Department of Mathematical Sciences

MA30086 Medical Statistics Open Book Examination

医学统计代写 This is an open book exam. You may refer to your own course and revision notes and look up information in offline or online resources,

Please read the Guidance for Students before attempting this exam. The Guidance contains information about submitting your exam attempt and choosing to defer.

This is an open book exam. You may refer to your own course and revision notes and look up information in offline or online resources, for example textbooks or online journals.

This exam is designed to take 3 hours (including up to 1 hour for upload) to complete.

Which questions should be answered: Answer THREE of the four questions. Only the BEST three answers will contribute to the assessment.

Additional materials needed to complete the assessment: You may use a calculator and program R for this assessment.

Further instructions: In marking, emphasis will be placed upon clear mathematical argument and precision.

Do NOT submit your rough work. Please show full working and indicate where and how you have used R.

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1.  医学统计代写

A randomised controlled trial has been conducted to assess the effect ofrecommending that face masks be worn when outside the home on the risk of infection with the Covid-19 virus. The trial recruited individuals who spend more than 3 hours per day outside the home without occupational mask use. They were randomised to either be recommended to wear a mask when outside the home or not. Those randomised to be recommended to wear a mask were also given a supply of 50 surgical masks. The primary outcome was whether or not the individual became infected with the Covid-19 virus within one month.

The table below shows the number of infections and patients according to a baseline variable recording whether they typically spend more than 4.5 hours a day outside or not.

Explain what is meant by blinding in a clinical trial and discuss the feasibility of blinding in this trial. [3]

(b) Showing your workings, use the data to estimate the risk ratio comparing the face mask group to the control group and its 95% confidence interval, without adjustment for whether they typically spend more than 4.5 hours a day outside or not. What do you conclude about the effect of recommending people wear a face mask when outside (and giving them 50 masks)? [6]

(c) Showing your workings, calculate a p-value to test the null hypothesis that

recommending to wear a face mask and providing 50 masks has no effect on the risk of infection with the Covid-19 virus. Comment on your answer in relation to your calculations in part (b). [3]

(d) State an estimate of the odds ratio comparing the face mask group to the control group, with explanation for the value you state. [2]

(e) Showing your workings, assess the evidence for whether the risk ratio for the effect of recommending people wear a face mask differs according to whether the person typically spends more than 4.5 hours a day outside or not. [6]

2.  医学统计代写

A group of researchers used routinely collected hospital data from patients hospitalised with Covid-19 to investigate how smoking status predicts outcomes. Patients were categorised as being current smokers (smoker=1) orex/non-smokers (smoker=0). The following partial output from R shows results from a Cox proportional hazards model fitted to the data. The time to event variable t was time from hospitalisation to discharge from hospital or time to censoring. The variable d is the event indicator, with d=1 indicating the time was time to discharge and d=0 indicating the time was the time of censoring. The sole covariate was the smoking status variable smoker.

Call:
coxph(formula = Surv(t, d) ~ smoker, data = mydat)

  n= 2000, number of events= 1838

           coef exp(coef) se(coef)
smoker -0.67878 0.50724 0.04782

(a) Showing your workings, use the output to calculate a 95% confidence interval for the hazard ratio comparing current smokers to ex/non-smokers. [2]

(b) Showing your workings, calculate the p-value for a test of the null hypothesis that the hazard ratio equals 1. [3]

(c) Interpret the results of the fitted Cox model and your answers from parts (a) and (b). [3]

The plot on the following page shows non-parametric estimates of the cumulative hazard functions from the two smoking groups.

(d) Given the plot, explain what you conclude about the appropriateness of the

proportional hazards assumption made when fitting the earlier Cox model. [3]

(e) Given your answer to (d), suggest with justification an alternative to Cox regression that you could use to analyse the data. Give an advantage of your alternative compared to the Cox regression for analysing these data. [3]

(f) Showing your workings, use the plot to estimate the probability that a current smoker will be discharged from hospital within 20 days. [3]

(g) In the analyses for time to discharge from hospital, patients who died were censored at the time of death. What implications does this have for your answer to part (f)? [3]