STATISTICAL METHOD
Relative Risk & Odds Ratio Analysis
Statistical Consulting for 2x2 Effect Measures
We apply relative risk and odds ratio analysis within your study design, choosing the measure the design supports, adjusting with a suitable model and reporting ratios with 95% confidence intervals and absolute risks in publication-ready form.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Are Relative Risk and Odds Ratios?
The relative risk, or risk ratio, and the odds ratio are ratio measures for a binary outcome, comparing an exposed with an unexposed group or one treatment arm with another. The relative risk divides the risk of the event in one group by the risk in the other. The odds ratio divides the odds. When the outcome is rare the two are close, but when it is common the odds ratio lies further from 1 than the risk ratio. Case-control designs allow only odds ratios. Both are reported with 95% confidence intervals, crude and adjusted. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides relative risk and odds ratio analysis within your study design, with the relevant checks, effect estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Are Risk and Odds Ratios Appropriate?
Ratio measures fit a binary outcome compared across exposure or treatment groups, and these are the research situations in which researchers most often ask us to build or confirm the estimates.
Binary Outcome in a Cohort Study Event risk is compared between exposed and unexposed groups or treatment arms, and the effect must be stated as a risk ratio with its interval and the absolute difference.
Case-Control Odds Ratio Reporting Sampling by outcome status allows only odds ratios to be estimated, and the text must interpret them correctly instead of calling them relative risks.
Common Outcomes and Adjustment The outcome is frequent and covariates must be adjusted, so odds ratios from logistic regression may mislead and a model for the risk ratio is needed.
Reviewing an Effect Measure Report An odds ratio was described as a risk reduction, or the reference group was unclear. Independent Statistical Review rechecks the measure, the coding and the model.
ANALYTICAL APPROACH
How We Apply Risk and Odds Ratios
Within the family of Clinical, Survival & Epidemiological, the effect measure is chosen from the design and the outcome frequency, not from the default of the software.
Odds Ratio or Risk Ratio We choose the measure from the design and event frequency. When events are common, the odds ratio lies further from 1, so reading it as a relative risk exaggerates the effect.
Models for Adjusted Risk Ratios Logistic models give odds ratios. Adjusted risk ratios come from log-binomial regression, or Poisson regression with robust variance if the log-binomial model fails to converge.
Collapsibility and Adjustment Odds ratios are non-collapsible: adjusting for a prognostic variable can change them without any confounding. We state whether each estimate is conditional or marginal.
Reference Group and Coding We fix the event coding and reference group before estimation, and report raw counts with the risk difference or number needed to treat, so direction and size are explicit.
DELIVERABLES
What You Receive
As part of our Quantitative Data Analysis service, the effect estimates are delivered with the checks and files needed to report and defend them.
Data & Variable Review Exposure and outcome coding, the reference group, event counts per cell, missing data and any matching or clustering are reviewed before an effect measure is chosen.
Method-Specific Checks Convergence, sparse cells, influential observations and fit are examined, with Firth or exact methods for small counts and cluster-robust variance for clustered data.
Statistical Results Risk ratios or odds ratios with 95% confidence intervals, risk differences and numbers needed to treat, crude and adjusted estimates, and the underlying event counts.
Publication-Ready Tables & Figures A 2x2 table, an effect measure table and a forest plot, prepared in line with CONSORT or STROBE reporting or the journal's requirements, ready to insert.
Interpretation Estimates are read as ratios of risks or odds with the absolute effect beside them, and as associations, not causal effects, unless the design supports more.
Reproducible Analysis Files Syntax, do-files or R scripts reproduce every model and table, including the coding of exposure and outcome, so the analysis can be rerun if the data change.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
A 2x2 ratio measure suits a binary outcome in two groups. These methods fit better when many predictors, small counts, person-time or heavy confounding enter the question.
01
Logistic Regression
With several covariates, or in a case-control design, logistic regression returns an adjusted odds ratio per predictor, the natural measure when risks cannot be estimated.
