A 2016 article in JAMA reports the results of a study of treatment outcomes for children with mild gastroenteritis who were given oral rehydration therapy. Enrolled children were randomized to received either rehydration with diluted apple juice (DAJ), or an electrolyte maintenance solution (EMS). As per the study authors:
“The primary outcome was a composite of treatment failure defined by any of the following occurring within 7 days of enrollment: intravenous rehydration, hospitalization, subsequent unscheduled physician encounter, protracted symptoms, crossover, and 3%or more weight loss or significant dehydration at in-person follow-up. Secondary outcomes included intravenous rehydration, hospitalization, and frequency of diarrhea and vomiting.”
Of the 323 children randomized to DAJ, 54 experienced treatment failure. (17 %). Of he 324 children randomized to EMS, 81 experienced treatment failure. (25 %)
1. For this study, what is the outcome of interest?
2. For this study what is the primary exposure of interest?
3. Estimate the risk difference (difference in proportions) of treatment failure for children in the DAJ group compared to children in the EMS group. (DAJ-EMS)
4. Interpret the estimate from item 3 in a sentence.
5. Estimate the relative risk (risk ratio) of treatment failure for children in the DAJ group compared to children in the EMS group.
6. Interpret the estimate from item 5 in a sentence.
7. Estimate the relative odds (odds ratio) of treatment failure for children in the DAJ group compared to children in the EMS group.
8. Interpret the estimate from part f in a sentence.
9. Do the estimated risk difference, relative risk and odds ratio agree in terms of the direction of association?
Question 2
A pilot study was designed to evaluate the potential efficacy of a program designed to reduce prison recidivism amongst inmates who have a documented long-term history of drug and/or alcohol problems. A sample of 11 prisoners was followed for up to 24 months after their most recent release from prison. Six of the inmates returned to prison at 3, 7 9, 11, 14 and 21 months respectively. Five of the inmates had not returned to prison as of the last time they were last contacted which was at 4, 8, 16, 24, and 24 months respectively.
Use the Kaplan Meier approach to estimate the survival curve for this set of inmates
(which tracks the proportion who have not yet returned to prison over time). It will be
helpful to construct a table like the ones appearing in lecture 5: however, all you will
need to report in the quiz generator are certain quantities from this table for specific
times.
10. What is the estimated proportion of the total sample who had not returned to prison by 7 months after enrolling in the study?
11. What is the estimated proportion of the total sample who had not returned to prison by 11 months after enrolling in the study?
12. What is the estimated proportion of persons who did not return to prison at 11 months among those who were still at risk of returning to prison at 11 months?
13. What is the estimated percentage of the original sample had not return to prison by 16 months?
14. Why does the Kaplan-Meier curve not reach 0% by the end of the follow-up period?
Question 3
In a July, 2010 article published in the New England Journal of Medicine[footnoteRef:1], researchers report the results of a randomized clinical trial to evaluate mortality differences in HIV infected subjects in Haiti. Subjects were randomized to receive early versus the current standards for implementation of Antiretriviral therapy. [1: Sever P, et al. Early versus Standard Antiretroviral Therapy for HIV-Infected Adults in Haiti. New England Journal of Medicine. (2010). Vol 363, No 3. ]
As per the abstract:
In summarizing the findings, the researchers present the following Kaplan-Meier curve
Statistical Reasoning in Public Health 1, 2016: Homework 2 10
15. Why do the curves for both groups start at 1 (100%) at time = 0 month?
16. What is the estimated proportion of persons surviving (remaining alive) beyond 36 months in the Early Retroviral Treatment sample?
17. What is the estimated proportion of persons surviving (remaining alive) beyond 36 months in the Standard Retroviral Treatment sample?
18. Based only on this graphic, what can you say about the estimated incidence rate ratio of mortality for standard treatment group compared to the early treatment group? (greater than, less than, or equal to 1). Why?
Question 4
In an August 2013 article published in American Journal of Public Health[footnoteRef:2], researchers report the results of a two-site (San Francisco and NYC) randomized trial: here is a description of the trial and the sample from the article abstract: [2: Masson C, et al. A Randomized Trial of a Hepatitis Care Coordination Model in Methadone Maintenance Treatment. American Journal of Public Health. 2013. Published online ahead of print August 15, 2013]
Objectives. We evaluated the efficacy of a hepatitis care coordination intervention
to improve linkage to hepatitis A virus (HAV) and hepatitis B virus
(HBV) vaccination and clinical evaluation of hepatitis C virus (HCV) infection
among methadone maintenance patients.
Methods. We conducted a randomized controlled trial of 489 participants
from methadone maintenance treatment programs in San Francisco, California,
and New York City from February 2008 through June 2011. We randomized
participants to a control arm (n = 245) and an intervention arm (n = 244), which
included on-site screening, motivational-enhanced education and counseling,
on-site vaccination, and case management services.
Of the 150 participants in the intervention group who needed the combined HAV—
HBV vaccine, 115 received the vaccine within 30 days of the vaccine being recommended. Of the 150 participants in the control group who needed the combined HAV-HBV vaccine,18 received the vaccine within 30 days of the vaccine being recommended.
19. In the above results presented, what is the outcome ?
20. In the above results presented, what is the exposure (predictor)?
21. Estimate the risk difference (difference in proportions) of getting the vaccine within 30 day of recommendation for the intervention group compared to the control group.
