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Health. 2004;58(8):635-641. doi:10.1136/jech.2003.008466
research. Plast Reconstr Surg. 2023;151(6):1115-1122.
doi:10.1097/prs.0000000000010173
https://t.me/med1917
CHAPTER 16 Basic Statistics for the Practicing
Physician
Soumen Das De and Teemu Karjalainen
KEY POINTS
A good understanding of statistics is essential to assess clinical
studies, apply new concepts to practice, and perform high-quality
research.
Descriptive statistics are useful to summarize large quantities of
information in a meaningful way.
Inferential statistics enable us to estimate the magnitude of effects
of our decisions on the population level given the observation in the
study.
The choice of appropriate statistical tests depends on the type of
variables.
A statistician should be involved during the planning stages of a
study.
Case Vignette: A 62-year-old man presents to clinic with fixed contractures of
the right middle and ring fingers. Clinical assessment indicates thickened
palmar cords and joint flexion contractures that are consistent with Dupuytren
disease (DD). He has heard about an injection that breaks up the abnormal,
thickened tissue and requests more information. As this is your first Hand
Surgery rotation, your attending suggests you review the landmark trial that
evaluated injectable collagenase clostridium histolyticum for DD by Hurst et al.
1
INTRODUCTION
The abovementioned scenario is a typical everyday occurrence. Physicians
routinely need to review new information and decide how much a new test,
medication, or procedure might benefit their patient. A good understanding of
the principles of biostatistics helps us understand what the effects of our
decisions are. The chapter does not try to prepare the reader to plan and
conduct statistical analyses independently (in fact, we advise against such
practice) but merely to understand how basic statistics work and how to
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interpret research findings, as well as appreciate the uncertainty related to
study findings. We have tried as much as possible to avoid mathematical
jargon but, instead, focused on key concepts and examples to clarify the
underlying principles of various analyses that clinicians encounter.
TYPES OF DATA
One of the things physicians need to consider is if the findings of a study can
be applied to their practice—are their patients comparable with the patients in
the study cohort? Before embarking on a research study, it is essential to
review the type of variables you will be working with. Common and easily
measurable factors, such as demographics (eg, age, gender, race), disease
manifestations (eg, number of digits involved, joint motion), and predisposing
risk factors (eg, diabetes, epilepsy, alcohol intake) provide vital information
about the reference population. Table 16.1 indicates how such data may be
presented. The types of data can be broadly broken down into two categories:
quantitative and qualitative data (Table 16.2).
TABLE 16.1. DESCRIPTIVE DATA
Variable
Collagenase
Group
(N = 204)
Placebo
Group
(N = 104)
All Patients
(N = 308)
P
Value
Age (years) 62.3 ± 9.7 63.3 ± 9.1 62.7 ± 9.5 0.40
Male sex—
no. (%)
171 (83.8) 74 (71.2) 245 (79.5) 0.01
Total
contracture
index
Mean 149.1 ± 127.6 149.3 ± 111.4 149.1 ± 122.2 0.99
Median 105.0 119.0 115.0
Range 20-860 20-489 20-860
Family history
of DD—no.
(%)
85 (41.7) 53 (51.0) 138 (44.8) 0.15
Adapted from Hurst LC, Badalamente MA, Hentz VR, et al. Injectable collagenase Clostridium
histolyticum for Dupuytren’s contracture. N Engl J Med. 2009;361(10):968-979.
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doi:10.1056/NEJMoa0810866.
TABLE 16.2. TYPES OF DATA
Type of Data Examples
Quantitative
data
Continuous Weight, age
Discrete Number of
complications
Interval IQ value
Qualitative Categorical nominal Sex
Categorial ordinal Likert scale
Other Responses to open questions;
recordings
Quantitative data refers to observations that can be given a numerical value
and have both order and magnitude. These types of data include continuous
and discrete data.2 Continuous data are values on a numerical scale that can
take on any value within a range, without being restricted to whole numbers.
An example of continuous data is joint range of motion (ROM), which can have
intermediate values such as 0.5°. Discrete data are actual measurable
quantities on a numerical scale that can take on whole numbers, such as the
number of postoperative complications. Interval data refers to specific types of
numerical data that are measured along a scale and the distance between two
points on the scale is standardized and equal.
