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　　4.2 Innovative methodology and Result analysis

　　Figure1：Flow chart of the experimental process in Part 4.2.
　　For determining the number of optimal experimental groups for this tumor chemo- sensitive assay in vitro and classifying patients according to their sensitivity to the drug (Questions 2 and 3 in Part 3), I combined classical statistical analysis methods described in Part 4.1, inflection point detection method and cluster analysis method to come up with an innovative experimental design, as shown in Figure 1.

　　Firstly, for Question 2, I have to introduce the concept of “inflection point detection” here. In a curve with an upward or downward trend, if the overall trend changes significantly after a certain point, this point is called an inflection point. This study conducted the inflection point detection using the kneed package in Python.

　　The tumor chemosensitive assay in vitro in this study set three concentration groups, namely A-group (0,4,20,100,500), B-group (0,2,10,50,250) and C-group (0,2,5,10,25, 50,100,250). Since the more data provided for curve fitting, the effect is better, I only selected the data of T-class in group C for curve fitting and inflection point detection, namely the data of 6 patients from 11T to 16T. This process conducted in Python and the results are shown below.

　　Patient Inflection point detection
　　11T 5,10,50
　　12T 5,25
　　13T 5,10,50
　　14T 5,10,25
　　15T 10,25
　　16T 2,25
　　Table1：Inflection point of 8-point group in T-class.

　　Note: In Figure 2, drug concentration is shown on the horizontal axis and cell inhibition rate on the vertical axis.
　　Figure2：Curve fitting results of 8-point group in T-class (Python).
　　As can be seen from Table 1, the inflection point occurs at the following five concentration points: 2, 5, 10, 25, and 50, which are respectively named as groups A~E. According to the results of paired T-test, there are only significant differences between A and B, and between B and E, that is P-value is less than 0.05, so I discard the concentration point 10. In addition, I set the concentration points of 100 and 250 as F and G respectively, and conducted pair-to-pair paired T-test for the three groups of E, F and G, and the results showed that there are significant differences between E and F, and between F and G, so these two concentration points were retained. At the same time, since the difference between E and F is particularly significant, it is recommended to increase the concentration point 75. Therefore, based on the above analysis, I think the following 8-point concentration combinations are the most appropriate: 0, 2, 5, 25, 50, 75, 100, 250.