Describing Variation in Data

9 Describing Variation in Data

Variation is evident in almost every characteristic of patients, including their blood pressure and other physiologic measurements, diseases, environments, diets, and other aspects of their lifestyle. A measure of a single characteristic that can vary is called a variable. Statistics enables investigators to do the following:

I Sources of Variation in Medicine

Although variation in clinical medicine may be caused by biologic differences or the presence or absence of disease, it also may result from differences in the techniques and conditions of measurement, errors in measurement, and random variation. Some variation distorts data systematically in one direction, such as measuring and weighing patients while wearing shoes. This form of distortion is called systematic error and can introduce bias. Bias in turn may obscure or distort the truth being sought in a given study. Other variation is random, such as slight, inevitable inaccuracies in obtaining any measure (e.g., blood pressure). Because random error makes some readings too high and others too low, it is not systematic and does not introduce bias. However, by increasing variation in the data, random error increases the noise amidst which the signal of association, or cause and effect, must be discerned. The “louder” the noise, the more difficult it is to detect a signal and the more likely to miss an actual signal. All these issues are revisited here and in subsequent chapters. The sources of variation are illustrated in this chapter using the measurement of blood pressure in particular.

Biologic differences include factors such as differences in genes, nutrition, environmental exposures, age, gender, and race. Blood pressure tends to be higher among individuals with high salt intake, in older persons, and in persons of African descent. Tall parents usually have tall children. Extremely short people may have specific genetic conditions (e.g., achondroplasia) or a deficiency of growth hormone. Although poor nutrition slows growth, and starvation may stop growth altogether, good nutrition allows the full genetic growth potential to be achieved. Polluted water may cause intestinal infections in children, which can retard growth, partly because such infections exacerbate malnutrition.

Variation is seen not only in the presence or absence of disease, but also in the stages or extent of disease. Cancer of the cervix may be in situ, localized, invasive, or metastatic. In some patients, multiple diseases may be present (comorbidity). For example, insulin-dependent diabetes mellitus may be accompanied by coronary artery disease or renal disease.

Different conditions of measurement often account for the variations observed in medical data and include factors such as time of day, ambient temperature or noise, and the presence of fatigue or anxiety in the patient. Blood pressure is higher with anxiety or following exercise and lower after sleep. These differences in blood pressure are not errors of measurement, but of standardizing the conditions under which the data are obtained. Standardizing such conditions is important to avoid variation attributable to them and the introduction of bias.

Different techniques of measurement can produce different results. A blood pressure (BP) measurement derived from the use of an intra-arterial catheter may differ from a measurement derived from the use of an arm cuff. This may result from differences in the measurement site (e.g., central or distal arterial site), thickness of the arm (which influences reading from BP cuff), rigidity of the artery (reflecting degree of atherosclerosis), and interobserver differences in the interpretation of BP sounds.

Some variation is caused by measurement error. Two different BP cuffs of the same size may give different measurements in the same patient because of defective performance by one of the cuffs. Different laboratory instruments or methods may produce different readings from the same sample. Different x-ray machines may produce films of varying quality. When two clinicians examine the same patient or the same specimen (e.g., x-ray film), they may report different results1 (see Chapter 7). One radiologist may read a mammogram as abnormal and recommend further tests, such as a biopsy, whereas another radiologist may read the same mammogram as normal and not recommend further workup.2 One clinician may detect a problem such as a retinal hemorrhage or a heart murmur, and another may fail to detect it. Two clinicians may detect a heart murmur in the same patient but disagree on its characteristics. If two clinicians are asked to characterize a dark skin lesion, one may call it a “nevus,” whereas the other may say it is “suspicious for malignant melanoma.” A pathologic specimen would be used to resolve the difference, but that, too, is subject to interpretation, and two pathologists might differ.

Variation seems to be a ubiquitous phenomenon in clinical medicine and research. Statistics can help investigators to interpret data despite biologic variation, but statistics cannot correct for errors in the observation or recording of data. Stated differently, statistics can compensate for random error in a variety of ways, but statistics cannot fix, “after the fact” (post hoc), bias introduced by systematic error.

