, Chao & Fonseca,  2002). Thus, due to the weak association for allergies (outcome) with a family history of allergies (exposure), the causal effect cannot be confirmed to be statistically significant (Glass et al., 2013)

## Odds Ratio OR and Relative Risk RR Conclusion

In conclusion, it is clear that OR and RR can be used to determine the causal effect or causality of an exposure to a particular medical or epidemiological characteristic (i.e. diabetes and allergies). OR is used to determine not only the presence of the association, but also whether it is statistically significant, whereas RR determines how strong the association is. Using OR, association with higher odds outcome between exposure (i.e. family history of diabetes) and diabetes (outcome) has been determined to be statistically significant; while RR shows weak association between allergies (outcome) with a family history of allergies (exposure).

### Odds Ratio OR and Relative Risk RR References

Bailey, R. A. (2008). Design of Comparative Experiments. Cambridge: Cambridge University Press.

EasyCaculation.com (2015). Relative Risk Confidence Interval Calculator. Retrieved from https://www.easycalculation.com/statistics/relative-risk.php (Accessed on November 5, 2015).

EasyCaculation.com (2015). Odds Ratio Confidence Interval Calculator. Retrieved from https://www.easycalculation.com/statistics/odds-ratio.php (Accessed on November 5, 2015).

Glass, T. A., Goodman, S. N., Hernán, M. A., & Samet, J. M. (2013). Causal inference in public healthAnnual Review of Public Health, 34(3), 61–75. Doi: 10.1146/annurev-publhealth-031811-124606

Robbins, A. S., Chao, S. Y., & Fonseca, V. P. (2002). What’s the relative risk? A method to directly estimate risk ratios in cohort studies of common outcomesAnnual Epidemiology, 12(7), 452–454. Doi: 10.1016/S1047-2797(01)00278-2

Viera, A. J. (2008). Odds ratios and risk ratios: what’s the difference and why does it matter? Southern Medical Journal, 101(7), 730–734. Doi: 10.1097/SMJ.0b013e31817a7ee4

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