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CHAPTER 7

Statistics: Making Sense of Uncertainty

Statistics

Is a set of concepts and methods used to analyze data in order to extract information

Is the science used to interpret the numbers that describe the health of the population

Makes possible the translation of data into information about causes and effects, health risks, and cures of diseases

The Uncertainty of Science

Most science is of a probable nature.

In many cases, there is not enough data to give us a degree of certainty, or the existing data is too ambiguous to allow a valid conclusion.

Science is ongoing; studies may contradict each other.

The science of statistics can quantify the degree of uncertainty.

Probability

The probable is what usually happens.

Probabilities are used to describe the variety and frequency of past outcomes under similar conditions as a way of predicting what should happen in the future.

A p-value:

When p ≤ 0.05, it usually means that a result is statistically significant.

When p = 0.05, there is still a 5% chance that the result is wrong.

Key concepts are:

Confidence interval

Law of Small Probabilities

Power of a Study

There is the probability of finding an effect if there is, in fact, an effect.

Large numbers confer power.

Studies with low power are likely to produce false-negative results.

Statistics of Screening Tests

Examples of screening:

Mammography for breast cancer

HIV tests

Newborn screening

Sensitivity versus specificity

False positives versus false negatives

Lead-time bias

Overdiagnosis bias

Rates

Rates relate raw numbers to the size of the population being considered.

Birth rates

Mortality rates

Other rates commonly used as indicators of community health are:

Infant mortality rate

Maternal mortality rate

Crude rates

Adjusted rates

Age adjusted

Group specific rates

Gender specific

Other Calculated Statistics

Life expectancy

Years of potential life lost (YPLL)

Risk Assessment and Risk Perception

Risk assessment:

Identifies events and exposures that may be harmful to humans

Estimates the probabilities of their occurrence

Estimates the extent of harm they may cause

For well-known risks, we can calculate from historical data.

For poorly understood risks, we must make many assumptions.

Risk perception:

Involves psychological factors

Is the result of the apparent irrationality of the public in response to risks that experts estimate to be small

Is classified on two scales: dread and knowability

Cost–Benefit Analysis

Weighs the estimated cost of implementing a policy against the estimated benefit, usually in monetary terms

Costs are easier to calculate than benefits.

What monetary value can we put on a life saved?

Analysis is often controversial.

Cost-effectiveness analysis compares the efficiency of different methods of attaining the same objective.

Discussion Question 1

Why is statistics so important for public health?

Discussion Question 2

Try organizing a group of students in a coin-tossing experiment.

How often does the same side come up five times in a row?

Ten times in a row?

Discussion Question 3

Think of a medical test that you or someone you know has undergone.

Was it more important for the test to be sensitive or for it to be specific? Why?

What would be the implications if the result was a false positive?

What if there had been a false-negative result?

Discussion Question 4

Consider the list of activities and technologies presented in Table 7-4.

Rank them in order of your willingness to accept the risk.

How does your ranking compare with those of the other groups shown in the table?

Discussion Question 5

Visit Rice Virtual Lab in Statistics by statistician David Lane, onlinestatbook.com/rvls.html.

Choose one of Lane’s case studies that is relevant to health and describe the experimental design.

What are the conclusions of the experiment?

Are the results significant?

Is a p-value given?