Qualitative data refers to nonnumerical data. The data value is just a label,
and it cannot be quantified or expressed as a number. This type of data can be
broken down into categorical nominal and categorical ordinal data, as well as
other nonnumeric data such as text-based data from patient notes or survey
responses. Nominal data fall into distinct groups where there is no underlying
order or magnitude, such as previous treatment received (none; surgery; hand
therapy; injection). Data with two mutually exclusive states (eg, yes/no) are
dichotomous. Ordinal data have an inherent order among the categories, such
as the stages of disease. However, the differences between categories are not
calibrated to scale. For instance, stage 3 disease is not thrice as severe as
stage 1.
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SUMMARY MEASURES
It is not feasible to describe each patient individually, especially in a large study
involving hundreds or thousands of subjects. Descriptive statistics present a
large amount of data in a more digestible form that immediately conveys
important information about the cohort of patients. Nominal and ordinal data
are described as proportions or percentages. Continuous data are summarized
using measures of central tendency and measures of dispersion.
Measures of Central Tendency
The mean, median, and mode each try to describe the center of a data set
using a single value. However, their definitions and interpretations differ.
Consider a cohort of five patients with DD of the following ages: 59, 62, 65, 65,
and 70 years. The mean is the sum of the ages divided by the number of data
points. The value is 64 years, rounded to the nearest whole number. But what
happens if the oldest patient is now 90 years old instead of 70? The mean
changes to 68 years, although four of the five patients are younger than the
mean. As seen, the mean is sensitive to such extreme values, or outliers. The
median is a more stable representation of the center when such outliers are
present. It is the middle value when all the observations are ranked in order. In
the aforementioned examples, the median is 65 years in both hypothetical
cohorts. The mode is the most commonly occurring value in a set of
observations, in this case 65 years. Ordinal data cannot be mathematically
aggregated and the “average stage of disease” for a cohort of patients is
meaningless. Instead, it is more useful to report the proportion or percentage
of patients in each group.
Measures of Dispersion
As seen in the above-mentioned situations, a single value does not fully
describe a data set because it does not depict the dispersion of data.
Dispersion can be described using standard deviation (SD), interquartile range
(IQR) or range. The SD quantifies the scatter of data around the mean value.
Simplistically, the SD indicates how far, on average, each patient data point
lies from the mean. A small SD implies a set of values that are close to the
mean. Continuous data such as age and joint ROM are usually presented as
mean ± SD (Table 16.1). IQR divides the data into quartiles and displays the
data in the middle half (between the 25th and 75th per centile). It is typically
used along with median values for skewed distributions. Range presents the
highest and lowest values.
DATA DISTRIBUTIONS
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A distribution refers to the pattern of values that a variable can take and how
frequently it takes each of those values. Consider a continuous variable such
as weight. There are theoretically limitless values that weight can take and
may be distributed following a normal (or Gaussian) distribution (Figure 16.1)
where most values are concentrated symmetrically around the mean value of
the population. Other data distributions include the binomial distribution for
dichotomous (eg, presence of complications—yes/no) outcomes and the
Poisson distribution for rare discrete events.
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FIGURE 16.1 Normal distribution of weight with mean of 70 kg and
standard deviation (SD) of 13 kg. The area under the curve
represents probability. With continuous outcomes, we can calculate
the probability of observing values greater or smaller than a
particular value. For example, the probability of an observation larger
than 90 kg is 0.06 (gray area).
What Is the Best Way to Display Data?
A picture paints a thousand words, and this cannot be truer than in statistics.
Graphs and tables are the best way to present large amounts of data in a
concise form that avoids excessive jargon. They also enable us to immediately
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see broad trends or potential problems, such as skewed data. However,
graphs and charts can also be manipulated to mislead the reader.3 Figure 16.2
shows some commonly used graphs that are crucial to describe data.
