Interpreting Statistics in the Urological Literature

Purpose: Knowledge of statistical terminology and the ability to critically interpret research findings are critical skills in the practice of evidence based medicine. Materials and Methods: We provide a series of nontechnical explanations of basic statistical concepts commonly encountered in the urological literature. In addition, we provide examples of common statistical pitfalls to increase awareness of limitations to consider when applying research findings to practice. Results: Statistical goals encountered in the urological literature can be broadly categorized as summarizing outcome variables, comparing 2 or more groups, measuring association among variables or predicting 1 variable from another. Errors frequently include the use of an inappropriate test for the data type of interest or using statistical testing in a manner that increases the likelihood of false-positive results. Such errors pose a threat to the validity of research findings and they may undermine study conclusions. Conclusions: Editors and reviewers alike should strive for high standards of statistical analysis and reporting, and promote the publication of high quality evidence in the urological literature. The understanding of basic statistical concepts and the principles of the hypothesis testing framework is essential to the critical appraisal process and, therefore, important to all urologists. Statistical literacy should be fostered through educational materials and courses in the urological community. Key Words: urology, statistics, evidence-based medicine K nowledge of statistical terminology and methods has a pivotal role in the conduct of clinical research and it is an essential tool for the urologist critically appraising the literature. 5 Curricular trends in undergraduate and graduate medical education now emphasize a basic knowledge of clinical research and statistical methods as part of a broader preparation for evidence based patient care. 6 -8 Despite these efforts recent evidence suggests that statistical literacy and a knowledge of clinical research methods among urologists may be suboptimal, as among other physicians. Studies in the urological literature and other subspecialties frequently contain statistical errors or they are underpowered. 9 -12 These errors threaten to undermine the validity of published studies and flawed investigations may influence medical practice in undesirable ways. RESULTS Outcome Measures Three types of outcome measures or variables are common in biomedical research, including continuous, categorical and time to event. 15 Continuous variables have values, such that the distance between the values 3 and 5, for example, is the same as the distance between 20 and 22 or the distance between 66 and 68. Examples of continuous measures are age in years, tumor size in cm and length of hospital stay in days. Categorical variables, of which dichotomous and ordinal are special cases, are measures that have 2 or more categories with no intrinsic numerical value, eg renal cell carcinoma histology (clear cell, papillary and other). Dichotomous (binary) variables have only 2 categories, eg side right/left or stone recurrence yes/no. Many specialized statistical procedures, such as logistic regression, are used for the analysis of dichotomous data. Ordinal variables are categorical variables in which the categories can be ordered. Examples in the urology literature are Gleason score and the visual analog pain scale. Time-to-event data are frequently found in oncological studies of mortality or disease recurrence. Examples are time to death or biochemical failure as well as time to stone passage and time to urethral stricture recurrence. 16,17 Summarizing Continuous Data The first question that should arise in the analysis of a continuous outcome variable is whether the data have a normal (also called Gaussian) distribution. Since normal distributions have a bell-shaped symmetry, an approximate assessment of normality can be made by making a histo- In contrast, SEM measures variability in the distribution of sample means from the population mean. Summarizing Nonnormal Continuous Data and Ordinal Data For nonnormal continuous data or ordinal data the median and IQR are often the preferred descriptive statistics. In these cases the median is preferred over the mean because the mean may be affected by outliers or a skewed distribution. For example, let us consider a simple case of 5 men with prostate cancer who have PSA 3.5, 3.5, 4.0, 4.5 and 4.5 ng/ml, respectively. In this case the mean and median are identical (4.0 ng/ml). However, if instead we have a group of men with PSA 3.5, 3.5, 4.0, 4.5 and 15.0 ng/ml, respectively, the mean becomes 6.1, while the median remains unchanged (4.0 ng/ml). In this case when an outlier is present, the median is less affected than the mean. IQR is the range of values from the 25th to the 75th percentile of the group of subjects and it gives the reader a sense of the variability in the data. Although SD characterizes the variance of distribution even for nonnormal distributions, it cannot be interpreted in the same way. SD values are easily interpretable only if the distribution is normal.