Home  |  About us  |  Editorial board  |  Ahead of print  | Current issue  |  Archives  |  Submit article  |  Instructions |  Search  |   Subscribe  |  Advertise  |  Contacts  |  Login 
  Users Online: 488Home Print this page Email this page Small font sizeDefault font sizeIncrease font size  

 Table of Contents      
Year : 2015  |  Volume : 6  |  Issue : 4  |  Page : 222-224

Common pitfalls in statistical analysis: Odds versus risk

1 Department of Anaesthesiology, Tata Memorial Centre, Parel, Mumbai, Maharashtra, India
2 Department of Gastroenterology, Sanjay Gandhi Postgraduate Institute of Medical Sciences, Lucknow, India
3 Department of Surgical Oncology, Division of Thoracic Surgery, Tata Memorial Centre, Parel, Mumbai, Maharashtra, India

Date of Web Publication12-Oct-2015

Correspondence Address:
Priya Ranganathan
Department of Anaesthesiology, Tata Memorial Centre, Ernest Borges Road, Parel, Mumbai - 400 012, Maharashtra
Login to access the Email id

Source of Support: None, Conflict of Interest: None

DOI: 10.4103/2229-3485.167092

Rights and Permissions

In biomedical research, we are often interested in quantifying the relationship between an exposure and an outcome. “Odds” and “Risk” are the most common terms which are used as measures of association between variables. In this article, which is the fourth in the series of common pitfalls in statistical analysis, we explain the meaning of risk and odds and the difference between the two.

Keywords: Biostatistics, odds ratio, risk

How to cite this article:
Ranganathan P, Aggarwal R, Pramesh C S. Common pitfalls in statistical analysis: Odds versus risk. Perspect Clin Res 2015;6:222-4

How to cite this URL:
Ranganathan P, Aggarwal R, Pramesh C S. Common pitfalls in statistical analysis: Odds versus risk. Perspect Clin Res [serial online] 2015 [cited 2021 Nov 27];6:222-4. Available from: https://www.picronline.org/text.asp?2015/6/4/222/167092

   Introduction Top

Researchers are often interested in evaluating the association between an exposure and an outcome. In other words, they are interested in knowing whether the presence of a risk factor or performing an intervention alters the risk of an outcome as compared to the absence of the risk factor or of the intervention (the “control” situation).

   Risk and Odds: Definitions Top

“Risk” refers to the probability of occurrence of an event or outcome. Statistically, risk = chance of the outcome of interest/all possible outcomes. The term “odds” is often used instead of risk. “Odds” refers to the probability of occurrence of an event/probability of the event not occurring. At first glance, though these two concepts seem similar and interchangeable, there are important differences that dictate where the use of either of these is appropriate.

Let us look at the hypothetical example of a randomized trial comparing endoscopic sclerotherapy (n = 65) versus band ligation (n = 64) for the treatment of bleeding esophageal varices [Table 1]. The overall risk of death = 47/129 ([number of deaths]/[all outcomes i.e., all deaths + survivors]) =0.36. The overall odds of death = 47/82 ([number of deaths]/[number of nondeaths, i.e., survivors]) =0.57. The risk of death in the ligation group was 18/64 (28% or 0.28), and the risk of death in the sclerotherapy group was 29/65 (44% or 0.44). By contrast, the odds of death in the two groups was 18/46 (0.39) and 29/36 (0.81), respectively.
Table 1: A randomized trial of sclerotherapy versus ligation for esophageal varices (hypothetical data)

Click here to view

   Relationship of Risk and Odds Top

In the example above, for the same data set, the chances of death appear markedly different when expressed as risks and odds.

[Table 2] shows the risk and odds for different event rates. As “a” decreases with respect to “b” (probability of outcome becomes less), the odds and risk are similar. For rare events (i.e., if “a” is small and “a + b” approaches “b”), a/(a + b) ≈ a/b and risk approximates odds. Therefore, though “odds” does not represent true risk, its value is close to risk when the event rates are low (typically <10%).[1]
Table 2: Risk and odds for different event rates

Click here to view

   Relative Risk and Odds Ratio Top

The relative risk (also known as risk ratio [RR]) is the ratio of risk of an event in one group (e.g., exposed group) versus the risk of the event in the other group (e.g., nonexposed group). The odds ratio (OR) is the ratio of odds of an event in one group versus the odds of the event in the other group.