FIGURE 16.2. The same data for two hypothetical groups were
used for graphs (A-D). A bar graph (A) contains much less
information compared with a box plot (B) , scatter plot (C) , or
histogram (D). A two-way scatter (E) plot is a useful way to present
association of two continuous variables. A Kaplan-Meier survival
curve (F) presents time to an event, like death; implant failure; or
recurrence.
MEASURES OF EFFECT
An effect refers to a change caused by some factor. In medicine, we are
typically interested in factors such as genes, lifestyle and environmental
factors, and treatment interventions. These are called exposures. For example,
certain genes (exposure) can cause palmar fascia to thicken and contract
resulting in Dupuytren contracture. The severity of the contracture can be
measured and is referred to as an outcome. The treatment effect is the
difference between treatment and no treatment or some other treatment. For
example, in the randomized controlled trial (RCT) by Hurst et al, the treatment
effect (of collagenase) was the difference between the success rates in the
active treatment group and the placebo group.
4
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How Is the Magnitude of an Effect Expressed?
The effect size is a measure that quantifies the relationship between an
exposure and an outcome. The observed change after an intervention should
not be considered as the treatment effect (Figure 16.3). The change contains
both specific effects (from the treatment) as well as nonspecific effects, such
as natural course and regression to the mean. To measure the effect of an
intervention, we need to compare the outcome in the active group with a group
that did not receive the intervention or a group that received a different
intervention. The effect size can be measured by comparing mean values
(continuous outcomes), proportions (binary outcomes), or distributions (ordinal
outcomes). How the effect size is expressed depends on the type of variables
in question.
FIGURE 16.3. Mean symptoms in two hypothetical groups before
and after the intervention. Active (black) group improves more
compared with the control (placebo) group (red). The treatment
effect is the difference between active and control (green area). The
change after intervention comprises both treatment effect (green
area) and nonspecific effects (blue area).
Risk Difference, Relative Risk, and Odds Ratio
With binary outcomes (eg, proportion with good outcome), the effect can be
expressed as risk difference (RD), relative risk (RR), or odds ratio (OR). For
example, Hurst et al found that 103/203 (51%) participants who had
collagenase injection met the primary end point of <5° of residual extension lag
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while 7/103 (7%) of participants who received placebo injection met the
primary end point. This corresponds with RD of 44% (51%-7%), RR of 7.5
(0.51/0.07), and OR of 14 (1.03/0.073).
1
The benefit of expressing the effect as RD is that it conveys the absolute risk
level as well as the difference. RR is also easy to understand, but it does not
convey the absolute level of risk. However, RR is useful because it conveys
information across different levels of baseline risk while the RD is linked to a
specific risk. The downside of RR is that it can be misleading; trivial effects
may appear large when the baseline risk is low. For example, if an intervention
increases the risk of adverse events from 0.5% to 1%, the RD is 0.5% but the
RR is 2. Thus, the absolute risk level is important to consider along with the
RR.
OR is much harder to interpret. The odds are the probability of an event
occurring versus the probability of it not occurring, and the OR is a ratio of two
odds. For example, OR of 0.16 is not “84% risk reduction” or “16% risk of”
(Table 16.3). However, because of its mathematical properties, the OR is
useful when the analysis needs to be adjusted with other variables (see the
section on regression analysis).
TABLE 16.3. MEASURES OF TREATMENT EFFECT
Risk in
Treatment Group
Risk in Control
Group
Risk
Difference
Relative
Risk
Odds
Ratio
1/100 2/100 1% 0.5 0.49
10/100 20/100 10% 0.5 0.44
20/100 40/100 20% 0.5 0.38
40/100 80/100 40% 0.5 0.16
98/100 99/100 1% 0.99 0.49
Sometimes the exposure is not categorical such as treatment group but is
measured on a continuous scale. For example, consider a study that measures
the association between HbA1c level and the risk of postoperative infection.
Because the outcome is binary (yes/no), the effect can be expressed as RD,
RR, or, but the effect size conveys how much one unit increment in HbA1c
increases the risk of postoperative infection. If a study measures the effect of a
continuous variable on a continuous outcome, the effect can be expressed as
how much one unit changes the outcome. For example, “one additional year of
age decreases the range of motion (ROM) of the finger on average by 0.24°.”
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