II Statistics and Variables

Statistical methods help clinicians and investigators understand and explain the variation in medical data. The first step in understanding variation is to describe it. This chapter focuses on how to describe variation in medical observations. Statistics can be viewed as a set of tools for working with data, just as brushes are tools used by an artist for painting. One reason for the choice of a specific tool over another is the type of material with which the tool would be used. One type of brush is needed for oil paints, another for tempera paints, and another type for watercolors. The artist must know the materials to be used to choose the correct tools. Similarly, a person who works with data must understand the different types of variables that exist in medicine.

A Quantitative and Qualitative Data

The first question to answer before analyzing data is whether the data describe a quantitative or a qualitative characteristic. A quantitative characteristic, such as a systolic blood pressure or serum sodium level, is characterized using a rigid, continuous measurement scale. A qualitative characteristic, such as coloration of the skin, is described by its features, generally in words rather than numbers. Normal skin can vary in color from pinkish white through tan to dark brown or black. Medical problems can cause changes in skin color, with white denoting pallor, as in anemia; red suggesting inflammation, as in a rash or a sunburn; blue denoting cyanosis, as in cardiac or lung failure; bluish purple occurring when blood has been released subcutaneously, as in a bruise; and yellow suggesting the presence of jaundice, as in common bile duct obstruction or liver disease.

Examples of disease manifestations that have quantitative and qualitative characteristics are heart murmurs and bowel sounds. Not only does the loudness of a heart murmur vary from patient to patient (and can be described on a 5-point scale), but the sound also may vary from blowing to harsh or rasping in quality. The timing of the murmur in the cardiac cycle also is important.

Information on any characteristic that can vary is called a variable. The qualitative information on colors just described could form a qualitative variable called skin color. The quantitative information on blood pressure could be contained in variables called systolic and diastolic blood pressure.

B Types of Variables

Variables can be classified as nominal variables, dichotomous (binary) variables, ordinal (ranked) variables, continuous (dimensional) variables, ratio variables, and risks and proportions (Table 9-1).

Table 9-1 Examples of the Different Types of Data

Information Content Variable Type Examples
Higher Ratio Temperature (Kelvin); blood pressure*
  Continuous (dimensional) Temperature (Fahrenheit)*
  Ordinal (ranked) Edema = 3+ out of 5
Perceived quality of care = good/fair/poor
  Binary (dichotomous) Gender; heart murmur = present/absent
  Nominal Blood type; color = cyanotic or jaundiced; taste = bitter or sweet

Note: Variables with higher information content may be collapsed into variables with less information content. For example, hypertension could be described as “165/95 mm Hg” (continuous data), “absent/mild/moderate/severe” (ordinal data), or “present/absent” (binary data). One cannot move in the other direction, however. Also, knowing the type of variables being analyzed is crucial for deciding which statistical test to use (see Table 11-1).

*For most types of data analysis, the distinction between continuous data and ratio data is unimportant. Risks and proportions sometimes are analyzed using the statistical methods for continuous variables, and sometimes observed counts are analyzed in tables, using nonparametric methods (see Chapter 11).

2 Dichotomous (Binary) Variables

If all skin colors were included in one nominal variable, there is a problem: the variable does not distinguish between normal and abnormal skin color, which is usually the most important aspect of skin color for clinical and research purposes. As discussed, abnormal skin color (e.g., pallor, jaundice, cyanosis) may be a sign of numerous health problems (e.g., anemia, liver disease, cardiac failure). Researchers might choose to create a variable with only two levels: normal skin color (coded as a 1) and abnormal skin color (coded as a 2). This new variable, which has only two levels, is said to be dichotomous (Greek, “cut into two”).

Many dichotomous variables, such as well/sick, living/dead, and normal/abnormal, have an implied direction that is favorable. Knowing that direction would be important for interpreting the data, but not for the statistical analysis. Other dichotomous variables, such as female/male and treatment/placebo, have no a priori qualitative direction.

