CHAPTER 3: Comparing Disease Frequencies

Learning Objectives

• Organize disease frequency data into a two-by-two table.

• Describe and calculate absolute and relative measures of comparison, including:

  • Rate/risk difference

  • Population rate/risk difference

  • Attributable proportion among the exposed and the total population

  • Rate/risk ratio

• Verbally interpret each absolute and relative measure of comparison.

• Describe the purpose of standardization and calculate directly standardized rates.

Epidemiological Context

• Epidemiology is the study of the distribution and determinants of disease frequency in human populations and the application of this study to control health problems.

• Disease frequency: Involves counting cases of disease in a population over a specific time period to measure:

  • Prevalence: Total number of cases at a specific time.

  • Cumulative Incidence: New cases over a specified time period.

  • Incidence Rates: Rate of new cases occuring during a specified period.

True or False Statements

1. Only the population at risk contributes to the denominator of cumulative incidence. True

2. When calculating the incidence rate of disease, it is necessary to follow subjects for the same amount of time. True

3. All other things being equal, when a treatment is developed that prolongs the life of people with a disease, the prevalence of the disease will increase over time. True

4. In 2023, the incidence rate of breast cancer for Alabama will be higher than for Alaska due to predicted cases. True

Incidence Rate Calculation Example

• Case Study: 60 cases of myocardial infarction (heart attack) reported over 2 years in a city with a population of 100,000 people.

  • Incidence rate (per 100,000 person-years) can be calculated as:

  • Assumption: Each individual in this population has equal risk.

  • Formula: $\text{Incidence Rate} = \frac{\text{Number of cases}}{\text{Population} \times \text{Time period}} = \frac{60}{100,000 \times 2} = 30/ \text{100,000 person-years}$

Study Example: Tuberculin Reactors among Navy Recruits

• Data Context: 2,212 male recruits tested; 55 had positive reactions.

  • Overall prevalence calculation:
    

    $\text{Prevalence per 100 recruits} = \frac{55}{2,212} \times 100 = 2.48$

Age Group and Race/Ethnic Group Prevalence

• Prevalence table for three age groups:

  • Age 17-19: 24 reactors, 1,225 tested (\rightarrow) $\text{Prevalence} = \frac{24}{1,225} \times 100 = 1.96$

  • Age 20-24: 22 reactors, 855 tested (\rightarrow) $\text{Prevalence} = \frac{22}{855} \times 100 = 2.57$

  • Age 25+: 9 reactors, 134 tested (\rightarrow) $\text{Prevalence} = \frac{9}{134} \times 100 = 6.72$

• Race/Ethnic Group Analysis:

  • White: 12 reactors from 1,588 (\rightarrow) 0.76%

  • Black: 20 reactors from 386 (\rightarrow) 5.18%

  • Hispanic: 9 reactors from 167 (\rightarrow) 5.39%

  • Asian/Pacific Islanders: 14 reactors from 53 (\rightarrow) 26.42%

  • Other: 0 reactors from 20 (\rightarrow) 0%

• Highest prevalence: Recorded among Asian/Pacific Islander group.

Calculation of Prevalence: Histoplasmosis

• Two Surveys: 5,000 surveyed, 25 reported antibodies initially vs. 35 after 12 months (including original 25).

  • Prevalence at second survey:
    

    \text{Prevalence}_\text{after 1 year}} = \frac{35}{5000} \times 100 = 0.7 \text{%}

  • 1-year Incidence: $\text{Incidence} = \text{New cases} = 35 - 25 = 10$ (\rightarrow) 0.2% incidence over 1-year.

Purpose of Measures of Association

• Determinants: Factors influencing disease (preventative, causative, or curative). Non-exposure vs exposure analysis assists in identifying associations.

• Measures of Disease Frequency Comparison: Evaluating incidences based on exposure status highlights associations:

  • If disease occurrence varies significantly between exposed and unexposed groups, it indicates a potential association.

  • Examples of exposures include smoking and diet context.

