MPH 515 Week 2 Epidemiologic Measures Write-Up Example

Epidemiologic Measures: Incidence Rates, Rate Ratios and Rate Differences for Nonfatal Opioid Overdose Among Bellamy County Residents, 2023 to 2024

Student Name

Chamberlain University

MPH 515: Epidemiology and Biostatistics for Public Health Application I

Instructor Name

Month Day, Year

Epidemiologic Measures: Incidence Rates, Rate Ratios and Rate Differences for Nonfatal Opioid Overdose Among Bellamy County Residents, 2023 to 2024

The Question

This write-up calculates and interprets measures of the occurrence of nonfatal opioid overdose treated in emergency departments among residents of Bellamy County, a composite Midwestern county used throughout this course. The question is how often new overdoses occurred, among whom, and how large the differences between groups were. Data are composite surveillance figures for January 1, 2023, to December 31, 2024. A case is a resident's first qualifying emergency department visit for opioid overdose in the period; repeat visits by the same person are reported separately. The county's population was about 412,000 in 2023 and 415,000 in 2024, giving 827,000 person-years.

Overall Incidence Rate

Formula: incidence rate equals new cases divided by person-years, multiplied by 100,000.

Substitution: 1,241 new cases divided by 827,000 person-years, multiplied by 100,000.

Result: 150.1 per 100,000 person-years.

Interpretation: over the two years, about 150 county residents per 100,000 had a first emergency department visit for nonfatal opioid overdose each year. Put another way, roughly 1 resident in 670 had such a visit in an average year.

Rates by Sex

Table 1

Incidence of First Nonfatal Opioid Overdose Visits by Sex, Bellamy County, 2023 to 2024

Note. Note. Composite surveillance data constructed for this course.

Rate ratio, men compared with women. Formula: rate in men divided by rate in women. Substitution: 195.4 divided by 105.5. Result: 1.85. The 95% confidence interval, calculated on the log scale from the case counts, runs from 1.65 to 2.08. Interpretation: men in the county had first overdose visits at about 1.85 times the rate of women. The interval describes the range of ratios reasonably compatible with these data, given the model's assumptions, rather than a range that contains the true value with 95% probability (Greenland et al., 2016); either way, it rules out equal rates comfortably. Women are the reference group, as the group with the lower rate.

Rate difference, men compared with women. Formula: rate in men less rate in women. Substitution: 195.4 less 105.5. Result: 89.9 per 100,000 person-years. Interpretation: for every 100,000 men followed for a year, there were about 90 more first overdose visits than among the same number of women. The rate difference describes the excess burden in absolute terms, which is the figure a program would use to estimate how many cases might be prevented if men's rate fell to women's.

Rates by Age

Table 2

Incidence of First Nonfatal Opioid Overdose Visits by Age, Bellamy County, 2023 to 2024

Note. Note. Composite surveillance data constructed for this course.

The rate among residents aged 25 to 44 was 322.4 per 100,000 person-years, more than twice the county average. Using residents aged 45 to 64 as the reference, the rate ratio for ages 25 to 44 was 322.4 divided by 156.1, or 2.07, and the rate difference was 166.3 per 100,000 person-years. More than half of all new cases, 690 of 1,241, occurred in this age group, although it holds only about a quarter of the county's person-time.

Repeat Visits as a Separate Measure

The 1,241 residents made 1,489 qualifying visits in the period, so 248 visits, 16.7% of all visits, were repeats by people already counted. This proportion is not an incidence measure; it describes how often the same people return. It matters for planning, because a repeat visit is a signal of continued risk. Patients treated for nonfatal opioid overdose have a high risk of death afterward: a Massachusetts study found that 5.5% died within a year and 1.1% within a month of their emergency visit (Weiner et al., 2020).

Which Measure Answers Which Question

Each measure answers a different question. The incidence rate answers how common new overdoses are in the county. The rate ratio answers how much more likely one group is than another to have a first overdose, which is useful for understanding risk and for comparisons across places of different size. The rate difference answers how many excess cases a group contributes, which is the measure most useful for deciding where prevention could prevent the most cases. For the county's health department, the rate difference for ages 25 to 44 points to where most avoidable cases sit, while the rate ratio for men points to a group at higher relative risk.

What These Measures Cannot Show

These rates count only overdoses that reached an emergency department and were coded as opioid related. Residents revived at home with naloxone, or who died before reaching care, are not included, so the true incidence of overdose is higher than these figures. The rates also cannot show why men or younger adults are affected more; differences in drug use, in the drug supply and in who is brought to an emergency department could all play a part. And because person-time is estimated from midyear population figures rather than followed individually, the denominators are approximate.

Crude Rates and Why Age Matters

The overall rate of 150.1 per 100,000 is a crude rate: it divides all cases by all person-time without regard to age. Because the age-specific rates differ more than sixfold between the 25 to 44 group and residents 65 and older, the crude rate depends heavily on the county's age structure. If Bellamy County were compared with a county that has an older population, its higher crude rate might reflect its younger population as much as any difference in risk. For comparisons with other counties or with the state, the rates should be age-adjusted to a standard population, such as the 2000 U.S. standard used in most federal reports, so that differences in age structure are removed. Within the county, comparing men and women is less affected, because the two groups have similar age distributions, but a sex comparison within each age group would confirm this.

Checking the Arithmetic

Each rate was checked by confirming that the age-specific cases and person-years add to the county totals: 6, 146, 690, 331 and 68 cases sum to 1,241, and the person-years sum to 827,000. The sex-specific counts also sum to the total. A check like this catches transcription errors that would otherwise carry into every ratio.

References

Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: A guide to misinterpretations. European Journal of Epidemiology, 31(4), 337-350. https://doi.org/10.1007/s10654-016-0149-3

Weiner, S. G., Baker, O., Bernson, D., & Schuur, J. D. (2020). One-year mortality of patients after emergency department treatment for nonfatal opioid overdose. Annals of Emergency Medicine, 75(1), 13-17. https://doi.org/10.1016/j.annemergmed.2019.04.020