An RR (or OR) of 1.0 indicates that there is no difference in risk (or odds) between the groups being compared. An RR (or OR) more than 1.0 indicates an increase in risk (or odds) among the exposed compared to the unexposed, whereas a RR (or OR) <1.0 indicates a decrease in risk (or odds) in the exposed group. As for other summary statistics, confidence intervals can be calculated for RR and OR.

In the same example, the RR of death in ligation group versus sclerotherapy group = 0.28/0.44 = 0.63. This means that the risk of death after ligation is 63% of the risk of death after sclerotherapy. This implies that ligation decreases the risk of death by 37% (calculated as 100 minus 63%) as compared with sclerotherapy. The OR for death in ligation group versus sclerotherapy group = 39/81 = 0.48. This means that the odds of death after ligation is 48% of the odds of death after sclerotherapy, or that ligation decreases the odds of death by 52% as compared with sclerotherapy.

   Relationship of Risk Ratio and Odds Ratio Top

Though OR also indicates the nature of association between exposure and outcome, it is not identical to RR. The relationship of OR and RR is complex. [Table 3] shows RR and OR for different event rates. When there is no association between exposure and outcome, both OR and RR are identical and equal to 1.0 [Table 3]a. When there is an association between an exposure and an outcome, OR exaggerates the estimate of their relationship (is farther from 1.0 than RR). Thus, when RR <1, OR is lower than RR [Table 3]b; by contrast, when RR is more than 1.0, OR is higher than the RR [Table 3]c,[Table 3]d,[Table 3]e. When the outcome is rare (typically <10%), the value of OR is not too different from that of RR, and the two can be used interchangeably irrespective of whether the risk is lower [Table 3]b or higher [Table 3]c in the exposed group as compared to the unexposed.[1] As event rates increase [Tables 3]d or [Table 3]e, the two ratios diverge and can no longer be used interchangeably.
Table 3: RR and OR for different event rates

Click here to view

   When Should One Use Risk Ratio and Odds Ratio? Top

Calculation of risk requires the use of “people at risk” as the denominator. In retrospective (case-control) studies, where the total number of exposed people is not available, RR cannot be calculated and OR is used as a measure of the strength of association between exposure and outcome. By contrast, in prospective studies (cohort studies), where the number at risk (number exposed) is available, either RR or OR can be calculated.

Multiple logistic regression, a frequently used multivariate technique, calculates adjusted ORs and not RRs.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

   References Top

Sedgwick P. Relative risks versus odds ratios. BMJ 2014;348:g1407.  Back to cited text no. 1


  [Table 1], [Table 2], [Table 3]

