Odds ratios

The odds ratio is defined as the probability of the presence of a specific disease divided by the probability of its absence. The odds ratio reflects the prevalence of the disease in a population. For example, the probability of the occurrence of a 1.3-cm carcinoma in a 75-yeai -old man is about 8%. The odds ratio of finding histological carcinoma greater than 1.3 cm in size after sectioning the prostate from the autopsy specimen of a man older than 70 years is thus 0.08/(1-0.08), or 1 11.5. Findings from a digital rectal examination, from transrectal ultrasonography, or firom both are other data that affect the previous probability of the presence of prostatic disease. 

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Najem er al. LISA Hospital-based, tobacco- Printing industry 1 year) M + 7/5 - j 0.8-9.6 Crude odds ratio... 

Silverman et Population-based Printing industry (ever) M 50/45 1.1 0.7-1.7 Crude odds ratio... 

In the case-control design, a group with a disease (cases) is compared with a selected group of nondiscased (control) individuals with respect to exposure. The relative risk in control studies can only be estimated as the incidence rate among exposed individuals and cannot be calculated. The estimator used is the odds ratio, which is the ratio of the odds of exposure among the cases to that among the controls. 

Odds Ratio (OR)—A means of measuring the association between an exposure (such as toxic substances and a disease or condition) which represents the best estimate of relative risk (risk as a ratio of the incidence among subjects exposed to a particular risk factor divided by the incidence among subjects who were not exposed to the risk factor). An odds ratio of greater than 1 is considered to indicate greater risk of disease in the exposed group compared to the unexposed. 

In a case-control study of the relation between occupational exposures to various suspected estrogenic chemicals and the occurrence of breast cancer, the breast cancer odds ratio (OR) was not elevated above unity (OR=0.8 95% 01=0.2-3.2) for occupational exposure to endosulfan compared to unexposed controls (Aschengrau et al. 1998) however, the sample sizes were very small (three exposed seven not exposed), and co-exposure to other unreported chemicals also reportedly occurred. Both of these factors may have contributed to the high degree of uncertainty in the OR indicated by the wide confidence interval. 

FIGURE 3.2 Differences between IV rt-PA and placebo-treated patients on four assessment scales using data taken from part II of the 1995 NINDS trial. Values do not total 100% because of rounding. The odds ratio for a global favorable outcome with intravenous rt-PA was 1.7 (95% Cl 1.2-2.6, p = 0.008). The global favorable outcome was defined as NIHSS, 0-1 Barthel Index, 95-100 modified Rankin Scale, 0-1 and Glasgow Outcome Scale, 5. 

The combined experience with IV rt-PA treatment beyond 3 hours, therefore, suggests reduced effectiveness compared to treatment within 3 hours. A pooled analysis of the ATLANTIS, ECASS, and NINDS rt-PA studies confirmed that the odds of a favorable 3-month outcome, defined as minimal or no poststroke disability on the BI, mRS, and NIHSS, decreased with increasing stroke onset to start of treatment time (OTT) (p = 0.005). The odds ratios for favorable outcome with rt-PA treatment were 2.8 (95% Cl 1.8. 5) for OTT 0-90 minutes, 1.6 (95% Cl 1.1-2.2) for 91-180 minutes, 1.4 (95% Cl 1.1-1.9) for 181-270 minutes, and 1.2 (95% Cl 0.9-1.5) for 271-360 minutes. This finding, that earlier treatment is associated with more therapeutic efficacy, supports the adage that in the delivery of acute stroke therapy time is brain. " The rate of sICH was not associated with OTT. ... 

One meta-analysis examined the safety and efficacy of LMWH and heparinoids in 11 randomized trials of 3048 patients with acute ischemic stroke. It reported a reduction in the incidence of deep venous thrombosis (DVT) (odds ratio (OR) 0.27,... 

NEGRI L, LAVECCHiA c and FRANCESCHi s (2002) Relations between vegetable, fruit and micronutrient intake. Imphcations for odds ratios in a case-control stndy , Eur J Clin Nutr, 56, 166-70. 

Common Clinical Trial Graphs 200 Scatter Plot 200 Line Plot 201 Bar Chart 202 Box Plot 203 Odds Ratio Plot 203... 

As a part of logistic regression analysis, odds ratio plots are an excellent way to see how much more likely a condition is to exist based on the presence of another condition. Just by glancing at an odds ratio plot, you can see whether an independent variable is significant to the dependent variable. For instance, if the odds ratio confidence interval does not cross the value of 1, then the independent variable odds ratio is significant. Examine the following graph. 

In this example, we see that Active Therapy vs. Placebo, or drug therapy, has a significant odds ratio because the 95% confidence interval line does not cross 1. It appears that patients on active therapy are almost four times as likely to experience clinical success as those who are not on active therapy, while controlling for the variables White vs. Black, Male vs. Female, and Baseline Pain (continuous). ... 

The following is an example of an odds ratio plot. It shows the odds ratios for clinical therapy, race, gender, and baseline pain score with regard to the overall clinical success of a patient. 

Here is the SAS program that creates the preceding graph. It is a bit complex, because SAS/GRAPH does not provide horizontal box plots and this is typically what is desired for odds ratio plots. So, this sample program relies extensively on the Annotate facility to produce the plot. Notes follow the program. 

Program 6.7 Creating an Odds Ratio Plot Using PROC GPLOT... 

GET ADJUSTED odds ratios them IN DATA SET WALD. ods output CloddsWald = odds proc logistic data = pain descending ... 

DEFINE GRAPHICS OPTIONS SET DEVICE DESTINATION TO MS OFFICE CGM FILE, REPLACE ANY EXISTING CGM FILE, RESET ANY SYMBOL DEFINITIONS, AND DEFINE DEFAULT FONT TYPE. filename fileref C odds ratio.cgm goptions... 

CREATE THE ODDS RATIO PLOT. THIS IS DONE PRIMARILY THROUGH THE INFORMATION IN THE ANNOTATION DATA SET. PUT A HORIZONTAL REFERENCE LINE AT 1 WHICH IS THE LINE OF SIGNIFICANCE. proc gplot... 

Here we use PROC LOGISTIC to obtain our adjusted odds ratios and 95%... 

Note that hazard ratios can be plotted in the same way that odds ratios are plotted. 

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