02
Poisson Regression
For a risk ratio from a binary outcome in a cohort, Poisson regression with robust variance is a stable option, and with person-time offsets it models rates.
03
Propensity Score Matching (PSM)
When groups differ on many measured confounders, matching on the propensity score builds comparable groups before risks are compared, though unmeasured confounding remains.
04
Fisher's Exact Test
With small expected counts in a 2x2 table, an exact test and exact limits avoid the large-sample approximation behind the usual Wald interval for a ratio.
CASE EXAMPLE
How We Work in Practice
An illustration of how an effect measure moves from a prespecified model to risk ratios that can be reported and defended.
ILLUSTRATIVE EXAMPLE · HOSPITAL INFECTION CONTROL · UNITED STATES
A hospital infection-control unit compared surgical site infection between patients managed with a new wound care bundle and those on routine care, in a cohort where infections were common.
The team had planned logistic regression, but with common infections the odds ratio would have overstated the risk reduction. Before the outcome data were examined, we proposed a log-binomial model for the adjusted risk ratio, with Poisson regression with robust variance as the prespecified fallback if estimation failed. The log-binomial model did not converge with the full covariate set, so the fallback was used as planned. We reported raw counts, the risk difference and the number needed to treat beside the ratio, and named the reference group in every table.
Outcome: The unit received crude and adjusted risk ratios with 95% confidence intervals, the risk difference and number needed to treat, event counts, a methods paragraph on the model choice and the analysis scripts.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Effect Measures
Risk ratios, odds ratios and their intervals are run in the statistical software researchers already use, with syntax or scripts provided where applicable.
RESEARCH DISCIPLINES
Effect Measures Across Research Fields
Risk and odds ratios appear across research fields, each with its own exposure definitions, outcome frequencies and reporting conventions.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from a researcher who knew the direction but needed effect estimates and confidence intervals calculated and reported correctly.
“We knew Relative Risk & Odds Ratios was probably the right direction, but how effect sizes and confidence intervals should be calculated and reported was where we were stuck. OnlineSPSS reviewed the data and model rather than just rerunning the software output. The final tables included the effect estimates and 95% confidence intervals we needed for reporting.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your effect estimates, and the study, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your risk and odds ratio analysis, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The exposure definition, the clinical meaning of the effect and your conclusions remain with you, and our interpretation stays within what the ratios and the design support.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About Relative Risk and Odds Ratios
Short answers to what researchers ask before reporting an effect measure, from odds versus risk to confidentiality and the assessment process.
Can I report an odds ratio as if it were a relative risk?
Only when the outcome is rare, because then the two are close. As the outcome becomes common, the odds ratio moves further from 1 than the risk ratio, so describing it as a percentage increase in risk exaggerates the effect. We either estimate the risk ratio directly or interpret the odds ratio as odds, and we report the event counts with the estimate.
Which model estimates an adjusted risk ratio directly?
Log-binomial regression estimates it with a log link, but it can fail to converge when predicted risks approach 1. Poisson regression with robust variance is a widely used alternative that gives valid risk ratios for binary outcomes, at some cost in efficiency. We choose between them from convergence and the data, and report the confidence intervals.
Why do case-control studies report only odds ratios?
Cases and controls are sampled by outcome status, so the study cannot estimate the risk of the outcome in the exposed or unexposed groups, and a risk ratio is not identifiable. The odds ratio is still valid, and it approximates the risk ratio when the outcome is rare. We state this limit and avoid causal wording the design cannot support.
Can you review an analysis that has already been completed?
Yes, we can review a completed analysis of risk or odds ratios before submission or a response to reviewers. We check the choice of measure for the design, the reference group and event coding, the model and its convergence, the adjustment set, the intervals and whether absolute risks are reported, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your exposure and outcome data, model code and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With
Risk or Odds Ratios?
Share your research question, study design and data. We assess which effect measure and model fit your outcome and confirm the approach before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014