Comparisons in Epidemiology

• Index Group (E): Exposed (e.g., smoker) vs. Comparison Group (C): Unexposed (e.g., non-smoker).

• Duration, Intensity, and Timing variables can also be analyzed.

Measures of Association Calculations

• Two Approaches:

  1. Difference between two measures of disease frequency.

  2. Ratio between two measures of disease frequency.

• Absolute Measures: Prevalence difference, Risk difference, Rate difference.

  • General Formula:

  • $\text{Prevalence difference (PD)} = P<em>E - P</em>U$

  • $\text{Risk difference (RD)} = CIE - CIU$ (no units)

  • $\text{Rate difference (RD)} = IRE - IRU$ (person-time units)

Example: Risk Difference Practice - Nurses' Health Study

• Among 13,422 women with hypertension, 117 had MI over 10 years, and among 106,541 women without hypertension, 125 had an MI.

  • Risk Difference Calculation:
    

    $\text{RD} = \frac{117}{13422} - \frac{125}{106541} = 0.0087 - 0.0012 = 0.0075$

  • Indicates an excess of 75 cases of MI per 10,000 over a 10-year follow-up period.

2 (\times) 2 Table General Organization

• Demonstrates organization of cumulative incidence or prevalence.

| Disease | Exposure | Yes | No | Total |
|---------|----------|-----|------|-------|
| Yes | a | b | a+b |
| No | c | d | c+d |
| Total | a+c | b+d | a+b+c+d |

• Counts the total number in the study and number diseased.

Example: Six Cities Study 2 (\times) 2 Table with Count Data

| Dead | Exposure | Yes | No | Total |
|------------------------|----------|-----|------|----------|
| Lived in most polluted city | 291 | 1,060| 1,351 |
| Lived in least polluted city | 232 | 1,399| 1,631 |
| Total | 523 | 2,459| 2,982 |

Six Cities Study: Calculating Absolute Measures of Association

• Incidence Rate Difference:

  • $\text{IRD} = \frac{291}{17,914 p-y} - \frac{232}{21,618 p-y} = 16.24/1,000 p-y - 10.73/1,000 p-y = 5.51/1,000 p-y$

  • Indicator of worse outcomes for the most polluted city.

Relative Measures of Association

• Prevalence ratio $\text{PR} = \frac{PE}{PU}$

• Risk ratio $\text{RR} = \frac{CIE}{CIU}$

• Rate ratio $\text{IRR} = \frac{IRE}{IRU}$

• General Formula: $\text{RR} = \frac{RE}{RU}$

Interpretations of Relative Risk

• If $RR = 1$ (\rightarrow) No association;

• If RR > 1 (\rightarrow) Increased risk;

• If RR < 1 (\rightarrow) Decreased risk.

Example: Six Cities Study Relative Measure of Association

• Incidence Rate Ratio Calculation:

  • $\text{IRR} = \frac{291/17,914 p-y}{232/21,618 p-y} = \frac{16.24}{10.73} = 1.51$

  • Interpretation: Residents of the most polluted city have 1.51 times the death rate of residents in the least polluted city.

Excess Relative Risk Interpretation

• \text{Excess RR} = (RR - 1) \times 100 \text{%}

  • If $RR = 1.51$, residents of Steubenville have a 51% higher risk of death compared with Portage.

Differentiating RD vs. RR

• RD focuses on the strength of the association, while RR provides public health impact insights.

  • RD indicates how much more likely exposed individuals are to develop disease.

  • RR quantifies impact prevention could have on disease occurrence.

Summary of Association vs. Causation

• Association: Established relationship between exposure and disease (may imply causation).

  • Risk factors can be identified through observational data, but causation must be inferred cautiously.

Summary of Measures of Comparison

• The amount of disease occurring in exposed groups can be compared to unexposed to find associations.

  • Absolute (difference) or relative (ratio) measures are utilized for insights in research.

  • Standardization is crucial for fair comparisons between crude measures of disease frequencies.