# Study Design Description — Prediction Task

You are being asked to predict the results of an analysis you have not seen. Read the design carefully and answer the questions at the end. Do not search for this study.

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## 1. Data sources

Two administrative registries from a single US state, record-linked:

1. **Vital records death registry** (includes date of death, cause of death coded to ICD-10)
2. **State immunization information system** (includes day-of-life of each administration and the CVX product code for each vaccine given)

## 2. Cohort construction

- All children who died before their 3rd birthday in the state, 2013–2024: **~5,800**
- Of these, **1,775** could be exactly matched to a record in the immunization registry. Matching required the child to have **at least one documented immunization** on file. The remaining ~4,025 decedents were not matched and are absent from the analysis.
- Of the 1,775 matched, **550 died before day 90 of life** and were excluded.
- **Final analytic set: 1,225 children.**

**Critical structural feature:** every child in the analytic set died before age 3. There are no survivors in the dataset. The state did not release records for living children.

## 3. Demographics of the analytic set (n = 1,225)

- Male 57.0%, Female 43.0%
- Black 58.6%, White 38.0%, other 3.4%
- Non-Hispanic 94.1%
- Deaths distributed across 2013–2024, ranging 6.6%–10.4% per year (no strong time trend)

## 4. Exposure definition

- **"Vaccinated"**: documented receipt of the vaccine of interest between **day 60 and day 90 of life**
- **"Unvaccinated"**: no documented receipt of that vaccine within the day 60–90 window (may have received other vaccines, or the same vaccine at another time)
- For individual-vaccine analyses, children whose **first** dose of that vaccine was before day 60 were excluded (n excluded: DTaP 84, HIB 80, polio 85, pneumococcal 85, rotavirus 77; 67 common to all five). No exclusions applied for HepB, since a birth dose is schedule-compliant.

## 5. Outcome definition

- **"Died"**: death between **day 90 and day 120** of life
- **"Alive"**: death **after** day 120 (but still before the 3rd birthday)

The outcome is therefore the proportion of each arm's decedents whose death fell in the 30-day window immediately following the exposure window.

## 6. Analysis method

2×2 contingency tables. Odds ratios with 95% CIs and p-values, computed in SciPy. **No regression, no covariate adjustment, no propensity scores, no weighting, no matching.** Raw counts only.

Contrasts run:

1. Each of 6 individual vaccines (DTaP, HepB, HIB, polio, pneumococcal, rotavirus) vs. unvaccinated
2. Combination of 5 (all of DTaP + rotavirus + HIB + polio + pneumococcal) vs. receiving none of the 5
3. Combination of 6 (the above plus HepB) vs. receiving none of the 6
4. Three branded multivalent formulations vs. receiving none of their components
5. Each of the above stratified by race (Black, White) and by sex (Male, Female)

**~55 contrasts total.**

## 7. Group sizes

| Exposure group (day 60–90) | N |
|---|---|
| Unvaccinated | 343 |
| DTaP | 777 |
| HepB | 717 |
| HIB | 772 |
| polio | 772 |
| pneumococcal | 759 |
| rotavirus | 611 |
| all 5 | 589 |
| all 6 | 536 |
| Brand A (pentavalent) + HIB | 408 |
| Brand B (pentavalent) + HepB | 214 |
| Brand C (hexavalent, US-marketed from ~2021 only) | 62 |

Note that the unvaccinated reference group (n = 343) is the **same group** for every individual-vaccine contrast.

## 8. Background context

- US infant mortality ≈ 5.6 per 1,000 live births; ≈ 10.5 per 1,000 for Black infants
- Roughly two-thirds of US infant deaths are neonatal (< 28 days)
- The recommended 2-month visit includes up to 6–7 immunizations administered same-day
- US birth-dose HepB coverage is roughly 75–80%
- SUID/SIDS peaks at 1–4 months of age and is the leading cause of postneonatal mortality
- SIDS has an approximately 60:40 male:female predominance
- US SUID rates rose beginning in 2020, with the largest single-year increase in 2021

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## Questions

**Part A — under the assumption that these vaccines have exactly zero causal effect on mortality:**

1. What odds ratio would you predict for each individual vaccine? Give a point estimate and range.
2. Would you predict meaningful variation *across vaccine types*? If so, how much, and which would be highest?
3. Would you predict a gradient across 1 vaccine → 5 vaccines → 6 vaccines? Direction and magnitude?
4. Would you predict a **sex** difference in the ORs? Direction and magnitude? Be specific about whether any such difference would appear in the vaccinated arms, the unvaccinated arms, or both.
5. Would you predict a **race** difference? Direction and magnitude?
6. What fraction of the ~55 contrasts would point in the same direction?
7. Enumerate every bias you can identify in this design. For each, give the **sign** (toward or away from the null) and an estimate of **magnitude**. Be quantitative where you can.

**Part B — under the assumption that these vaccines DO cause an increase in mortality in the 30 days following administration:**

8. How would each of your answers to 1–6 change?

**Part C:**

9. Which specific observations, if any, would **discriminate** between Part A and Part B? Which would not?
10. What additional table or cross-tabulation, obtainable from the variables listed in §1, would be most informative for distinguishing the two hypotheses?

Answer Part A fully before reading your own Part B reasoning. Do not adjust Part A to be consistent with anything.