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Biostatistics
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The aim of this exam is for you to illustrate that you have sufficiently comprehended the basics of survival analysis

INSTRUCTIONS TO CANDIDATES
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Instructions (Read Carefully)

The aim of this exam is for you to illustrate that you have sufficiently comprehended the basics of survival analysis, and that you can analyze a set of survival data on your own and correctly interpret the results.

The questions posed below have been on purpose formulated in a general tone in order to give you the freedom to delve into the data and find interesting patterns. These sorts of questions you will also face in your own research. In addition, to mimic again a real data situation, purposefully mistakes may have been added in the database you received. If you find any of those, it has been a part of your assignment to identify them and make a documented decision on how to handle them (i.e., you should write in your report what you did).

In your report use Word tables (i.e., do not copy and paste tables from software). It is not the purpose to give a report full of irrelevant output. You have to carefully choose the bits of output that are relevant to the statements you want to make.

Description of Database

We are interested in studying the effect of a number of variables in the time to death for patients in the late stages of Pompe disease. You received a simulated database with the following variables:

• id: patient id number

• TimeDeath: time to death (months)

• age: the age of the patients (years)

• sex: the sex of the patients

 • mutation: do the patients have a mutation in the gene of interest (‘no’ or ‘yes’)

• BM1: the values of Biomarker 1 (mg/dL)

• BM2: the values of Biomarker 2 (mg/dL)

 Each student has a different database with different features and relationships between the variables, leading to different results.

Descriptive Analysis

1. Start by producing summary statistics regarding the sample at hand (i.e., median survival time, a number of males, females, how many mutations, etc.). 

2. Following focus on the main outcome of interest, namely, the time to death. Produce descriptive figures for these outcomes and study graphically and with simple statistical tests if there are differences between males and females and the existence of mutation. 

Main Analysis – Time to Death

3. The researchers in this study are interested in the relationship between the expected time to death and the above mentioned covariates (i.e., age, sex, mutation, BM1, BM2). Build an appropriate AFT model for the time to death to answer this question. Describe all the steps you have performed to reach your final model. In particular, a. With which model you start (think about how many coefficients you can “safely” estimate)

 b. Which steps you take to simplify your initial model.

 c. How you test the assumptions behind the model.

 d. For your final model present the results you obtained in ‘simple words’ (i.e., such that a non-statistician would understand – you may also use effect plots if deemed necessary). Formulate conclusions as in a research paper.  

e. In addition, calculate the expected failure time of a male patient who is 51 years old, he did not have the gene mutation, and for BM1 he had the value 3.7 mg/dL and for BM2 the value 251 mg/dL. Explain how this calculation was done.                       

4. Do exactly the same as in Question 3 but now using a Cox model. Follow the same steps as when you fitted the AFT model. a. In addition, calculate the probability of surviving more than 6 months (and the associated 95% confidence interval) for a 50-year-old female patient, with the gene mutation and who has BM1 value 2.8 mg/dL and for BM2 the value 229 mg/dL. Explain how this calculation was done.

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