MPH 515 Week 5 Biostatistics Write-Up Example

Biostatistics Write-Up: Was Starting Buprenorphine in the Emergency Department Associated With Fewer Repeat Overdose Visits Within 30 Days in Bellamy County?

Student Name

Chamberlain University

MPH 515: Epidemiology and Biostatistics for Public Health Application I

Instructor Name

Month Day, Year

Biostatistics Write-Up: Was Starting Buprenorphine in the Emergency Department Associated With Fewer Repeat Overdose Visits Within 30 Days in Bellamy County?

The Question

This write-up analyzes composite surveillance and hospital data from Bellamy County, the composite county used throughout this course, to ask whether residents who started buprenorphine in the emergency department after a first nonfatal opioid overdose visit in 2024 were less likely to return with another overdose within 30 days than those who did not. The analysis covers 640 residents with a first qualifying visit in 2024 who were discharged alive and lived in the county for the following 30 days.

Variables and Their Measurement Levels

The exposure is buprenorphine started in the emergency department before discharge, recorded as yes or no: a nominal, two-category variable. The outcome is a repeat emergency department visit for opioid overdose within 30 days of discharge, also yes or no. Both variables are categorical, and each resident contributes one observation, so the observations are independent. Age, in years, is a continuous variable used to describe the groups but not in the main test.

Choosing the Test From the Levels

With two categorical variables and independent observations, the question is whether the proportion with a repeat visit differs between two groups. A chi-square test of independence for a two-by-two table is appropriate, with the risk ratio and risk difference reported as effect sizes and 95% confidence intervals. A t-test would be wrong here, because the outcome is not continuous. Fisher's exact test would be preferred if any expected cell count were below 5.

The Data

Table 1

Repeat Overdose Visits Within 30 Days by Emergency Department Buprenorphine Start, Bellamy County Residents, 2024

Note. Note. Composite data constructed for this course.

Assumptions Checked

Each resident appears once, using only the first 2024 visit, so observations are independent. Expected counts were calculated for each cell as the row total times the column total divided by the grand total. The smallest expected count, for repeat visits among those who started buprenorphine, was 168 times 82 divided by 640, or 21.5, well above 5, so the chi-square approximation is acceptable and Fisher's exact test is not needed.

Output in Required Form

The chi-square statistic with one degree of freedom was 6.56, p = .010. The risk of a repeat visit was 7.1% among those who started buprenorphine and 14.8% among those who did not. The risk ratio was 0.48, 95% confidence interval 0.27 to 0.87. The risk difference was 7.7 percentage points lower in the buprenorphine group, 95% confidence interval 2.6 to 12.7 percentage points lower.

Effect Size First

The effect size is the main result: residents who started buprenorphine in the emergency department had about half the risk of a repeat overdose visit within 30 days, about 8 fewer repeat visits for every 100 residents. The confidence intervals show that the data are compatible with a reduction as small as about a 13% relative reduction or as large as about a 73% relative reduction, and with an absolute reduction between about 3 and 13 percentage points. The p value of .010 says that data like these would be unusual if there were no association in the population, but it says nothing about the size or practical weight of the difference (Wasserstein & Lazar, 2016).

Interpretation About the Population

Among Bellamy County residents with a first overdose visit in 2024, starting buprenorphine in the emergency department was associated with a lower risk of returning with another overdose within 30 days. This is consistent with trial evidence: a randomized trial in one urban emergency department found 78% of the patients started on buprenorphine there still in addiction care a month on, against 37% of those simply referred (D'Onofrio et al., 2015).

But this analysis is observational, and the association cannot be read as the effect of buprenorphine. Patients who agreed to start buprenorphine may not resemble those who declined, and the differences could themselves predict a repeat overdose, such as readiness for treatment, housing, or having a phone and a ride to a follow-up appointment. Clinicians may also have offered buprenorphine more often to patients they judged more likely to follow up. Either pattern would make the treatment look more protective than it is. Adjusting for measured differences, such as age, prior visits and insurance, in a regression model would be a next step, but unmeasured differences would remain.

Limitations Specific to These Data

Repeat visits to hospitals outside the county are missed, which could differ by group if those who started treatment were referred to clinics near other hospitals. Deaths within 30 days are not counted as repeat visits, so a patient who died would appear as having no repeat visit; a separate check against death records is needed. Thirty days is a short window, and the association may weaken over longer periods. And the 168 residents who started buprenorphine are a small group, which is why the interval around the risk ratio is wide.

Describing the Groups Before Comparing Them

Before the test, the two groups were described. Residents who started buprenorphine had a mean age of 36.2 years, compared with 38.9 years among those who did not; 61% were men in both groups; and 22% of those who started buprenorphine had a prior overdose visit in 2023, compared with 31% of those who did not. The difference in prior visits matters. A prior visit is itself a risk factor for a repeat visit, and the group that did not start buprenorphine had more of them. Part of the difference in repeat visits could therefore reflect who the groups were rather than what treatment they received. A logistic regression including prior visits, age and insurance would estimate the association with those differences held constant, and is the recommended next step before the result is presented to the county board.

A Reporting Sentence

In a report for the health department, the result would be written as follows: among 640 county residents treated for a first nonfatal opioid overdose in 2024, those who started buprenorphine in the emergency department had a lower risk of a repeat overdose visit within 30 days (7.1% versus 14.8%; risk ratio 0.48, 95% CI 0.27 to 0.87), although differences between the groups in prior overdose history mean the association may overstate any effect of treatment.

References

D'Onofrio, G., O'Connor, P. G., Pantalon, M. V., Chawarski, M. C., Busch, S. H., Owens, P. H., Bernstein, S. L., & Fiellin, D. A. (2015). Emergency department-initiated buprenorphine/naloxone treatment for opioid dependence: A randomized clinical trial. JAMA, 313(16), 1636-1644. https://doi.org/10.1001/jama.2015.3474

Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129-133. https://doi.org/10.1080/00031305.2016.1154108