MSDB 735 chapter 4: Design Strategies and Statistical Methods in Descriptive Epidemiology

Data Types and Geographic Distributions in Breast Cancer Epidemiology

• Variable Categorization: The variables presented in epidemiological tables regarding race and geographic location represent nominal data.

• Extent of Public Health Problem by Place: Analysis of female breast cancer rates across geographic areas reveals that rates are generally highest in Detroit for nearly every racial group. The exception is the Asian or Pacific Islander group, where the highest rates are observed in San Francisco.

• Appropriateness of Age-Adjusted Rates: Age-adjusted rates are more appropriate than crude rates when comparing the risk of female breast cancer among geographic areas and racial groups. This is because differences in crude rates often arise from variations in the age distribution across different populations rather than actual differences in risk.

Analyzing the Impact of Age Distribution on Race-Based Rate Ratios

• Crude Rate Ratio (White to Black): Calculated as $\frac{167.8}{131.4} = 1.27$. This indicates that without accounting for age, White females have a $27\%$ higher rate of the outcome compared to Black females.

• Age-Adjusted Rate Ratio (White to Black): Calculated as $\frac{136.4}{132.1} = 1.03$. After adjusting for age, the rate ratio drops significantly, showing that White females have only a $3\%$ higher rate compared to Black females.

• Confounding Factors: The discrepancy between the crude ($1.27$) and age-adjusted ($1.03$) ratios suggests that age is a significant confounding factor in the relationship between race and breast cancer.

• Population Aging Patterns:

  • White females likely have an older population distribution. Since breast cancer occurs more frequently at older ages, this older distribution inflates the crude rate for Whites.

  • Black females likely have a younger population, resulting in lower crude rates.

  • In summary, age distribution is a primary driver of the observed differences in crude breast cancer incidence between these racial groups.

Race as a Risk Factor and Necessary Descriptive Clues

• Race as an Independent Risk Factor: Provided data (dropping from a $31\%$ crude difference to a $3\%$ adjusted difference) suggests that race itself may not be a strong independent risk factor for breast cancer in this population.

• Guidance for Further Investigation: Factors such as socioeconomic status (SES), access to healthcare, lifestyle, and genetic predisposition likely play more significant roles in documented disparities.

• Essential Descriptive Data for Identifying Causes: To identify the causes of female breast cancer, epidemiologists should collect data on:

  • Lifestyle: Smoking status, history of breastfeeding, parity (number of births), and obesity.

  • Medical History: Family history of cancer, history of benign breast disease, and age at menopause.

  • Environmental/Social: Exposure to ionizing radiation, SES, first pregnancy at a late age, and presence of nodular densities on mammograms.

Comparative Demographic Data and Relative Frequencies

• Total Population by Racial Group (Standard Areas):

  • White: $10,975,702$

  • Black: $4,691,621$

  • American Indian/Alaska Native: $146,641$

  • Asian or Pacific Islander: $2,704,302$

• Relative Frequency Calculation: Calculated as $\frac{\text{Age-group Population}}{\text{Total Racial Population}}$.

• Relative Frequency Distributions by Age and Race:

  • < 50 Years: White ($0.625$), Black ($0.711$), American Indian/Alaska Native ($0.761$), Asian/Pacific Islander ($0.686$).

  • 50–54 Years: White ($0.075$), Black ($0.068$), American Indian/Alaska Native ($0.065$), Asian/Pacific Islander ($0.069$).

  • 55–59 Years: White ($0.072$), Black ($0.062$), American Indian/Alaska Native ($0.055$), Asian/Pacific Islander ($0.063$).

  • 60–64 Years: White ($0.062$), Black ($0.075$), American Indian/Alaska Native ($0.042$), Asian/Pacific Islander ($0.055$).

  • 65–69 Years: White ($0.052$), Black ($0.039$), American Indian/Alaska Native ($0.029$), Asian/Pacific Islander ($0.043$).

  • 70+ Years: White ($0.113$), Black ($0.068$), American Indian/Alaska Native ($0.047$), Asian/Pacific Islander ($0.085$).

Age-Specific Breast Cancer Incidence Rates

• Rate Calculation Formula: $\left( \frac{\text{Cases}}{\text{Population}} \right) \times 10^5$

• Age-Specific Rates for White Females:

  • < 50: $49.30$

  • 50–54: $243.98$

  • 55–59: $282.52$

  • 60–64: $360.15$

  • 65–69: $454.20$

  • 70+: $460.40$

• Age-Specific Rates for Black Females:

  • < 50: $43.46$

  • 50–54: $253.14$

  • 55–59: $291.22$

  • 60–64: $368.31$

  • 65–69: $428.64$

  • 70+: $431.73$

• Age-Specific Rates for Asian or Pacific Islander Females:

  • < 50: $48.74$

  • 50–54: $237.62$

  • 55–59: $218.29$

  • 60–64: $294.39$

  • 65–69: $309.97$

  • 70+: $281.02$

• Summary of Crude Rates: White ($167.84$), Black ($131.45$), Asian/Pacific Islander ($116.78$), American Indian/Alaska Native ($47.74$).

