# Algorithm Providing Ordered Integer Sequences for Sampling with Replacement Confidence Intervals
## 4 Discussion
### Question 3  
How should a real-world data analysis be conducted?  
Let us provide the answer by taking one case study from the literature. In [12], a study was conducted with \(20\) patients subject to dermal regeneration template placement over areas with exposed bone/tendon prior split-thickness skin grafting, all being confirmed clinically and microbiologically negative for previously treated infection. Utilizing non-invasive fluorescence imaging, bacterial load was identified using a defined threshold in eight out of twenty patients. Out of eight, four developed an infection. Three of the four infections were positive for Pseudomonas.  
There are certain sampling with replacement variables in the study data. Five research questions can be formulated (the null hypothesis is that the effect being studied does not exist; the observation can be merely by chance):  
* Q3.1: _Was the detection of the bacterial load with non-invasive fluorescence imaging statistically significant in the group, or can it be asserted as being observed by chance?_ Answer: The observed proportion was 8 out of 20. The sequence of integers for \(\alpha=0.05\) and \(m=20\) is 0 0 0 1 1 2 3 4 4 5 6 7 8 9 10 11 13 14 16 18 20. The CI for \(x=8\) is [4; 12]. The answer is Yes (detection of the bacterial load with non-invasive fluorescence imaging was statistically significant in the group), with a true risk (of being in error in the coverage) of 3.6%.
* Q3.2: _Was the development of a bacterial infection a real risk for the patients following the procedure, or can it be asserted as being observed by chance?_ Answer: The observed proportion was 4 out of 20. Using the same sequence of integers, the CI for \(x=4\) is [1; 7], and the answer is Yes (developing a bacterial infection was a real risk for the patients following the procedure), with a true risk of 4.3%.
* Q3.3: _Was Pseudomonas a real threat for the patients following the procedure, or can it be asserted as being observed by chance?_ Answer: The observed proportion was 3 out of 20. Using the same sequence of integers, the CI for \(x=3\) is [1; 6], and the answer is Yes (Pseudomonas was a real threat for the patients following the procedure), with a true risk of 6.1%.
* Q3.4: _Was the development of a bacterial infection a real risk for the patients possessing bacterial load detected by non-invasive fluorescence imaging, or can it be asserted as being observed by chance?_ Answer: The observed proportion was 4 out of 8. The sequence of integers for \(\alpha=0.05\) and \(m=8\) is 0 0 0 1 2 3 4 6 8. The CI for \(x=4\) is [2; 6], and the answer is Yes (developing a bacterial infection was a real risk for the patients possessing bacterial load detected by non-invasive fluorescence imaging), with a true risk (of being in error in the coverage) of 7.0%.
* Q3.5: _Was infection with Pseudomonas a real risk for the patients possessing bacterial load detected by non-invasive fluorescence imaging, or can it be asserted as being observed by chance?_ Answer: The observed proportion was 4 out of 8. The sequence of integers for \(\alpha=0.05\) and \(m=8\) is 0 0 0 1 2 3 4 6 8. The CI for \(x=3\) is [1; 5]. The answer is Yes (infection with Pseudomonas was a real risk for the patients possessing bacterial load detected by non-invasive fluorescence imaging), with a true risk (of being in error in the coverage) of 5.9%. With the sampled data, the answer was Yes in all cases since \(0\
otin CI\).