Risk and Life Expectancy in Statistical Reasoning

Definition of Travel Risk: Often quantified in terms of an accident rate or a death rate. This statistical expression serves as an expected value, which provides an associated probability.
Risk as Probability Example:
- Suppose an annual accident rate is reported as $750$ accidents per $100,000$ people.
- Interpretation: Within a group of $100,000$ people, on average, $750$ individuals will experience an accident over one year.
- Probabilistic Representation: The probability ( $P$ ) of a person being involved in an accident in one year is calculated as:

$P = \frac{750}{100,000} = 0.0075$

Objective: Use automobile fatalities and total miles driven (vehicle-miles) to determine if driving safety has improved over time.
Data Comparison (1980 vs. 2019):
- In 1980:
- Approximately $53,000$ total deaths.
- Approximately $1.5$ trillion ( $1.5 \times 10^{12}$ ) vehicle-miles driven.
- Death Rate: Approximately $3.5$ deaths per $100$ million vehicle-miles driven.
- In 2019:
- Approximately $39,000$ total deaths.
- Approximately $3.3$ trillion ( $3.3 \times 10^{12}$ ) vehicle-miles driven.
- Death Rate: Approximately $1.2$ deaths per $100$ million vehicle-miles driven.
Long-term Trend: From 1980 to 2019, the death rate for automobile crashes decreased from around $3.5$ to $1.2$ deaths per $100$ million vehicle-miles, representing an approximate $66\%$ decrease in risk per mile driven.
Pandemic Anomalies (2020–2021):
- In 2020 and 2021, the absolute number of deaths increased substantially.
- Total vehicle-miles driven during these years remained below the 2019 level.
- Conclusion: The death rate rose during 2020 and 2021. This is potentially attributed to riskier driving behaviors occurring during the COVID-19 pandemic.

Commercial Aviation Data (2010–2021):
- Total Fatalities: Only $2$ accident-related fatalities occurred over this $12$ -year period.
- Average Annual Fatalities: Approximately $0.167$ deaths per year.
- Average Annual Miles: Passengers flew approximately $6$ billion ( $6 \times 10^{9}$ ) passenger miles per year.
Death Rate Calculation: The death rate per $100$ million miles of air travel is calculated based on these figures as being extremely low.
Risk Comparison:
- The 2019 automobile fatality rate ( $1.2$ per $100$ million miles) is approximately $400$ times as large as the airline death rate per $100$ million miles flown.
- Conclusion: On a per-mile-traveled basis, flying is statistically much less risky than driving.

Definition: Vital statistics are data points regarding the births and deaths of citizens.
Utility: These metrics allow demographers and researchers to predict population trends and analyze risk-benefit tradeoffs.
Leading Causes of Death in the U.S. (2019):
- Heart disease: $569,000$
- Cancer: $599,600$
- Accidents (including car crashes): $173,000$
- Chronic respiratory diseases: $157,000$
- Stroke: $150,000$
- Alzheimer’s disease: $121,500$
- Diabetes: $87,700$
- Kidney disease: $51,600$
- Pneumonia/influenza: $49,800$
- Suicide: $47,500$
- (Note: All figures rounded to the nearest $100$ . Source: CDC)

Sample Calculation: Assume a total U.S. population of $330$ million ( $330 \times 10^6$ ).
Death Rate per Person (2019):
- Accidents: $\frac{173,000}{330,000,000} \approx 0.000524$
- Cancer: $\frac{599,600}{330,000,000} \approx 0.001817$
Death Rate per 100,000 People:
- To find deaths per $100,000$ , multiply the per-person rate by $100,000$ .
- Accidents: Approximately $52$ deaths per $100,000$ people.
- Cancer: Approximately $180$ deaths per $100,000$ people.

Fundamental Definition: Life expectancy is the number of additional years a person of a given age can expect to live on average.
Utility: Used to compare overall public health across different eras or different nations.
Mortality Rate (Death Rate): Measures deaths per $1,000$ people for specific age groups.
Biological Trend: Life expectancy is naturally higher for younger individuals because they have more years remaining in a standard lifespan.
Statistical Baseline (2019):
- Life expectancy at birth for Americans (combined genders): Approximately $79$ years.
- Note on COVID-19: The 2019 data does not reflect a subsequent drop of approximately $2$ years in life expectancy caused by the pandemic.

Empirical Statistics (as of 2019):
- Age 20: Average additional life expectancy is about $58$ years.
- Total expected age of death: $20 + 58 = 78$ years.
- Age 60: Average additional life expectancy is about $21$ years.
- Total expected age of death: $60 + 21 = 81$ years.
Analyzing the Statistical Paradox: It may appear contradictory that a $60$ -year-old has a higher total projected lifespan ( $81$ ) than a $20$ -year-old ( $78$ ).
- Reasoning: Life expectancies are based on specific current data. A $60$ -year-old has a higher probability of reaching age $81$ or $83$ simply because they have already survived the risks associated with the first $60$ years of life.
- Public Health Caveat: This assumes no changes in medicine. In reality, if medical technology improves, current $20$ -year-olds are likely to eventually outlive current $60$ -year-olds.

The 20th and 21st Century Trends:
- Progress has generally been upward, but major health crises cause significant fluctuations.
- 1918 Flu Pandemic: Resulted in a large, sharp dip in life expectancy.
- 2020 COVID-19 Pandemic: Resulted in an approximate $2$ -year dip in life expectancy.
- Gender Variance: There remains a distinct difference between the life expectancies of men and women.

Fear of Flying: Consider whether the fact that driving is $400$ times riskier than flying per mile should logically eliminate a fear of flying, or if psychological factors outweigh the statistics.
Age-Based Causes of Death: Statistics for all age groups combined can be misleading. Younger people generally face higher relative risks from accidents, while older populations face higher risks from chronic conditions like heart disease and cancer.
Gender and Social Policy: Observations of different life expectancies between men and women have implications for:
- Social policy and retirement planning.
- Actuarial science and the determination of insurance rates.