Dichotomous variables, although common and important, often are inadequate by themselves to describe something fully. When analyzing cancer therapy, it is important to know not only whether the patient survives or dies (a dichotomous variable), but also how long the patient survives (time forms a continuous variable). A survival analysis or life table analysis, as described in Chapter 11, may be done. It is important to know the quality of patients’ lives while they are receiving the therapy; this might be measured with an ordinal variable, discussed next. Similarly, for a study of heart murmurs, various types of data may be needed, such as dichotomous data concerning a murmur’s timing (e.g., systolic or diastolic), nominal data on its location (e.g., aortic valve area) and character (e.g., rough), and ordinal data on its loudness (e.g., grade III). Dichotomous variables and nominal variables sometimes are called discrete variables because the different categories are completely separate from each other.

3 Ordinal (Ranked) Variables

Many types of medical data can be characterized in terms of three or more qualitative values that have a clearly implied direction from better to worse. An example might be “satisfaction with care” that could take on the values of “very satisfied,” “fairly satisfied,” or “not satisfied.” These data are not measured on a measurement scale. They form an ordinal (i.e., ordered or ranked) variable.

There are many clinical examples of ordinal variables. The amount of swelling in a patient’s legs is estimated by the clinician and is usually reported as “none” or 1+, 2+, 3+, or 4+ pitting edema (puffiness). A patient may have a systolic murmur ranging from 1+ to 6+. Respiratory distress is reported as being absent, mild, moderate, or severe. Although pain also may be reported as being absent, mild, moderate, or severe, in most cases, patients are asked to describe their pain on a scale from 0 to 10, with 0 being no pain and 10 the worst imaginable pain. The utility of such scales to quantify subjective assessments such as pain intensity is controversial and is the subject of ongoing research.

Ordinal variables are not measured on an exact measurement scale, but more information is contained in them than in nominal variables. It is possible to see the relationship between two ordinal categories and know whether one category is more desirable than another. Because they contain more information than nominal variables, ordinal variables enable more informative conclusions to be drawn. As described in Chapter 11, ordinal variables often require special techniques of analysis.

D Combining Data

A continuous variable may be converted to an ordinal variable by grouping units with similar values together. For example, the individual birth weights of infants (a continuous variable) can be converted to ranges of birth weights (an ordinal variable), as shown in Figure 9-1. When the data are presented as categories or ranges (e.g., <500, 500-999, 1000-1499 g), information is lost because the individual weights of infants are no longer apparent. An infant weighing 501 g is in the same category as an infant weighing 999 g, but the infant weighing 999 g is in a different category from an infant weighing 1000 g, just 1 g more. The advantage is that now percentages can be created, and the relationship of birth weight to mortality is easier to show.

Three or more groups must be formed when converting a continuous variable to an ordinal variable. In the example of birth weight, the result of forming several groups is that it creates an ordinal variable that progresses from the heaviest to the lightest birth weight (or vice versa). If a continuous variable such as birth weight is divided into only two groups, however, a dichotomous variable is created. Infant birth weight often is divided into two groups, creating a dichotomous variable of infants weighing less than 2500 g (low birth weight) and infants weighing 2500 g or more (normal birth weight). The fewer the number of groups formed from a continuous variable, however, the greater is the amount of information that is lost.

III Frequency Distributions

A Frequency Distributions of Continuous Variables

Observations on one variable may be shown visually by putting the variable’s values on one axis (usually the horizontal axis or x-axis) and putting the frequency with which that value appears on the other axis (usually the vertical axis or y-axis). This is known as a frequency distribution. Table 9-3 and Figure 9-2 show the distribution of the levels of total cholesterol among 71 professional persons. The figure is shown in addition to the table because the data are easier to interpret from the figure.

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Aug 27, 2016 | Posted by in PUBLIC HEALTH AND EPIDEMIOLOGY | Comments Off on Describing Variation in Data

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