Statistics in Medicine
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Statistics in Medicine

Robert H. Riffenburgh, Daniel L. Gillen

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eBook - ePub

Statistics in Medicine

Robert H. Riffenburgh, Daniel L. Gillen

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About This Book

Statistics in Medicine, Fourth Edition, helps medical and biomedical investigators design and answer questions about analyzing and interpreting data and predicting the sample size required to achieve useful results. It makes medical statistics easy for the non-biostatistician by outlining common methods used in 90% of medical research. The text covers how to plan studies from conception to publication, what to do with data, and follows with step-by-step instructions for biostatistical methods from the simplest levels, to more sophisticated methods now used in medical articles. Examples from almost every medical specialty, and from dentistry, nursing, pharmacy and health care management are provided.

This book does not require background knowledge of statistics or mathematics beyond high school algebra and provides abundant clinical examples and exercises to reinforce concepts. It is a valuable source for biomedical researchers, healthcare providers and anyone who conducts research or quality improvement projects.

  • Expands and revises important topics, such as basic concepts behind descriptive statistics and testing, descriptive statistics in three dimensions, the relationship between statistical testing and confidence intervals, and more
  • Presents an easy-to-follow format with medical examples, step-by-step methods and check-yourself exercises
  • Explains statistics for users with little statistical and mathematical background
  • Encompasses all research development stages, from conceiving a study, planning it in detail, carrying out the methods, putting obtained data in analyzable form, analyzing and interpreting the results, and publishing the study

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Planning studies: from design to publication


This chapter provides procedures and tips to plan a medical study. It starts with underlying knowledge about science, clinical decisions, and statistics and then goes to the basics of study that your sample size will satisfy your objective design and statistical sampling, and planning for statistical analyses. It gives advice on reading and then on writing medical articles. It ends with comments on statistical ethics.


Planning a study; designing a study; sampling; reading medical articles; writing medical articles; statistical ethics
(A few statistical terms commonly appearing in medical articles appear in this chapter without having been previously defined. In case, a reader encounters an unfamiliar one, a glossary at the chapter’s end provides interim definitions pending formal definitions later in this book.)

1.1 Organizing a Study

A study must be organized sooner or later. Planning in advance from an overview down to details increases efficiency, reduces false starts, reduces errors, and shortens the time spent. By definition an impactful scientific study must be credible to the scientific community. This implies that the study must meet minimal scientific standards, including valid methods, valid measurements of study outcomes, valid quantification of empirical results, and appropriate interpretations of study results. The most common pitfalls of most studies stem from a lack of a priori design and planning. If that is not enough motivation, the lazy and least stressful way to conduct a study, in the sense of least work overall, is thorough planning upfront.

1.2 Stages of Scientific Investigation


We gather data because we want to know something. These data are useful only if they provide information about what we want to know. A scientist usually seeks to develop knowledge in three stages. The first stage is to describe a class of scientific events and formulate hypotheses regarding the nature of the events. The second stage is to explain these events. The third stage is to predict the occurrence of these events. The ability to predict an event implies some level of understanding of the rule of nature governing the event. The ability to predict outcomes of actions allows the scientist to make better decisions about such actions. At best, a general scientific rule may be inferred from repeated events of this type. The latter two stages of a scientific investigation will generally involve building a statistical model. A statistical model is an abstract concept but in the most general of terms it is a mathematical model that is built on a (generally) simplifying set of assumptions that attempts to explain the mechanistic or data-generating process that gave rise to the data one has observed. In this way a statistical model allows one to infer from a sample to the larger population by relying upon the assumptions made to describe the data-generating process. While the topic may seem abstract, the reader has undoubtedly encountered and possibly utilized multiple statistical models in practice. As an example, we might look at body mass index, or BMI. BMI is an indicator of body weight adjusted for body size. The model is BMI = weight/height2, where weight is measured in kilograms and height in meters. (If pounds and inches are used, the equation becomes BMI = 703 × weight/height2).
A 6-ft person (1.83 m) weighing 177 lb (80 kg) would have 80/1.832 = 23.9 BMI. To build such a model, we would start with weights and heights recorded for a representative sample of normal people. (We will ignore underweight for this example.) For a given height, there is an ideal weight and the greater the excess weight, the lower the health. But ideal weight varies with body size. If we plot weights for various heights, we find a curve that increases in slope as height increases, something akin to the way y2 looks when plotted for x, so we try height2. For a fixed weight the body mass measure goes down as height goes up, so the height term should be a divider of weight, not a multiplier. Thus we have the BMI formula. Of course, many influences are ignored to achieve simplicity. A better model would adjust for muscle mass, bone density, and others, but such measures are hard to come by. Height and weight are normally in every person’s medical history.
The model gives an estimate of, or approximation to, the body weight’s influence on the person’s health. More generally, a model approximates a state or condition based on measurements of influencing variables, whence its name, a model of the state, not a direct measure. The greater the predictive accuracy and reliability of a model, the more complicated the model needs to be. Usually, models are trade-offs between accessibility of measures and simplicity of interpretation versus the requirement for accuracy.
Sometimes it is necessary to formulate more complicated models in order to ensure better predictive accuracy. For example, The American College of Cardiology utilizes a model to estimate an individual’s 10-year risk of atherosclerotic cardiovascular disease (ASCVD). This model utilizes 13 variables to obtain an estimate of the probability that an individual will experience ASCVD within the next 10 years. These variables include factors such as age, sex, weight, smoking status, systolic and diastolic blood pressure, cholesterol levels, and medication use. The model then weights each of these factors in order to compute an estimate of ASCVD risk. Due to the complexity of the model, it is not easy to write down and communicate, as is the case with BMI. Instead, it is easier to produce an “online calculator” that takes in each of the influencing variables and, behind the scenes, feeds these values into the model to report a final estimate of the probability of ASCVD. As an example, the ASCVD online calculator from The American College of Cardiology can be found at
Following is a brief explanation of the three stages of gathering knowledge.

