Exam May 2011, questions PDF

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PAPER CODE NO.

MATH364

EXAMINER: DEPARTMENT:

TEL. NO.

MAY EXAMINATIONS 2011 Bachelor of Science: Year 3 Master of Mathematics: Year 3

MEDICAL STATISTICS TIME ALLOWED: Two Hours and a Half

INSTRUCTIONS TO CANDIDATES

There are seven possible questions.

Full marks will be given for complete answers to FIVE questions.

Only the best FIVE answers will be taken into account.

Statistical tables of z-scores and the chi-squared distribution are provided after the seven questions Graph paper will also be provided

PAPER CODE ............... MATH364 ............. PAGE ............... 1 ............... OF ............... 16

Question 1 a) Morbidity statistics are used by epidemiologists in the analysis of ill-health. What are the prevalence and incidence of disease? Calculate the incidence rate, per 1000person years if a population contains 2000 non-diseased individuals and 88 develop a specific condition over 4 years of observation [3 Marks] b) The age standardised mortality rates for women from Breast Cancer in Southport are given in the table below.

Age Group

Observed deaths

Female population

(2001-2005)

2001 Census

National mortality rate per 1000person years

35-44

16

10,100

0.5

45-54

81

8,200

2.4

55-64

105

7,500

3.1

65-74

128

7,000

4.2

Calculate the expected number of deaths for each age group. You have been asked to perform an hypothesis test to determine whether the mortality rate from breast cancer in Southport is different from the national average. State the null hypothesis (H 0) and the alternative hypothesis (HA). Write down the test statistic you will use and perform the hypothesis test at the 5% significance level. What is your conclusion? [5 Marks] c) The prevalence of breast cancer in women aged 65+ is thought to be 12%. The local health authority wanted to set up a study to estimate prevalence and wanted 95% confidence that the estimate had an accuracy of +/- 3%. Write down the formula you would use to calculate the sample size and then determine how many individuals they need to sample. [2 Marks] d) It was decided to conduct a prospective cohort study to determine if there was an association between professional social class and the risk of breast cancer. How would you carry out such a study? The results of the study are presented in the table below.

Question 1 continues on the next page

PAPER CODE ............... MATH364 ............. PAGE ............... 2 ............... OF ............... 16

Question 1 continued

Breast Cancer Social class

Yes

No

Professional

38

667

Other

21

595

Calculate the Relative Risk for the professional group compared to the other group, calculate the 95% confidence interval for your estimate and comment on your findings. [6 Marks] e) If it was decided that a cohort study was too expensive, what other type of observational study could be undertaken? How is this type of study carried out? Why might an adjusted odds ratio be preferred to a non-adjusted odds ratio? [4 Marks]

PAPER CODE ............... MATH364 ............. PAGE ............... 3 ............... OF ............... 16

Question 2 a) A screening tool has been developed to classify the severity of Broncholitus in children. The tool classifies the severity of illness as being mild, moderate or severe. The tool was validated against the gold standard (clinical assessment) and the results are given in the table below.

Screening tool

Mild Moderate Severe

Mild 61 21 7

Clinical assessment Moderate 17 56 16

Severe 4 14 63

What statistical value would you calculate to assess the level of agreement between the tool and gold standard? Calculate the level of agreement between the tool and the gold standard, with appropriate 95% confidence interval. [5 Marks] b) It was decided to combine the mild and moderate categories into a single category (no treatment required) and to use the tool to determine those that require treatment (old severe category). Write down the new table, define sensitivity and specificity and calculate these values for the new table. [5 Marks] c) Because the test is being applied to an high risk group, it is known that the prevalence of children requiring treatment is over estimated. From previous studies the true prevalence rate is 15%. What approach might you use to estimate the positive and negative predictive values? Why is this approach often preferred by clinicians? Calculate the Positive and Negative predictive values when this approach is applied to the data in part b. [5 Marks] d) In the context of screening, what does the likelihood ratio indicate? Calculate the positive and negative likelihood ratios for the data in part b. Using the prevalence rate given in part c, calculate the post test odds of requiring treatment if a child has a positive test result. Also calculate the post test odds that a child requires treatment if they have a negative test result. [5 Marks]

PAPER CODE ............... MATH364 ............. PAGE ............... 4 ............... OF ............... 16

Question 3 a) You have been asked by a medical professional to explain a regression model that has been published in the BMJ. The model relates age (years) and smoking status (yes=1, no=0) to an individual’s cholesterol level. The model is in the form, Cholesterol =  0  1 Age   2Smoking status If  0 ,  1 and  2  0 provide a sketch of the model. What do the regression coefficients 1 and 2 represent? [4 Marks] b) Imatinhib is a drug used to treat individuals with leukaemia. A linear regression model is being constructed to estimate patient specific individualised doses (in mg). The final list of parameter values are given in the table below. Variable (Constant) Age (yrs) Gender (male=1, female = 0) Body Weight (kilograms) M420del (Wild type = 0, heterozygous = 1) M420del (Wild type = 0, homozygous=1)

 8.50 0.03 1.42 0.04 -0.91

P value...