This article has been cited by
1 Systemic corticosteroids for the treatment of COVID-19
Carina Wagner,Mirko Griesel,Agata Mikolajewska,Anika Mueller,Monika Nothacker,Karoline Kley,Maria-Inti Metzendorf,Anna-Lena Fischer,Marco Kopp,Miriam Stegemann,Nicole Skoetz,Falk Fichtner
Cochrane Database of Systematic Reviews. 2021; 2021(8)
[Pubmed] | [DOI]
2 Bankruptcy among insured patients with surgical breast cancer: Who is at risk?
Samilia Obeng-Gyasi,Lava R. Timsina,Oindrila Bhattacharyya,Carla S. Fisher,David A. Haggstrom
Cancer. 2021;
[Pubmed] | [DOI]
3 Multiple imputation analysis of Miettinen-Nurminen interval for difference in proportions
Kaifeng Lu,Hua Guo
Pharmaceutical Statistics. 2021;
[Pubmed] | [DOI]
4 The Association Between Poor Sleep and the Incidence of Sport and Physical Training-Related Injuries in Adult Athletic Populations: A Systematic Review
Devon A. Dobrosielski,Lisa Sweeney,Peter J. Lisman
Sports Medicine. 2021;
[Pubmed] | [DOI]
5 An analysis of US domestic migration via subset-stable measures of administrative data
Ben Klemens
Journal of Computational Social Science. 2021;
[Pubmed] | [DOI]
6 Reply to “Commentary on: Risk factors for postoperative morbidity after thyroid surgery in a PROSPECTIVE cohort of 1500 patients (Int. J. Surg. 2021, Epub ahead of print)”
Klaas Van Den Heede,Sam Van Slycke,Nele Brusselaers
International Journal of Surgery. 2021; : 105994
[Pubmed] | [DOI]
7 Intimate Partner Violence and Adult Asthma Morbidity: A Population-Based Study
Eileen Wang,Bryan Simmons,Kristen E. Holm,Rafeul Alam,Frederick S. Wamboldt
The Journal of Allergy and Clinical Immunology: In Practice. 2021;
[Pubmed] | [DOI]
8 The role of gender in the evolution of peer networks: Individual differences in relation to the Big Five
Stefanie Powazny,Simone Kauffeld
Personality and Individual Differences. 2021; 170: 110447
[Pubmed] | [DOI]
9 Does lower-limb asymmetry increase injury risk in sport? A systematic review
Mark Helme,Jason Tee,Stacey Emmonds,Chris Low
Physical Therapy in Sport. 2021;
[Pubmed] | [DOI]
10 The Flip Side of Turnover: Employment Transitions and Occupational Attachment Among Low-Wage Care Workers in the United States
Mignon Duffy,Reagan Baughman,Kristin Smith
Feminist Economics. 2021; : 1
[Pubmed] | [DOI]
11 Neonatal mortality rates, characteristics, and risk factors for neonatal deaths in Ghana: analyses of data from two health and demographic surveillance systems
Shadrach Dare,Abraham R. Oduro,Seth Owusu-Agyei,Daniel F. Mackay,Laurence Gruer,Alfred Kwesi Manyeh,Ernest Nettey,James F. Phillips,Kwaku Poku Asante,Paul Welaga,Jill P. Pell
Global Health Action. 2021; 14(1): 1938871
[Pubmed] | [DOI]
12 Group decision quality, conscientiousness and competition
Lukman Nul Hakim,Guritnaningsih A. Santoso,Bagus Takwin,Yos Sunitiyoso,Juneman Abraham,Delane Botelho
Cogent Psychology. 2021; 8(1): 1872907
[Pubmed] | [DOI]
13 Cardiovascular immunotoxicities associated with immune checkpoint inhibitors: a safety meta-analysis
Charles Dolladille,Julia Akroun,Pierre-Marie Morice,Anne Dompmartin,Emilien Ezine,Marion Sassier,Angélique Da-Silva,Anne-Flore Plane,Damien Legallois,Jean-Mathieu L’Orphelin,Joachim Alexandre
European Heart Journal. 2021;
[Pubmed] | [DOI]
14 Pregnancy complications among refugee women: A systematic review
Hawa-Idil Harakow,Lone Hvidman,Christian Wejse,Andreas H. Eiset
Acta Obstetricia et Gynecologica Scandinavica. 2021;
[Pubmed] | [DOI]
15 Targeted caspofungin prophylaxis for invasive aspergillosis in high-risk liver transplant recipients, a single-center experience
Arpita Chakravarti,Guillaume Butler-Laporte,Francois Martin Carrier,Marc Bilodeau,Genevieve Huard,Daniel Corsilli,Patrice Savard,Me-Linh Luong
Transplant Infectious Disease. 2021;
[Pubmed] | [DOI]
16 True Differences in Poor Outcome Risks Between Revision and Primary Lumbar Spine Surgeries
