Nearly half of all the scientific manuscripts that are published in leading medical journals have statistical errors or omissions, often serious enough to call the authors' conclusions into question. Although there have been many textbooks written on the subject of statistics, they are usually focused on formulas and derivations requiring a statistical background. Recently, the American College of Physicians published guidelines (1) on presenting statistical data in an effort to improve both clarity and credibility in medical research. The authors of these guidelines begin their book by describing some critical differences between clinical and statistical significance. We are reminded of several important distinctions:

One statistical technique commonly used in orthopaedic clinical research is logistic regression analysis. During the 1940's at the Mayo Clinic in Rochester, MN, Berkson found a logistic relationship between dosage of a drug and death of animals. In 1953, he introduced the logistic equation into bioassay. (2) Analysis of data from the Framingham Heart Study (3) in the 1960's brought into prominence the development of the most popular statistical method in modern epidemiology, the logistic regression model.

The logistic regression model is currently used in orthopaedic research when the outcome of interest is a binary ("yes/no") event. In fact, when analyzing the effect of a predictor variable (e.g., age, gender, anatomical location, stage of disease, extent of tear) on mortality or need for surgery or reoperation, the logistic equation is an appropriate tool. In practice, the outcome variable has the values 0 (no event) or 1 (event), and the explanatory or predictor variables are potential risk factors. Logit units are related to probability (P) by the logistic relation, z = ln[P/(1-P)], where ln denotes the natural logarithm and z is a function of the ratio of P, the probability of the event, and 1-P, the complementary probability that the event does not occur. Orthopaedic researchers often wish to analyze the relationship between a predictor variable and an outcome variable, each of which has two possibilities. Logistic regression can be performed to evaluate several predictor variables simultaneously to determine which variables are independently associated with the outcome.

The odds ratio is only a point estimate. The precision of this estimate can be described with a confidence interval (CI), which describes the statistical significance of the association between two variables within a specific range. The width of the CI reflects the amount of variability inherent in the OR. There is a tradeoff between precision and confidence. Wider confidence intervals provide great certainty but are less precise. Narrower intervals are more specific but less certain that the truth is within the confidence interval. The most common CI in medicine is 95%.

Several methods are commonly used to construct confi-dence intervals around the odds ratio. A simple method for constructing confidence intervals (5) , based on a Taylor series expansion, can be expressed as follows: CI = (ad/bc) exp(± z sqrt (1/a + 1/b + 1/c + 1/d)), where z is the value of the standard normal distribution with the specific level of confidence, and exp is the base of the natural logarithm. The 95% CI would be derived as follows:

95% CI = (ad/bc) exp(± 1.96 sqrt (1/a + 1/b + 1/c = 1/d))

= [(67 x 79) / (7 x 15)] exp (± 1.96 sqrt (1/67 + 1/7 + 1/15 + 1/79))

= (50.4) exp(± 0.95)

Lower limit = (50.4) exp(-0.95) = (50.4) (0.39) = 19.7

Upper limit = (50.4) exp(+0.95) = (50.4) (2.58) = 130.0

Therefore, among children presenting with an acutely irritable hip, those with a history of fever are on average 50 times more likely to have septic arthritis compared to those with no history of fever. Based on a 95% CI, the lower limit of the OR is approximately 20 and the upper limit is 130. These limits provide the ballpark for the OR. Since the 95% CI does not include 1.0, the results are significant at the 0.05 level (i.e., P <0.05).

Odds ratios and confidence intervals can be quickly and easily obtained by surgeons with a small hand calculator. These tools are useful in clinical and laboratory research, and can also be used to determine confidence intervals (if not provided) while reading the literature. Proper understanding and utilization of the fundamental statistical principles and calculations presented here will allow for more reliable analysis, interpretation, and communication of clinical information by all physicians.