22. Interpret the estimate from item 21 in a sentence.
23. Estimate the relative risk (risk ratio) of getting the vaccine within 30 day of recommendation for the intervention group compared to the control group.
24. Interpret the estimate from item 23 in a sentence.
25. Estimate the relative odds (odds ratio) of getting the vaccine within 30 day of recommendation for the intervention group compared to the control group.
26. Interpret the estimate from part c in a sentence.
27. Do the estimated risk difference, relative risk and odds ratio agree in terms of the direction of association?
28. How do the estimated relative risk and estimated odds ratios compare in value?
29. Suppose you were to misinterpret the odds ratio as the relative risk. What would this do to the reported efficacy of the intervention program with regard to the vaccination outcome (under estimate or over estimate the efficacy)?
Homework 2, Part B: (the question in part a will be presented as fill in the blank/short answer questions in the Quiz Generator version):
Question 1
An October 25, 2012 article in the New England Journal of Medicine reports the results of a study examining aspirin and survival among patients with colorectal cancer. The following pieces of text are taken directly from the article abstract: (my edits are in italics)
“METHODS
We obtained data on 964 patients with rectal or colon cancer from the Nurses’
Health Study and the Health Professionals Follow-up Study, including data on aspirin
use after diagnosis and the presence or absence of PIK3CA mutation……
RESULTS
Among patients with mutated-PIK3CA colorectal cancers, regular use of aspirin after
diagnosis was associated with superior colorectal cancer–specific survival (adjusted relative risk for cancer-related death, 0.18; 95% confidence interval [CI], 0.06 to
0.61; P<0.001 by the log-rank test) and overall survival (adjusted relative risk for
death from any cause, 0.54; 95% CI, 0.31 to 0.94; P = 0.01 by the log-rank test). In
contrast, among patients with wild-type PIK3CA, regular use of aspirin after diagnosis
was not associated with colorectal cancer–specific survival (adjusted relative risk,
0.96; 95% CI, 0.69 to 1.32; P = 0.76 by the log-rank test) ) or overall survival (adjusted relative risk, 0.94; 95% CI, 0.75 to 1.17; P = 0.96 by the log-rank test)”
The authors present the following graphic as part of the article: (on the next page)
1. What is the outcome of interest for this study?
2. What is the primary predictor of interest?
3. What type of study design is this?
4. Describe the findings with regards to aspirin and survival in patients with colorectal cancer with respect to the presence or absence of the PIK3CA mutation.
5. Even though the authors estimated the association between aspirin and survival separately for the mutated-PIK3CA and wild-type PIK3CA, each of the two associations was adjusted for multiple factors including age, sex, year of diagnosis etc… Why was it potentially necessary to do this adjustment?
Question 2
A 2003 article in New England Journal of Medicine[footnoteRef:3] reports the results from a randomized trial comparing weight change and comorbidity development between severely obese subjects randomized to either receive a low carbohydrate diet or a low fat diet regimen. Both diet regimens lasted for six months. The results with regards to weight change are in the following table: [3: Samaha F, et al. A Low-Carbohydrate as Compared with a Low-Fat Diet in Severe Obesity. New England Journal of Medicine 2003;348:2074-81. ]
With regards to the weight change portion of these study:
6. What is the main outcome of interest for this study?
7. What is the main exposure of interest for this study?
8. Did the subjects in the low-carb diet group gain or lose weight?
9. Did the subjects in the low-fat diet group gain or lose weight?
10. In which diet group were the individual weight change values more variable?
11. Estimate and report the mean difference in weight change for the low-carb diet group compared to the low-fat diet group.
12. Interpret the estimate from item 11 in a sentence.
13. What is the estimated mean difference in weight change for comparing the low-fat diet group to the low-carb diet group? How does this estimate compare to the estimate from item 11?
14. Write a sentence describing the findings conveyed by the following with regards to weight-loss and diet group over the study follow-up period. (While this resembles a Kaplan-Meier curve, it is not)
Suppose the researchers had been able to randomize 300 severely obese
subjects into the two weight-loss groups , such that 154 received the low-carb diet, and 146 the low-fat diet. How should the following quantities compare in value (larger, smaller etc..) to the estimates from the actual study of 132 subjects. Explain your reason for each answer.
15. The standard deviations of the individual weight change values in each diet group
16. The mean difference in weight change for the low-carb group compared to the low fat group.
Question 3
A 2015 article in JAMA Psychiatry5 investigates factors associated suicide, including a history of self-harm via poisoning.
The primary outcome of interest was suicide. Subjects were followed until this outcome or censoring (still alive, death by other causes, lost to follow-up).
The following Kaplan-Meier curves show the time-to-outcome curves for the exposure (self-poisoning) and control groups. Time-zero was the discharge date for the self-poisoning subjects. (and the corresponding matched control)
17. Suppose the incidence rate ratio (IRR) of suicide is computed for the DS cohort compared to the Control group. How will this IRR compare to 1 (<1, >1. =1)?
18. There are 65,784 subjects who had a self-poisoning episode. However, at
10 years of follow-up, only 21 are at-risk of suicide. In other words, less that 0.1 %
is still at-risk at 10 years. However, the corresponding Kaplan-Meier curve estimate
at 10 years is approximately 98% (98% had not committed suicide). How is this
possible?