The causative process is of interest, not the data

A process, or set of forces, generates data related to an event. It is this process, not the data per se, that interests us.
Description: The stage in which we seek to describe the data-generating process in cases for which we have data from that process. Description would answer questions such as: What is the range of prostate volumes for a sample of urology patients? What is the difference in average volume between patients with negative biopsy results and those with positive results?
Explanation: The stage in which we seek to infer characteristics of the (overall) data-generating process when we have only part (usually a small part) of the possible data. Inference would answer questions such as: Based on a sample of patients with prostate problems, are the average volumes of patients with positive biopsy results less than those of patients with negative biopsy results, for all men with prostate problems? Such inferences usually take the form of tests of hypotheses.
Prediction: The stage in which we seek to make predictions about a characteristic of the data-generating process on the basis of newly taken related observations. Such a prediction would answer questions such as: On the basis of a patient’s negative digital rectal examination, prostate-specific antigen of 9, and prostate volume of 30 mL, what is the probability that he has prostate cancer? Such predictions allow us to make decisions on how to treat our patients to change the chances of an event. For example, should I perform a biopsy on my patient? Predictions usually take the form of a mathematical model of the relationship between the predicted (dependent) variable and the predictor (independent) variables.

1.3 Science Underlying Clinical Decision-Making

The scientific method

Science is a collection of fact and theory resting on information obtained by using a particular method that is therefore called the scientific method. This method is a way of obtaining information constrained by a set of criteria. The method is required to be objective; the characteristics should be made explicit and mean the same to every user of the information. The method should be unbiased, free of personal or corporate agendas; the purpose is to investigate the truth and correctness of states and relationships, not to “prove” them. The true scientific approach allows no preference for outcome. The method should involve the control of variables; ideally, it should eliminate as far as practicable all sources of influence but one, so that the existence of and extent of influence of that one source is undeniable. The method should be repeatable; other investigators should be able to repeat the experiment and come to the same conclusion. The method should allow the accumulation of results; only by accumulation does the information evolve from postulate to theory to fact. The scientific method is the goal of good study design.

Jargon in science

Jargon may be defined as technical terminology or as pretentious language. The public generally thinks of it as the latter. To the public, carcinoma is jargon for cancer, but to the professional, technical connotation is required for scientific accuracy. We need to differentiate between jargon for pomposity and jargon for accuracy, using it only for the latter and not unnecessarily. The same process occurs in statistics. Some statistical terms are used loosely and often erroneously by the public, who miss the technical implications. Examples are randomness, independence, probability, and significance. Users of statistics should be aware of the technical accuracy of statistical terms and use them correctly.


The accumulating information resulting from medical studies is evidence. Some types of studies yield more credible evidence than others. Anecdotal evidence, often dismissed by u...

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