In the pharmaceutical industry, quality engineers are responsible for maintaining the quality of drug products produced in the manufacturing process. The key to quality is an assessment of product characteristics through repeated measurements of the variable of interest. When the variable is the concentration of a particular constituent in a mixture, the process is called an assay. For the purpose of this analysis, we focus on a chemical assay to determine how fast a solid-dosage pharmaceutical product (e.g., an aspirin tablet or capsule) dissolves. Since variation in the dissolution of the drug can have harmful effects on the patient, quality inspectors require a test that accurately measures dissolution.
Two statisticians Russel Reeve and Francis Giesbrecht explored the dissolution characteristics of a new immediate-release drug product manufactured by a well-known pharmaceutical company. An immediate-release product is designed to dissolve and enter the bloodstream as fast as possible. To test for dissolution of the solid-dosage drug, the company uses an apparatus with six vessels or tubes, each tube containing a dissolving solution. Drug tablets or capsules are dropped and analyzed using high-performance liquid chromatography (HPLC). The HPLC device quantifies how much of the drug is in the solution; this value is expressed as percent of label strength (%LS).
Table. Dissolution Test Data (Percent Label Strength)
|
Site
|
Time (min.)
|
Vessel 1
|
Vessel 2
|
Vessel 3
|
Vessel 4
|
Vessel 5
|
Vessel 6
|
|
New Jersey
|
20
|
5
|
10
|
2
|
7
|
6
|
0
|
|
40
|
72
|
79
|
81
|
70
|
72
|
73
|
|
60
|
96
|
99
|
93
|
95
|
96
|
99
|
|
120
|
99
|
99
|
96
|
100
|
98
|
100
|
|
Puerto Rico
|
20
|
10
|
12
|
7
|
3
|
5
|
14
|
|
40
|
65
|
66
|
71
|
70
|
74
|
69
|
|
60
|
95
|
99
|
98
|
94
|
90
|
92
|
|
120
|
100
|
102
|
98
|
99
|
97
|
100
|
Based on the sample data provided above, do the two sites produce equivalent assay results?
(Apply test of hypotheses methods; eight-step procedure, P-value approach, and confidence interval approach to come up with your conclusions. State all the assumptions you make to perform this analysis. Verify that all the conditions for statistical analysis are fulfilled before performing the analysis).
Note:
- Calculate all the descriptive statistics for the data set.
- Perform hypothesis testing for each time period.
- Use both scenarios when, variances are equal and not equal.
- Perform pair-wise t-test to see if the result of analysis changes.
- Draw box-plots for each time period for each of the sites and compare them.
- Check for normality of the data set for each time period before proceeding with the statistical analysis.