Introduction to Statistics and Epidemiology

Statistics and Epidemiology in Medicine is important for clinicians to understand. There can often be a difference in clinical outcomes seen in patients in clinical trials, compared to real-world, community settings. Clinical trials usually exclude patients with multiple diagnoses or comorbidities, whereas in the real world, patients have multiple diagnoses and conditions all the time. This disconnect means it can be challenging for clinicians to interpret the efficacy of treatments from clinical trials, systematic reviews, and meta-analyses.^[1] Having a solid understanding of statistical principles can allow you to critically appraise the literature and understanding whether you should trust a study or not!

• Reliability = Precision/Replicability
• Validity = Accuracy
  • Is the degree to which a measurement is concordant with “the true value”?
  • Many different types validity, but it all relates how a test measures what it purports to actually measure
• Responsiveness = Sensitivity of measurement to a change in a patient's clinical condition
• Interpretability = Meaning of a given score (e.g. > 10 on the PHQ-9 suggests depression)

Fig. 1

In every research study, there is something called the null hypothesis. This means the default outcome of every study assumes there is no statistical significance between the two variables (e.g. - no relationship between smoking and risk of lung cancer) that you are looking at in your study. In most studies, a researcher or experimenter will try to disprove or discredit the null hypothesis (e.g. - the researcher will try to prove there is in fact a risk between smoking and lung cancer).

When one rejects or fails to reject the null hypothesis correctly, two types of errors can occur:

• Type I error (False Positive) is when the investigator rejects a null hypothesis that is actually true in the population
• Type II error (False Negative) is when the investigator fails to reject a null hypothesis that is actually false in the population

Fig. 1

Study Findings

If you were looking at a study looking at the association between smoking and lung cancer, you would apply the following table below to look at the probability of a Type I and Type II error.

Medical Tests

If you were looking at a study looking at how good a test was at detecting lung cancer, you would apply the following table below to look at the probability of a Type I and Type II error.

Sensitivity and Specificity are fixed properties of a test and their values never change:

• For sensitivity (the “true positive rate”), you are interested in knowing how many people with disease you are able to identify with your test. To determine sensitivity, you need to compare the number of patients who were identified as having the disease, compared to the number of patients who actually have the disease:
  • A highly sensitive test rarely misses people with the disease and rarely has false negatives
  • You want high sensitivity in a test when it is really bad to miss a disease (e.g. - brain cancer)
  • A highly Sensitive test when Negative rules OUT the disease (SNOut)
• For specificity (the “true negative rate”), this concept is slightly less intuitive, even though the equation is equally simple compared to sensitivity. Remember that with sensitivity, we focus on the patients who have disease. With specificity, we focus on the patients who do not have disease.
• Thus, a test that has high specificity will not identify healthy patients as having disease. With a highly specific test, we would expect that there are a lot of true negatives and only a small amount of false positives (or even better, none at all!).
• When we talk about specificity, we are interested in the proportion of people without disease who have a negative test.
  • A highly specific test rarely will rarely give false positives
  • You want a highly specific test when a false positive result might be harmful to the patient (e.g. - there is some debate that mammography in young women might not be highly specific for breast cancer, and place these patients at risk for further invasive procedures like biopsies and unnecessary psychological stress.)
  • A highly Specific test when Positive rules IN the disease (SPIn)

The terms prevalence and incidence are often used incorrectly in describing how common a disease or disorder is. Here are the correct definitions:^[2]

• Prevalence: looks at ALL existing cases of an illness or disease. Think about looking at a photo of 1,000 people (the population), and asking, how many people have black hair? The number of individuals with that feature is used to calculate prevalence.
  • Prevalence can also be calculated from a 2×2 table
  • Prevalence = (TP + FN) ÷ (TP + FN + FP + TN)
• There are 3 ways to express prevalence:
  • Point prevalence: The number of cases at a certain time (e.g. - a survey on December 2020 asking if you are actively smoking).
  • Period prevalence: The number of cases over a certain time frame, usually 12 months (e.g. - a survey asking if you have smoked between January 2020 to December 2020)
  • Lifetime prevalence: The number of cases over one's total lifetime. (e.g. - a survey asking if you have ever smoked in your life)
• Incidence: Incidence looks at the number new cases over a period of time. For example, in 1,000 people, if 50 were diagnosed with lung cancer over 2 years, the incidence is 50 cases per 1,000 persons, or 5.0% over a two year period, or 25 cases per 1,000 person-years (incidence rate) – because the incidence proportion (50 per 1,000) is divided by the number of years (2).

The prevalence of the disease in this specialist clinic is the number of real cases of disease, divided by the total number of individuals:

• (TP+FN) ÷ (TP+FP+FN+TN) = (50+5) ÷ (50+5+10+100) = 33% prevalence

The prevalence of the disease in the primary care setting is the number of real cases of disease, divided by the total number of individuals:

• (TP+FN) ÷ (TP+FP+FN+TN) = (50+5) ÷ (50+5+100+1000) = 3% prevalence

• Efficacy is the extent to which an intervention does more good than harm under ideal circumstances (i.e. - in a clinical trial under strict conditions).
• Effectiveness is the extent to which an intervention does more good than harm when provided under usual circumstances of healthcare practice (i.e. - in a real world setting). Effectiveness studies are also known as pragmatic trials in research studies, due to the pragmatic nature of the research.^[3][4]