Chad E. Cook,Alessandra N. Garcia,Christine Park,Oren Gottfried
HSS Journal®: The Musculoskeletal Journal of Hospital for Special Surgery. 2021; 17(2): 192
[Pubmed] | [DOI]
17 Effects of a Co-Design–Based Invitation Strategy on Participation in a Preventive Health Check Program: Randomized Controlled Trial
Trine Thilsing,Lars Bruun Larsen,Anders Larrabee Sonderlund,Signe Skaarup Andreassen,Jeanette Reffstrup Christensen,Nanna Herning Svensson,Marie Dahl,Jens Sondergaard
JMIR Public Health and Surveillance. 2021; 7(3): e25617
[Pubmed] | [DOI]
18 Factors Associated with Mortality in Ontario Standardbred Racing: 2003–2015
Peter Physick-Sheard,Amanda Avison,William Sears
Animals. 2021; 11(4): 1028
[Pubmed] | [DOI]
19 Being Born in Winter–Spring and at Around the Time of an Influenza Pandemic Are Risk Factors for the Development of Schizophrenia: The Apna Study in Navarre, Spain
Miguel A. Alvarez-Mon,Sara Guillen-Aguinaga,Victor Pereira-Sanchez,Luc Onambele,Moad J. Al-Rahamneh,Antonio Brugos-Larumbe,Francisco Guillen-Grima,Felipe Ortuño
Journal of Clinical Medicine. 2021; 10(13): 2859
[Pubmed] | [DOI]
20 Evolution of Nutritional Status after Early Nutritional Management in COVID-19 Hospitalized Patients
Dorothée Bedock,Julie Couffignal,Pierre Bel Lassen,Leila Soares,Alexis Mathian,Jehane P. Fadlallah,Zahir Amoura,Jean-Michel Oppert,Pauline Faucher
Nutrients. 2021; 13(7): 2276
[Pubmed] | [DOI]
21 Study designs: Part 8 - Meta-analysis (I)
Priya Ranganathan,Rakesh Aggarwal
Perspectives in Clinical Research. 2020; 0(0): 0
[Pubmed] | [DOI]
22 Custom Focal Trough in Cone-Beam Computed Tomography Reformatted Panoramic Versus Digital Panoramic for Mental Foramen Position to Aid Implant Planning
Khaled Beshtawi,Emad Qirresh,Mohamed Parker,Shoayeb Shaik
Journal of Clinical Imaging Science. 2020; 10: 34
[Pubmed] | [DOI]
23 Association of cardiovascular disease and 10 other pre-existing comorbidities with COVID-19 mortality: A systematic review and meta-analysis
Paddy Ssentongo,Anna E. Ssentongo,Emily S. Heilbrunn,Djibril M. Ba,Vernon M. Chinchilli,Jennifer A. Hirst
PLOS ONE. 2020; 15(8): e0238215
[Pubmed] | [DOI]
24 An Analysis of U.S. Domestic Migration via Subset-stable Measures of Administrative Data
Ben Klemens
SSRN Electronic Journal. 2020;
[Pubmed] | [DOI]
25 Crossing boundaries online: A hybrid method study of patients’ convergence of mass and interpersonal communication on forums. (Preprint)
Remco Sanders,Annemiek J. Linn,Theo Araujo,Rens Vliegenthart,Mies van Eenbergen,Julia C.M. van Weert
Journal of Medical Internet Research. 2020;
[Pubmed] | [DOI]
26 Associations Between Social Support Availability and HIV Risk and Protective Factors in a U.S. Sample of Adults with Diverse Transgender Identities
Bobbi V. Gass,Keith J. Horvath,Elliot Marrow,Brian A. Rood,David W. Pantalone
LGBT Health. 2020;
[Pubmed] | [DOI]
27 The school to prison pipeline: quantitative evidence to guide school counselor advocacy
Laura E. Welfare,Tameka Oliphant Grimes,Gerard Lawson,Kazuki Hori,Ghadir Asadi
Journal of Counselor Leadership and Advocacy. 2020; : 1
[Pubmed] | [DOI]
28 For a good selfie. Enhancing mobile phone recycling through simulated exposure to cobalt mining
Eva Garcia-Vazquez,Pilar Cartón,Micaela Domínguez,Noemí Rodríguez,Antonio Bustillos,Eduardo Dopico
Sustainable Production and Consumption. 2020; : e00388
[Pubmed] | [DOI]
29 Myelodysplastic syndrome and acute myeloid leukaemia in patients treated with PARP inhibitors: a safety meta-analysis of randomised controlled trials and a retrospective study of the WHO pharmacovigilance database
Pierre-Marie Morice,Alexandra Leary,Charles Dolladille,Basile Chrétien,Laurent Poulain,Antonio González-Martín,Kathleen Moore,Eileen Mary OæReilly,Isabelle Ray-Coquard,Joachim Alexandre
The Lancet Haematology. 2020;
[Pubmed] | [DOI]
