| Course | PHLT 8500 Advanced Biostatistics |
|---|---|
| Week | Week 11 |
| Paper type | Final modeling memo |
| Length | About 900 words, 5 pages |
| Format | Memo, APA 7 citations |
| School | Walden University |
| Program | PhD in Public Health |
| Updated | October 2026 |
Free sample paper for PHLT 8500 Week 11
Memorandum
To: County Environmental Health Director and Well-Testing Program Steering Committee
From: Biostatistics Analyst (PhD in Public Health student)
Date: Month Day, Year
Re: Final model for the association between private well arsenic and diabetes, with its rival and the conditions under which the conclusion would change
Bottom Line
Among 1,612 private-well users in the county who were free of diabetes at enrollment, each doubling of well water arsenic is associated with a 12% higher rate of developing diabetes over eight years (hazard ratio 1.12, 95% confidence interval 1.03 to 1.22), after accounting for age, sex, weight, smoking, schooling and rice consumption. In practical terms, about 17 in 100 people with wells at or above the federal limit developed diabetes over eight years, compared with about 13 in 100 below it. The association is modest, consistent across every specification tried this term and in line with prospective evidence from other populations (Kuo et al., 2015). It supports continued promotion of well testing and treatment, and it does not by itself prove that arsenic causes diabetes.
Every Term, With Its Week
Each element was justified before its result was seen, and each alternative examined during the term is reported, not hidden.
Table 1
Final Specification and Where Each Decision Was Made
| Element | Decision | Week | |
|---|---|---|
| Outcome | Time to incident diabetes, Cox model | 10 | |
| Exposure | Log base 2 well arsenic, linear | 2, 9 | |
| Confounders | Age, education | 3 | |
| Precision terms | Sex, body mass index, smoking, rice intake | 2, 3 | |
| Left out | Home treatment, urinary arsenic, fasting insulin, seafood | 3 | |
| Collinearity | Years at residence excluded; sensitivity model reported | 7 | |
| Interaction | Arsenic by obesity reported on both scales, not in primary model | 8 | |
| Competing risk | Death handled; subdistribution model as sensitivity | 10 | |
Note. Composite cohort.
Unadjusted and Adjusted, Side by Side
Adjustment reduced the estimate by about a quarter, mostly through age, as forecast in Week 1. After that, no specification moved it meaningfully. Westreich and Greenland (2013) advise against interpreting the covariates' own coefficients, so the table shows only the exposure.
Table 2
Hazard Ratio per Doubling of Well Arsenic Across Specifications (Composite Figures)
| Specification | Hazard ratio | 95% confidence interval | |
|---|---|---|
| Unadjusted | 1.17 | 1.08 to 1.27 | |
| Adjusted for age and education | 1.13 | 1.04 to 1.23 | |
| Final model | 1.12 | 1.03 to 1.22 | |
| Final plus years at residence | 1.11 | 1.02 to 1.21 | |
| Final with spline for arsenic, interquartile contrast | 1.35 for 2 to 14 micrograms per liter | 1.06 to 1.72 | |
| Fine-Gray, death as competing event | 1.11 | 1.02 to 1.21 | |
Note. Composite figures.
The Rival at Full Strength
The strongest alternative replaces well arsenic with urinary arsenic, the sum of inorganic arsenic and its methylated metabolites, which reflects what each person actually absorbed from water, rice and other sources. Built properly, the rival excludes arsenobetaine, the form from seafood that is considered of low toxicity and would otherwise add noise (Navas-Acien et al., 2011), and adjusts for urinary creatinine to account for dilution. In this cohort the rival gives a hazard ratio of 1.18 per doubling of urinary arsenic (95% confidence interval 1.05 to 1.33), somewhat larger than the well-water estimate.
