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Vaccination and severe COVID in Israel

统计分析作业代写 Background mRNA vaccines from Pfizer-BioNTech and Moderna received authorization for emergency use in the U.S. after being found to be

Background

mRNA vaccines from Pfizer-BioNTech and Moderna received authorization for emergency use in the U.S. after being found to be more 90% effective in randomized clinical trials. However, these trials preceded the emergence of COVID-19’s Delta variant. In countries where that variant is present, does the vaccine remain as effective? We don’t have experimental data to answer this question, but we can use public health data from Israel to try to approximate what a randomized trial might have given us. The same data can be used to explore a pitfall in the use of observational (non-randomized) data to answer questions like these.

Materials and Methods 统计分析作业代写

Data

The severe COVID data, from Israel’s national health service (via covid-datascience.com) as of August 15, 2021, are as follows:

ages	cases_unvax	cases_vax	pop_unvax	pop_vax
12-15	1	0	383,649	184,549
16-19	2	0	127,745	429,109
20-29	4	0	265,871	991,408
30-39	12	2	194,213	968,837
40-49	24	9	145,355	927,214
50-59	34	22	84,545	747,949
60-69	50	58	65,205	665,717
70-79	39	92	20,512	464,336
80-89	32	100	12,683	208,911
90+	16	18	3,132	46,602
all 12+	214	301	1,302,910	5,634,632

You can read the data directly into R using

read.delim("https://dept.stat.lsa.umich.edu/~bbh/s485/data/israel_severe_covid_2021_08_15.tsv")

Statistical analysis 统计分析作业代写

Your report should present:

1. For each age group a, a 95% confidence interval for the underlying rates of severe disease in the vaccinated (p_a^(v)) and unvaccinated (p_a^(u)) subpopulations.
2. For each age group a, a point estimate and 95% confidence interval for the vaccine efficacy, 1 − p_a^(v)/p_a^(u).
3. The estimated vaccine efficacy as calculated without adjustment for age, 1 − p^(v)/p^(u). (Where p^(v) and p^(u) denote severe COVID-19 rates across vaccinated and unvaccinated Israelis aged 12 and older.)

The confidence interval procedure you use for (1) must be defensible from the perspective articulated by Brown, Cai and Dasgupta (2001, “Interval estimation for a Binomial proportion”). Avoid any method that has been shown to be inferior to some other method we’ve learned about that you could have implemented. For (2), don’t track down or invent a confidence interval procedure for vaccine efficacies; instead, report the largest and smallest vaccine efficacies that are compatible with intervals you reported in (1).

For (3), present your overall efficacy estimate in the Results section of your report along with age-specific estimates and confidence intervals, but don’t present a confidence interval along with it. Rather, flag it as potentially misleading. Be sure to follow up with a clear explanation of what’s problematic about it, in the Discussion section of your report. (Regarding “Results” and “Discussion” sections of your report, see “Writing assignment (both options)”, below.)

Format: 统计分析作业代写

Prepare a brief paper describing your findings, along with a separate reproducibility appendix. Your report’s primary audience should be assumed to consist of college-educated professionals interested in COVID vaccines’ population efficacy (option A), or in U.S. economic opportunity (option B). They are not likely to have specialized statistical training, but they are likely to have passing acquaintances with statistical concepts such as sampling variability, standard error and confidence interval.  When you use statistical methods other than methods they would likely have learned when they took intro stats, you should be sure to indicate a reason for your choice. 

Organize your paper into 4 sections: Introduction, Methodology, Results, and Discussion. Aim for a length of 5-7 pages, double spaced and in 11 or 12 point font. This can include 1-2 figures or tables. Tables or figures that are essential to your story must go into the paper, and count toward the page limit; the reproducibility appendix does not count toward that limit.

Introduction. 统计分析作业代写

Presents and briefly motivates or justifies the research question; describes the data. Previews what you will do in the analysis. Indicates aspects of the research question, data, analysis strategy or findings that are likely to be surprising to the primary or secondary audience of the report.

Methods.

Your data and its origins should be described here, including information about the sample, mode of collection and mode of distribution that may be important to your analysis. State what methods of statistical analysis you used, along with their most important or relevant assumptions. Methods requiring specialized formulas and/or algorithms should not be explained in detail; rather you should provide a citation or citations to textbooks and/or research articles that discuss them. Don’t linger on methodological questions that may be of interest to you and/or your professor but are not needed to follow your analysis. (If you’d like to discuss why you selected the methods you used over other options, for example, put that in Discussion, not Methods.) Do indicate why you chose the method you did, particularly if your audience is likely to be expect or be more familiar with other methods. Highlight aspects likely to impress your audience.

Results. 统计分析作业代写

Present your weekly positivity or upmover confidence limits in a readable, clearly labeled table or graphical display. Numbers in tables should be reported to 2 or 3 significant digits. Tables and figures should be clearly labeled, and should be accompanied by a caption that’s sufficiently informative that a busy reader can understand the table while only skimming the rest of the text. Patterns in the table or figure should also be concisely described in the text. If you’re reporting hypothesis tests, emphasize whether the findings supported or did not support research hypotheses, not the p-value or whether the null was rejected. If presented, estimates and standard errors should be reported to 2 or 3 significant digits.

Discussion.

Start by summarizing your substantive findings in plain English. Go on to discuss both methodology and substantive results. If the method you choose has known shortcomings, or isn’t a perfect fit to the data or research question, acknowledge that here. Also say whether and how the shortcomings could in principle cause your findings to be incorrect or misleading, and offer an appraisal of the likelihood of that having occurred. (Do this without beating up on your own work any more than you need to to acknowledge the limitation.) If you used a different method than members of your primary audience may expect, explain advantages of your method. For your substantive discussion, address the bearing of your findings on such matters of public concern as the likely efficacy of current COVID vaccines against the Delta variant.

REPRODUCIBILITY APPENDIX 统计分析作业代写

Submit an edited, commented, reproducible R Markdown file containing all computations for your paper 1. (Detailed comments on format to be discussed during mtg1d.)  

Obtaining the data

If you’re doing Option A, Vaccination and severe COVID, then you can get the data set from 

https://dept.stat.lsa.umich.edu/~bbh/s485/data/israel_severe_covid_2021_08_15.tsv

or from the assignment prompt. To read the data directly into R, storing it as a data frame named “`covid`”, do 

covid = read.delim("https://dept.stat.lsa.umich.edu/~bbh/s485/data/israel_severe_covid_2021_08_15.tsv")

If you’re doing Option B,  Economic upward mobility in the U.S., then you should use one of 10 distinct data sets, as determined by your UMID number. 

If the last digit of your UM ID is 0, then get data from “http://dept.stat.lsa.umich.edu/~bbh/s485/data/mobility0.csv”.  If your last digit is 1, get your data from http://dept.stat.lsa.umich.edu/~bbh/s485/data/mobility1.csv .  And so forth, up through http://dept.stat.lsa.umich.edu/~bbh/s485/data/mobility9.csv.  To read the first of these directly into R, do

mydata = read.csv("http://dept.stat.lsa.umich.edu/~bbh/s485/data/mobility0.csv")

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