Statistical Precision and Confidence Intervals

• 95% Confidence Interval Formula: $95\% \text{ CI} = \text{Rate} \pm 1.96 \times \sqrt{\frac{\text{Number of new cases}}{(\text{Person-Time at risk})^2}}$

• Standardized CI Examples:

  • Whites: $0.0016784 \pm 0.00002423774$

  • American Indian/Alaska Native: $0.00058922777 \pm 0.00036557222$

Direct Method of Age Adjustment and Rate Ratios

• Procedure (Standard Population: White Females):

  1. Multiply the study group (e.g., Black female) age-specific rates by the White female population weights (relative frequencies).

  2. Sum these values to obtain the age-adjusted rate.

• Age-Adjusted Rate for Blacks (Age 50–69): $85.04 \text{ per } 100,000\, \text{person-years}$.

• Direct Adjusted Rate Ratio ($RR$): Using the age-adjusted rate of $161$ for Blacks vs. the White rate of $167.84$, the $RR = \frac{161}{167.84} = 0.96$.

• Interpretation of $RR$:

  • $RR = 1$: Incidence rates are equal.

  • $RR = 0.96$: If Black females had the same age distribution as White females, their cancer incidence would be $4\%$ lower than Whites.

Indirect Method and Standard Morbidity/Mortality Ratio (SMR)

• SMR Formula: $SMR = \frac{\text{Observed cases}}{\text{Expected cases}}$

• Criteria for using the Indirect Method:

  • Age-specific case data for the study population is missing or unreliable.

  • Comparing populations with significantly different age distributions.

  • Only the total number of events and the age distribution of the study population are known.

• Black Population Case Study:

  • Total Observed Cases: $6,167$

  • Total Expected Cases: $6,424.78$

  • Total SMR: $\frac{6167}{6424.78} = 0.96$ (SMR < 1 indicates fewer cases observed than expected).

  • Specific Age SMR (50–69): $\frac{3341}{3312.62} = 1.008$ (Slightly more cases observed than expected).

Epidemiological Definitions and Survival Concepts

• Incidence vs. Prevalence: Incidence rate measures risk (new cases over time), while prevalence proportion measures burden (all cases at a point in time). Prevalence is used for chronic conditions where onset is hard to identify (e.g., Type II Diabetes).

• Person-Time Incidence vs. Attack Rate:

  • Person-time: Used for chronic conditions and study groups with varying time-at-risk.

  • Attack rate: Used for rapid onset after specific exposure; the denominator is only those at risk at the beginning of the period. Rate base is typically $100$.

• Lethality and Survival: If Disease A has lower incidence but higher prevalence than Disease B (with similar cure rates), Disease A is less lethal (has better survival/lower mortality).

Secondary Attack Rate Calculation

• Scenario: 120 people diagnosed (Disease A) in a region. 440 people live in those households. 50 cases are primary.

• Step 1: Calculate New Cases Among Contacts: $120 - 50 = 70$.

• Step 2: Calculate Denominator: Total residents minus primary cases ($440 - 50 = 390$).

• Step 3: Calculate Ratio: $\frac{70}{390} \times 100 = 17.9 \text{ per } 100$.

Statistical Interpretation: Skewness, Correlation, and Regression

• Distribution Skewness: If Mean ($43$) < Median ($51$), the age distribution is skewed to the left. This implies the presence of young outliers despite a generally older participant pool.

• Correlation Coefficient ($r$): A value of $-0.3$ indicates a weak negative linear association (as exercise hours increase, pulse rate decreases).

• Coefficient of Determination ($r^2$): $\left( -0.3 \right)^2 = 0.09$ or $9\%$. This means $9\%$ of the variation in pulse is explained by exercise.

• Regression Slope Interpretation: A slope of $-0.05$ means that for every additional hour of exercise per week, the pulse decreases by an average of $0.05\text{ beats/minute}$. Extrapolation beyond the data range (e.g., from $0\text{–}20\, \text{hours}$ to $30\, \text{hours}$) is not appropriate.

• Adjusting for Confounding: To account for age as a confounder, perform analysis in stratified age groups or include age in a multiple regression or multiple logistic regression model.

Case Study: Person-Time Incidence of Disease X

• Data: 200 new cases in 2,000 person-years.

• Person-Time Rate Calculation: $\frac{200}{2000} \times 10^5 = 10,000 \text{ per } 100,000\, \text{person-years}$.

• 95% Confidence Interval:

  • $Standard Error = \sqrt{\frac{200}{(2000)^2}} = 0.00707$

  • $Margin of Error = 1.96 \times 0.00707 = 0.01386$

  • $95\% \text{ CI Calculation} = 10,000 \pm (0.01386 \times 100,000) = 10,000 \pm 1,386$

  • Final Range: $8,614\text{–}11,386 \text{ per } 100,000\, \text{person-years}$.