Basic Statistical Techniques for Medical and Other Professionals

A Course in Statistics to Assist in Interpreting Numerical Data

David Smith

• Publisher: Productivity Press
• Year: 2021
• ISBN:
  9781000469585
• Edition: 1
• Topic: Business
• Subtopic: Pharmaceutical, Biotechnology & Healthcare Industry
• Index: Business

We are bombarded with statistical data each and every day, and healthcare professionals are no exception. All sectors of healthcare rely on data provided by insurance companies, consultants, research firms, and government to help them make a host of decisions regarding the delivery of medical services. But while these health professionals rely on data, do they really make the best use of the information? Not if they fail to understand whether the assumptions behind the formulas generating the numbers make sense. Not if they don't understand that the world of healthcare is flooded with inaccurate, misleading, and even dangerous statistics. The purpose of this book is to provide members of medical and other professions, including scientists and engineers, with a basic understanding of statistics and probability together with an explanation and worked examples of the techniques. It does not seek to confuse the reader with in-depth mathematics but provides basic methods for interpreting data and making inferences. The worked examples are medically based, but the principles apply to the analysis of any numerical data.

Chapter 1

Why One Needs Statistical Techniques

DOI: 10.4324/9781003220138-1

We are frequently faced with numerical information (known as data) which, in its raw form, gives no clear picture of the trends that it might contain. The following simple example illustrates the point, as well as introducing two basic concepts.

The blood sugar levels in mmol/L (millimoles per litre), recorded by a diabetic patient over a period of 10 days, were

7.5, 7.2, 8, 6, 5.6, 5, 7, 5.5, 5, 5.5

The average can easily be calculated as 6.2 although it may not be obvious merely by glancing at the row of numbers. Furthermore, the graph (Figure 1.1) shows that the trend is, to some extent, downwards.

Figure 1.1 Simple graph of a variable against time

Thus, albeit at a very basic level, two important ideas have emerged:

An average (we use the word MEAN in statistical work)

and

Providing a visual plot of the trend (a linear GRAPH)

Both can be extremely helpful.

Notice the use of the word “linear” in the brackets. Linear means that the distances separating the days along the x axis and the distances separating the blood sugar levels, ascending the y axis, are equal. This will not always be the case in more advanced uses of the “graph” technique (Chapter 5). We will return to that subject later.

Taking the concept of a MEAN further we might add, providing the spread of values on either side is similar, that we can make statements such as “I am 50% sure (in statistics we use the word “confident”) that any value, taken at random, is greater than 6.2.” That idea will be developed in Chapter 4 to make more sophisticated inferences, such as being 90% confident of exceeding some stated value.

In order to do that, we need to think about the variability of the data. In other words, the spread (“distribution”) of values between the two extreme values which were the two sugar levels of 5 and 8 mmol/L in the earlier example. Chapter 4 will develop this idea further and later Chapters will provide techniques for making useful comparisons between different sets of data.

Variables and Attributes

At this point, it will be useful to distinguish between Variables and Attributes.

Variables are a measure of an item of interest (e.g., size, weight, time, blood sugar, systolic blood pressure) and can take any value in a given range (e.g., feet, ounces, minutes, mmol/L [blood sugar], mmHg [blood pressure].

Attributes, however, are binary and describe some state that either applies or does not apply. In a deck of cards any one card can be a heart (or not). A person can be either alive or dead. One cannot be a bit dead, only alive or dead. Thus, attributes are measured in numbers of items having that attribute (or state) and have no units.

Spread of a Variable

The blood sugar readings illustrated in Figure 1.1 are distributed (spread) around the mean value of 6.2 mmol/L. The “tightness” or “looseness” of that spread is important since it describes the consistency (or otherwise) of the measurement in question. In the blood sugar example, a consistent reading, shown by a tighter scatter, would be desirable. Statistics will provide a way of describing how consistent the readings are.

Correlation

Another problem, which statistics will help to unravel, is the need to establish if some variable is related to another. One example would be diastolic blood pressure and systolic blood pressure. One does not precisely dictate the value of the other, but it might be credible to assume that a change in one might be followed by a similar change in the other. Again, statistics will provide a more precise way of quantifying the strength of the interaction. This particular suggestion will be dealt with in Chapter 9 where we will test the strength of association between the two.

Taking Samples

Much of statistical analysis consists of drawing conclusions from a set of data or of comparing two or more sets of data. The data in question is nearly always a sample drawn from a wider (larger) population. It is therefore important to think about whether the data that one has gathered is, indeed, a representative sample of the population of interest.

Random sampling is the ideal way of collecting data from a population. To achieve this, each item in the population needs to have an equal chance of being chosen for the sample. If, for example, the total annual population of stroke sufferers is 115,000 (UK) and in conducting a comparison between two alternative treatment regimes, two sample groups of 50 patients were selected, there is always the possibility that the sample did not represent the population as a whole.

It is important to take an unbiased random sample from which to draw conclusions. Thus, when we selected the two samples of 50 patients from the total population of 115,000, there was the possibility that the researcher might have selected 50% men and 50% women for the sample even though the stroke population might contain say 67% men and 33% women. The sample would not then accurately reflect some gender-related factor.

Gender is, of course, not the only relevant factor since age, ethnicity, lifestyle, diet and occupation might all be argued to be relevant. The problem with random sampling is that it requires a complete knowledge of the population before selecting the sample.

Very Large and Very Small Numbers

In many fields, data involves numbers in the hundreds of thousands and greater and deals with factors such as one in a hundred thousand and so on. “One in a hundred thousand” is a cumbersome way of expressing data and for those not familiar with the convention of expressing numbers as positive and negative powers of ten, Chapter 9 provides a thorough grounding.

Chapter 2

Probability and Its Rules

DOI: 10.4324/9781003220138-2

Empirical versus À Priori

An estimate of the probability of an event is given by the ratio of the number of occurrences (i.e., successes) of that event to the number of items of data, and this can be arrived at in two ways. Revisiting what was mentioned in the introduction:

If it is established that, in the UK (population 67 Million), there are 4.7 Million diabetics then, from that information, the probability that a person, chosen at random, is diabetic is 7% (i.e., 4.7/67). This is a probability statement based on prior knowledge of the population and NOT by experimentally observing a sample. We call this an à priori statement of probability.

If, on the other hand, we estimate the probability by observing that, in a large medical practice covering 8,000 patients, there are 480 diabetics, then we might infer that the probability of being diabetic is 6% (i.e., 480/8,000). This is an empirical statement of probability being derived from sample data.

In both cases, the concept of probability is derived from a proportion of successes and is therefore a dimensionless quantity (that is to say it takes no units). A probability ...