Different Questions, Not Better and Worse
The two models are not competitors for the same job. The urinary model asks about the biological dose a person carries, and its larger estimate is consistent with less measurement error in dose. The well-water model asks about the exposure the county can act on: the concentration in a well, which can be tested and treated. The urinary measure also has drawbacks for that purpose: it reflects only recent days of intake, and creatinine adjustment can itself be affected by kidney function and diabetes. For a program deciding where to promote testing and treatment, the well-water model answers the relevant question. The memo therefore keeps it as the primary analysis and reports the urinary model as supporting evidence that the association holds when exposure is measured in the body.
What Would Change the Conclusion
Unmeasured Confounding
The E-value for the final hazard ratio is about 1.49 (VanderWeele & Ding, 2017). An unmeasured confounder would need to be associated with both well arsenic and diabetes by a risk ratio of about 1.5 each, beyond the measured covariates, to explain the association fully. The E-value for the lower confidence limit is about 1.21. Factors associated with diabetes at that strength are common, but they would also need to be that strongly associated with the arsenic in a person's well after accounting for age and education, which is less plausible because arsenic levels follow bedrock geology rather than personal behavior.
Measurement
Well arsenic was measured once. If concentrations changed substantially, or many participants drank bottled water, the estimate would likely be biased toward the null, so the true association could be larger.
Selection
If people who moved away were at higher diabetes risk and also had high-arsenic wells, censoring would bias the estimate; the 96 who moved did not differ from those who stayed in baseline arsenic or A1c.
Recommendation
The analysis supports the program's current message that private well owners should test for arsenic and treat water above the federal limit. Roughly 2.1 million people nationally rely on domestic wells above that limit (Ayotte et al., 2017), so even a modest association matters at scale. The memo recommends reporting the finding as an association consistent with other studies, not as proof of cause, and repeating the analysis when the next round of well tests and A1c measurements is complete.
References
Ayotte, J. D., Medalie, L., Qi, S. L., Backer, L. C., & Nolan, B. T. (2017). Estimating the high-arsenic domestic-well population in the conterminous United States. Environmental Science & Technology, 51(21), 12443-12454. https://doi.org/10.1021/acs.est.7b02881
Kuo, C.-C., Howard, B. V., Umans, J. G., Gribble, M. O., Best, L. G., Francesconi, K. A., Goessler, W., Lee, E., Guallar, E., & Navas-Acien, A. (2015). Arsenic exposure, arsenic metabolism, and incident diabetes in the Strong Heart Study. Diabetes Care, 38(4), 620-627. https://doi.org/10.2337/dc14-1641
Navas-Acien, A., Francesconi, K. A., Silbergeld, E. K., & Guallar, E. (2011). Seafood intake and urine concentrations of total arsenic, dimethylarsinate and arsenobetaine in the US population. Environmental Research, 111(1), 110-118. https://doi.org/10.1016/j.envres.2010.10.009
VanderWeele, T. J., & Ding, P. (2017). Sensitivity analysis in observational research: Introducing the E-value. Annals of Internal Medicine, 167(4), 268-274. https://doi.org/10.7326/M16-2607
Westreich, D., & Greenland, S. (2013). The Table 2 fallacy: Presenting and interpreting confounder and modifier coefficients. American Journal of Epidemiology, 177(4), 292-298. https://doi.org/10.1093/aje/kws412
Reading the PHLT 8500 Week 11 instructions
The final assignment in a modeling course usually asks students to present their chosen model to a decision maker and defend it. Instructors expect a bottom line stated plainly, a record of how each modeling decision was made, a comparison of unadjusted and adjusted estimates across specifications and a serious alternative evaluated fairly. Sensitivity analysis for unmeasured confounding, such as an E-value, is increasingly expected. Recommendations should follow from the evidence without overstating it. Memos generally run three to four pages with tables and draw on sources from across the term. A table showing the exposure estimate across specifications is a common requirement, as is a section on what would change the conclusion. The audience is usually a program leader, so plain language and a short bottom line matter as much as technical accuracy. Recommendations should be specific about what the evidence supports.
