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Created: Oct 13, 2017
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Drug Prices- Week 8
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DRUG PRICES

Introduction:

Many people have started using online pharmacies originating from Canada, while trying to save money on their monthly prescriptions.  This study will assess the differences in the mean cost of medications among the three pharmacies.

 

Data Collection:

This study included a random sample of 10 commonly purchased prescription drugs were taken and their prices recorded from two online pharmacies in the United States and at Apetche (the largest Canadian online pharmacy).  Repeated measures Anova was the statistical method used to analyze the information. We had three pharmacies to assess and it was best to use this type of test for that reason. We tested the same 10 drugs for each of the 3 pharmacies to analyze the final cost We could have also used the two-way Anova and selected the additive model (This would have been the same as the RM-Anova). 

 

Data Analysis:

We checked for validity. Data was measured at the interval/ratio level.  We checked for normality with a QQ PLOT. We also checked residuals and fitted values and displayed them with a scatter plot. No violations were observed.

Result 3: Scatter Plot   [Info]
Right click to copy

Result 1: Repeated Measures ANOVA DRUG PRICES   [Info]
Repeated measures ANOVA results:
Responses: Cost
Treatments: Pharmacy
Blocks: Drug

Response statistics by treatment
PharmacynMeanStd. Dev.Std. Error
Aptecha1083.27843.85281213.867477
US 110155.22542.16170413.332701
US 210175.6949.75283415.733227


ANOVA table
SourceDFSSMSF-StatP-value
Pharmacy247117.21623558.60849.648095<0.0001
Error188541.2128474.51182

Tukey 95% Simultaneous Confidence Intervals:
Aptecha subtracted from
DifferenceLowerUpperP-value
US 171.94747.08437796.809623<0.0001
US 292.41267.549377117.27462<0.0001
US 1 subtracted from
DifferenceLowerUpperP-value
US 220.465-4.397623345.3276230.1178

Fitted values stored in new column: Fit
Residuals stored in new column: Residuals

Result 2: Repeated Measures ANOVA page2   [Info]
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Upon finding a significant effect by pharmacy we can look at Confidence Intervals for comparison.

 1.      Average drug prices at US pharmacy 1 are somewhere between 47.08 and 96.80 dollars greater than drug prices at Aptecha. 2. Average drug prices at US Pharmacy 2 are somewhere between 67.55 and 117.27 dollars greater than drug prices at Aptecha. 3. There is no evidence of a difference in drug prices between US 1 and US 2 (the interval runs from -4.40 and 45.33 and includes zero). 

  Conclusion: 

This analysis was effective. The RM-Anova showed us evidence that the canadian pharmacy did have a difference in the mean cost of medications when compared with two US pharmacies. There was not enough evidence to show a difference in the mean costs between the two US pharmacies. 

Future Studies:

Future studies could include other drugs. Using the most commonly prescribed could have an impact on the price. Also, how were the pharmacies chosen. That could also have an impact on the price in the United States in comparison with Canada. 

 

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=72553">Drug Prices- Week 8</A>

Comments
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By nku.katie.waters
Oct 17, 2017

Hi Candace,
Good job. A few comments:
1. In addition to including the interaction plot, you should make some kind of comment on how the "no interaction" assumption seems to be satisfied.

2. Before interpreting the Tukey CIs, you should first interpret the F-stat p-value in the ANOVA table. Based on the p-value<0.0001 (F-Stat = 49.6), we do have evidence of a difference in average drug cost between at least two of the three pharmacies.

3. It is important to recognize here that these results may not apply to U.S. vs. Canada (but rather may apply only to these three particular pharmacies). To gain greater clarity on U.S. vs. Canada we would want to see a larger sample of pharmacies from each country.

4. Why is the RM-ANOVA a better choice than one-way ANOVA? We should recognize that there will be variability in cost due to the type of medication. Since there are three different pharmacies to compare it is appropriate to include “Drug” as the blocking factor. The variability in cost based on drug will be removed from consideration, thus giving greater statistical power. Please review the solutions for discussion on how the RM-ANOVA was indeed effective.

Please review the solutions and let me know if you have any questions.
By colleen.pfister28
Oct 14, 2017

Candace,
Nice work and unfortunate to see that the US has higher prices compared to Canada. I would be interested to see other medications compared for study. Depending on where you live in the US can affect your lifestyle and what health issues you may have which intern affects the medications you are on. So cost could still greatly differ for different people across the board. I do think more evidence is needed to draw better conclusion and for further study.
Colleen
By barrett.green
Oct 14, 2017

Candace,
Great job! I agree with you that knowing how the pharmacies were chosen for the study could have had an impact on the pricing. I suppose consideration of currency was taken into account for the study? That may have altered the data as well. I think a future study looking at more pharmacies and maybe more drug comparisons could give researchers much more data about pricing between the US and Canada.
-Barrett
By evva.allen
Oct 14, 2017

Candace,

This is interesting, but I could totally forsee that U.S. pharamcies would have higher prices than Canada, as that seems to be the trend in healthcare between the two countries. I agree with your future study recommendations- perhaps expand the study to generic vs. brand name drugs to see if there are difference there also. Also like you said, how can we guarantee that the pharmacies chosen are equivalent to compare? For example, Walmart always has different prices than local privately owned pharmacies in the United States.
Great job!
Evva

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