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Created: Nov 15, 2017
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Week 13 Hep A
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Week 13 StatCrunch




Hepatitis A is a highly contagious liver infection. This disease can be spread through contaminated food or water or through contact with an infectious person. While hepatitis A is not as serious as Hepatitis B and C, the effects can still be debilitating and cause substantial economic losses during epidemics. The risk of hepatitis A is known to include poor sanitation, dirty water, and poor hygiene. Literature does not reveal a large focus on relationship between Hep A and age. Our researchers have chosen to examine any possible relationship between bilirubin levels (mg/dL) and age (years) for patients over the age of 40 who have been diagnosed with Hep A but not hospitalized.




Researchers performed a retrospective chart review of 20 subjects over the age of 40 who had been diagnosed with acute hepatitis A but not hospitalized. Both data measurements, age and bilirubin levels, qualify as interval-ratio data. We must also check a scatter plot to ensure no non-linear pattern is found. Based off our scatter plot from last week,there does not appear to be any issues with non-linearity. It does appear to be random scatter though or possibly a very weak positive correlation making the predictive ability not entirely useful.  Regardless, it is appropriate to move forward with regression analysis.  We must first check our assumptions of normality and constant variability.


Result 1: QQ plot residuals- Week 13   [Info]
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Result 2: Residuals vs. Age- Week 13   [Info]
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Based off the above plots we do not have any issues with normality or constant variability




Based on our results last week (r= 0.4658, p=0.0385), we have evidence of a weak positive correlation between bilirubin levels and age. Now we move on to the regression analysis output.


Result 3: Simple Linear Regression- Week 13   [Info]
Simple linear regression results:
Dependent Variable: Bilirubin (mg/dl)
Independent Variable: Age (years)
Bilirubin (mg/dl) = -2.9841882 + 0.17932358 Age (years)
Sample size: 20
R (correlation coefficient) = 0.46576426
R-sq = 0.21693634
Estimate of error standard deviation: 4.4143462

Parameter estimates:
ParameterEstimateStd. Err.DF95% L. Limit95% U. Limit

Analysis of variance table for regression model:

Predicted values:
X valuePred. Ys.e.(Pred. y)95% C.I. for mean95% P.I. for new
505.98199091.0948969(3.6816979, 8.2822839)(-3.5732214, 15.537203)


We can estimate with 95% confidence that the slope of our true regression line is between 0.01 and 0.35.




Based on the results of the slope confidence intervals, the average bilirubin level will increase 0.01 to 0.35 mg/dl as age increases by 1 year.


Conclusions/Further Study


While we do see evidence that average bilirubin levels increase with age in patients with acute hepatitis A, the relationship between variables is very weak. Clinically, I would conclude that age is not a strong determinant of changes in bilirubin levels. I would recommend further studies explore other possible relationships associated with hepatitis A in order to guide future treatment and prevention research.


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By nku.katie.waters
Nov 19, 2017

Hi Ashleigh,
Good job! My only comment:
You were asked to predict the Bilirubin level for a patient who is age 45 (looks like you attempted age 50). A correct interpretation: We are 95% confident that an acute hepatitis A patient who is 45 years old will have bilirubin levels as high as 14.76 mg/dl (note that we know the levels can't be negative, so phrase accordingly). Remember that a PI is interpreted for an INDIVIDUAL - not average.

Please review the solutions and let me know if you have any questions.
By ekilburn81
Nov 18, 2017

Great job on your report. I found it very interesting. I did the same report and I was amazed by the results.
By sadouskasm
Nov 16, 2017

Good job! I did the same report. I find it interesting that there is a weak relationship. I would think age would play a role in these levels.

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