30 Intensive care utilization in patients with end-stage liver disease: A population-based comparative study of cohorts with and without comorbid hepatocellular carcinoma in taiwan
Jen-Kuei Peng,Hao-Hsiang Chang,Irene J Higginson,Wei Gao
EClinicalMedicine. 2020; 22: 100357
[Pubmed] | [DOI]
31 Early use of low dose tocilizumab in patients with COVID-19: A retrospective cohort study with a complete follow-up
Nicola De Rossi,Cristina Scarpazza,Chiara Filippini,Cinzia Cordioli,Sarah Rasia,Chiara Rosa Mancinelli,Damiano Rizzoni,Giuseppe Romanelli,Stefania Cossi,Nereo Vettoretto,Sergio Bove,Silvano Manfredini,Eva Andrea Beindorf,Carlo Mosca,Vittorio Scipione,Gigliola Flamminio,Elena Albini Albini,Paola Giansiracusa,Ruggero Capra
EClinicalMedicine. 2020; : 100459
[Pubmed] | [DOI]
32 Association Between Ethnicity and Severe COVID-19 Disease: a Systematic Review and Meta-analysis
Antony Raharja,Alice Tamara,Li Teng Kok
Journal of Racial and Ethnic Health Disparities. 2020;
[Pubmed] | [DOI]
33 Meta-Analysis and Meta-Regression of Risk Factors for Surgical Site Infections in Hepatic and Pancreatic Resection
Keno Mentor,Bathiya Ratnayake,Nasreen Akter,Giorgio Alessandri,Gourab Sen,Jeremy J. French,Derek M. Manas,John S. Hammond,Sanjay Pandanaboyana
World Journal of Surgery. 2020;
[Pubmed] | [DOI]
34 Economic access influences degenerative spine disease outcomes at rural Late Medieval Villamagna (Lazio, IT )
Katherine M. Kinkopf,Sabrina C. Agarwal,Caroline Goodson,Patrick D. Beauchesne,Trent M. Trombley,Francesca Candilio,Mauro Rubini,Alfredo Coppa
American Journal of Physical Anthropology. 2020;
[Pubmed] | [DOI]
35 Identifying sequential episodes of pharmacotherapy as a method for assessing treatment failure in comparative effectiveness research
Greg Carney,Malcolm Maclure,Ken Bassett,Suzanne Taylor,Colin R. Dormuth
Pharmacoepidemiology and Drug Safety. 2019;
[Pubmed] | [DOI]
36 Making sense of medieval mouths: Investigating sex differences of dental pathological lesions in a late medieval Italian community
Trent M. Trombley,Sabrina C. Agarwal,Patrick D. Beauchesne,Caroline Goodson,Francesca Candilio,Alfredo Coppa,Mauro Rubini
American Journal of Physical Anthropology. 2019;
[Pubmed] | [DOI]
37 Place of death and factors associated with hospital death in patients who have died from liver disease in England: a national population-based study
Jen-Kuei Peng,Irene J Higginson,Wei Gao
The Lancet Gastroenterology & Hepatology. 2019; 4(1): 52
[Pubmed] | [DOI]
38 Effects of racism on the socio-emotional wellbeing of Aboriginal Australian children
D. M. Macedo,L. G. Smithers,R. M. Roberts,Y. Paradies,L. M. Jamieson
International Journal for Equity in Health. 2019; 18(1)
[Pubmed] | [DOI]
39 Does ethnic-racial identity modify the effects of racism on the social and emotional wellbeing of Aboriginal Australian children?
Davi M. Macedo,Lisa G. Smithers,Rachel M. Roberts,Dandara G. Haag,Yin Paradies,Lisa M. Jamieson,Valsamma Eapen
PLOS ONE. 2019; 14(8): e0220744
[Pubmed] | [DOI]
40 Cardiologist and Diabetologist crosstalk in the era of cardiovascular outcome trials of novel glucose-lowering drugs
Francesco Maranta,Lorenzo Cianfanelli,Maria Regoni,Domenico Cianflone
IJC Heart & Vasculature. 2018; 21: 80
[Pubmed] | [DOI]
41 Risk factor for infection in spine surgery: Are the results correct?
Jonny Alejandro Garcia,Alejandra Del Castillo,Juan Camilo Hernández Vargas
American Journal of Infection Control. 2018;
[Pubmed] | [DOI]


    Similar in PUBMED
   Search Pubmed for
   Search in Google Scholar for
 Related articles
    Access Statistics
    Email Alert *
    Add to My List *
* Registration required (free)  

  In this article
    Risk and Odds: D...
    Relationship of ...
    Relative Risk an...
    Relationship of ...
    When Should One ...
    Article Tables

 Article Access Statistics
    PDF Downloaded6997    
    Comments [Add]    
    Cited by others 41    

Recommend this journal