How the PHLT 8500 Week 11 example is put together
The memo opens with the hazard ratio, eight-year risks and the limit of the evidence, citing prospective research. Table 1 traces each element of the final specification to the week it was decided. Table 2 shows the arsenic hazard ratio across six specifications, and the text notes that adjustment mattered mostly through age. A section builds the urinary arsenic rival, citing research on seafood arsenic. A section explains why the two models answer different questions. Subsections address unmeasured confounding with an E-value, measurement and selection. A recommendation closes the memo, citing national well data.
Where the marks sit in the PHLT 8500 Week 11 rubric
Final memos are graded on clarity for the audience, transparency of the modeling record and fairness to alternatives. The sample earns clarity credit with a bottom line a director can act on. Transparency comes from the decision table and the specification table. Building the urinary rival with the same care as the final model, and explaining that it answers a different question, shows intellectual honesty. The E-value and discussion of measurement and selection show the author knows what would overturn the conclusion. Measured recommendations, clear tables and correct references complete the grade. Noting that measurement error in a single well test would likely bias toward the null, and that movers did not differ at baseline, shows a complete account of threats beyond confounding.
PHLT 8500 Week 11 help from the desk
Final memos often present one model as though no other was considered. Lead with the answer in plain terms. Show how each modeling decision was made and where. Present the exposure estimate across specifications so readers see its stability. Build your strongest rival properly and explain whether it answers the same question. Quantify how strong unmeasured confounding would need to be. Separate the claims your data can carry from those they cannot. Our writers can prepare a final modeling memo for your project as a free sample. Address measurement and selection as well as confounding, and say which direction each would push the estimate. Tie the recommendation to the decision the reader actually faces, such as whether to keep promoting well testing, and avoid claiming more than an association supports.
Get a PHLT 8500 Week 11 example written to your instructions
Forward the final memo instructions and rubric with your earlier modeling work, or a summary of the decisions it contains. A modeling memo that traces every term, presents a fair rival and defends the choice from the question comes back in 24-48h, and nothing is owed the first time. Its cohort and estimates are composite; your memo defends your own specification.
More PHLT 8500 papers and PhD in Public Health samples
- PHLT 8500 Week 1: Regression Review Post
- PHLT 8500 Week 2: Model Build
- PHLT 8500 Week 3: Variable Selection
- PHLT 8500 Week 4: Coefficient Reading
- PHLT 8500 Week 5: Outcome Type Brief
- PHLT 8500 Week 6: Peer Challenge Post
- PHLT 8500 Week 7: Collinearity Diagnostic
- PHLT 8500 Week 8: Interaction Analysis
- PHLT 8500 Week 9: Model Comparison
- PHLT 8500 Week 10: Survival Model Brief
- PHLT 8520 Week 11: Final Methods Paper
- PHLT 8450 Week 11: Assessment Report
- PHLT 8331 Week 11: Plain-Language Findings Report
- PHLT 8270 Week 11: Surveillance Synthesis Paper
PHLT 8500 Week 11 questions, answered
Where can I find a free PHLT 8500 Week 11 sample paper?
The full Week 11 memo is published on this page, presenting a Cox model of diabetes on well arsenic, tested against a urinary arsenic rival with sensitivity analysis and real references.
What is an E-value?
It is the smallest risk ratio that a hidden confounder would have to share with both exposure and outcome, on the risk ratio scale, to fully explain an observed association. The sample's E-value is about 1.49.
Why is urinary arsenic a rival rather than a replacement?
Urinary arsenic measures absorbed dose, while well arsenic measures the exposure a program can test and treat. They answer different questions, so the memo keeps well arsenic as primary and urinary arsenic as support.
Why show the estimate across many specifications?
Stability across reasonable choices shows the conclusion does not depend on one modeling decision. In the sample, adjusted hazard ratios range from 1.11 to 1.13.
Does the memo claim arsenic causes diabetes?
No. It reports a consistent association in line with other studies, quantifies how much unmeasured confounding would be needed to explain it and recommends continued testing and treatment.