Is PCR examination useful and needed ?

Paper details:

ORDER STATUS: REVISION. Please revise the final according to the comments below Client: I told you that your calculation is not what I required and not enough as math Internal assessment paper. So PLEASE USE THE PRECONDITION TAHT I WROTE ITDOWN BELOW, As of September 1, 2020, a total of 68,712 people were infected in Japan. If we reduce 57,735 people who recovered from this and 1306 people who died, there are now 9,671 people who are currently infected. However, some experts say that it’s not amusing to actually have 10 to 20 times more patients of Covid-19. So, let’s estimate that actual number is 20 times. It means that there are 193,420 infected people in Japan. Since Japan has a population of 126.55 billion, it means that 1 in 654 people may be infected. We assume that 1 in 654 is infected. P ( Infected) = 1/10000 P( Not infected) = 9999/10000 P( Negative | Infected) = 1/10 P( Positive | Infected) = 9/10 P( Positive | Not infected) = 1/1000 P( Negative | Not infected) = 999/1000 P( Positive / infected) = {P (Positive | Infected) × P (infected)} / P (Positive | Infected) × P (Infected) + P (Positive | Not infected)× P( Not infected) = (9/10×1/10000) ÷ (9/10×1/10000 + 1/1000 × 9999/10000) = 900/ (900 + 9999) = 8.3% This means that Even with a positive result, there is only 8.3 percent chance of being infected. Conversely, the probability of non-infected false positives is 91.7 percent. The current PCR tests’ sensitivity is said to be about 50 to 70%, on the other hands, the specificity is about 99%. But this number is only an estimation, therefore, we cannot be certain about the number. Now, this essay aims to calculate both. 1 What sensitivity should it be to have a credibility on PCR test, assuming the specificity is same as the current estimation. 2 What specificity should it be to have credibility on PCR test, assuming the sensitivity is same as the current estimation. We say that the if 95% is correctly tested, meaning the probability of test positive, given people infected is 95%, the PCR test is credible. By calculating this, it is possible to know whether PCR test is credible or not. If both sensitivity that is calculated firstly, and the specificity calculated secondly, on this essay is too different from the current estimation, we can say that the PCR test is not credible. It is because even the current estimation is just an estimation, the actual test certainty should be not very different from it. 1. What sensitivity should it be to have a credibility on PCR test, assuming the specificity is same as the current estimation? Dependent variable: P( Positive├|infected┤) Fixed variable: specificity, fraction of people infected, percentage certainty to be credible Let test certainty be x(%) Now we can write down these probability P (infected)=150/(100000 )= 0.0015 P( not infected) =99850/100000 = 0.9985 P( negative├|infected┤)=x/100 = 0.01x P( Positive├|infected┤)=((100-x))/100= 1-0.01x P( Positive ├| not infected┤)=1/100 =0.01 P( negative ├| not infected┤)=99/100 =0.99 For the new corona PCR test, we assume a sensitivity of 50-70% (calculated here as 70%) and a specificity of about 99% So in this situation, the set up would be like this P (infected) = 150/ 100000 = 0.0015 P( not infected) =99850/100000 = 0.9985 P( negative / infected) = 3/10 = 0.3 P( Positive / infected) = 7/10 = 0.7 P( Positive / not infected) = 1/100 =0.01 P( negative / not infected) = 99/100 =0.99 P( Positive / infected) = {P (Positive /infected) × P (infected)} / P (Positive /infected) × P (infected) + P (Positive / not infected)× P( not infected) = (0.01x×0.0015)÷ ｛ 0.0015×(1-0.01x)+ ( 1- 0.0015)× 0.01 ｝ =x/(100-x) % Now, we can write down the graph on x and P( Positive / infected) and the 95% boarder. To be 95% accurate, we can calculate below: 95=x/(100-x) x=98.96% meaning that the probability that the sensitivity should be to be 95% certain is about 99%. This number is too different from current estimation of 50~70% so, this results PCR test in Japan is not very credible. From these results, the PCR test is questionable to be used in Japan. Therefore, the other different method that can be used in Japan is necessary to be developed. But the calculated result above is not very reasonable because only either sensitivity or specificity is very developed cannot happen. So, what sensitivity and specificity should it be? Now Changing both numbers (sensitivity and specificity) to be credible, assuming the fraction of these is not different from the PCR test Fraction of these on PCR test is Sensitivity/specificity = 30%/1% = 30 Now let the sensitivity be x Specificity =x/30 Independent variable: sensitivity, specificity Dependent variable: P( Positive├|infected┤) Fixed variable: fraction of people infected, percentage certainty to be credible, fraction of sensitivity/specificity Now we can write down these probability P (infected)=150/(100000 )= 0.0015 P( not infected) =99850/100000 = 0.9985 P( negative├|infected┤)=x/100 = 0.01x P( Positive├|infected┤)=((100-x))/100= 1-0.01x P( Positive ├| not infected┤)=0.0333x/100 =0.000333x P( negative ├| not infected┤)=0.0333x/100 =0.0333x P( Positive / infected) = {P (Positive /infected) × P (infected)} / P (Positive /infected) × P (infected) + P (Positive / not infected)× P( not infected)= please calculate this. What you have to do is to put the exact same paragraphs in an essay in correct place and develop the study from THESE paragraphs. I know those paragraphs are great, but I do not know how to fit in this internal assessment. So I want you to fit these in an essay. Also, calculate the last part of calculation to get an answer of last equation. INITIAL INSTRUCTIONS: This is IB course task called internal assignment for math, and I want you to write about PCR test which is about corona virus. You have to follow the IB rubric to finish this essay. So please check the IB math internal assignment rubric. https://www.lanternaeducation.com/ib-blog/how-to-structure-and-format-your-math-ia/ This site and the one on the material box will be useful for you. In this essay, I want you to use Bayes theorem to calculate the number. And then, you need to prove that PCR test isn’t useful as the result of Bayes’ theorem calculation. In this case, I want you to focus on country Japan, so use the Covid-19 data from Japanese government. You definitely need a lot of data and have to make graphs in order to achieve good grade. In addition, in this essay, you have to explain literally everything. For instance, when you use Bayes’ theorem, you need to explain what that is, and what you can do from that. I have made an essay about this by myself, but my professor told me it wasn’t very good, in particular, the structure and explanation was inferior. Hence please work from scratch. But please look at mine once, and them you might see what I was trying to do and what I want. Especially one written by red letters have significant ideas, because the guy from Cambridge wrote it down in this part. So please look at them, if you think it helps, then use it. I attached some 3 samples that got graded in high marks. Also there are comment and evaluation from the professor for each paper. Therefore, you are able to check what they want from this essay. SO please look through everythiagnng and make sure you know how to do this task and how you can get good grade on it.