Medical statistics.

1. Select, read and summarize a paper of your own interest. The paper has to be
related to the material we have covered in class. Submit the paper and a 2-3
page report that includes a short summary of the paper, the design of the study, its
findings, the statistical methods used, and anything else you think relevant. Further,
comment 011 anything you particularly liked or disliked about the paper. In class we
briefly discussed an article published 011 http: //authoritynutrit ion. com/. The
references that articles on that website provide could be used for this exercise. [20]

2. write an R function that takes as input binomial responses and covariates and uses
the Newton-Raphson algorithm to compute the coefficients of a binomial GLM. You
could use the ‘Kidney stone surgery’ data or any other dataset that includes at least
2 explanatory variables. For the ‘Kidney stone surgery” data, some of the steps could
(but don“t have to) be done as follows
First enter the data
intercept, small=0, keyhole=0, successes, failures
r1<-c(1,0,0,234,36)
r2<-c(1,0,1,81,6)
r3<-c(1,1,0,55,25)
r4<-c(1,1,1,192,71)

Put all data in a matrix
data<-rbind(r1,r2,r3,r4)
Write the function
bglm<-function(data){
beta<-matrix(c(x,x,x)) # X’s denote the initial values of your choice
Define the likelihood, its first and second derivatives
Newton-Raphson algorithm
Finish by returning the vector of coefficients
return(beta);

Double check your results by comparing them to results from a statistical software.
Note that, more general functions can be written by allowing more inputs, such as
initial values etc. (but this is not necessary for the current exercise).

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