HEALTH RESEARCH & SOCIAL SCIENCE

UNIVERSITY OF PORTSMOUTH
SCHOOL OF MATHEMATICS AND PHYSICS
FIRST ATTEMPT EXAMINATION 2018/2019
LEVEL 6
M342/U20732
STATISTICS METHODS IN HEALTH RESEARCH & SOCIAL
SCIENCE
Duration: 2 HOURS
Instructions: Answer Four questions from Five provided
Additional Information: This is a SEMI-OPEN book examination
please see the Permitted section for allowed material
Permitted: TWO A4 sheets of hand-written notes are permitted.
Non-programmable calculators are permitted.
No long-term data storage calculators are permitted.
Provided: Mathematics and Statistics Formula book will be provided.
Additional Formula Booklet.
Graph Paper.
Q1. (a) A study was conducted to determine if parental smoking is a risk factor for
childhood asthma. The table below records the status of 621 children (aged 3
– 16 yrs) classified according to whether or not one or both parents are smokers:

Carry out a test to determine if there is an association between parental smoking and childhood asthma. Estimate the Odds Ratio of asthma for children
exposed to smoking parents relative to non-smoking parents, and interpret
your result. [6 marks]
(b) Previous studies have reported a relationship between pet ownership, a potential confounder, and childhood asthma. The 621 children were sub-divided
into two strata according to whether or not the family owned a pet dog or cat:

Obtain a pooled” estimate of the Odds Ratio for the effect of parental smoking adjusting for pet ownership, giving 95% confidence limits for the true
value. [9 marks]
Question 1 continued on the next page.
M342/U20732 final examination 2018/2019
(c) The study data was analysed using Logistic regression, in order to adjust for
possible confounders and identify other factors predictive of childhood asthma.
The following model was fitted to the data:
ln 1 -p p = β0 + β1S + β2A + β3P + β4M
The predictor variables studied were:

The following output was obtained from R:
Using the information provided, obtain an estimate of the OR for exposure to

Total for Q1: 25 marks
M342/U20732 final examination 2018/2019
Q2. (a) The lifetime of individuals following diagnosis of a particular disease, T (in
months), is thought to follow an exponential distribution with probability density function
f(t) = λ exp(-λt); t ≥ 0 months
Derive expressions for the survivor function S(t), the mean and median lifetime in terms of the hazard (or incidence) rate λ. [6 marks]
(b) The data below record the lifetimes of patients undergoing treatment for a
particular condition. (+” denotes a right censored observation):
ti : 19 3 26 4 60+ 11 14+ 15 23+ 39 60+ 60+ months
Assuming an exponential model, obtain an estimate of λ giving approximate
95% confidence limits. [4 marks]
(c) A randomised control trial is planned to compare a new drug to the current
(control) treatment using a Log-rank test. Patients will be followed up for a
minimum of 2 years. The (current) two-year survival rate for patients is 20%.
It is hoped that the test treatment will increase survival to 40%. How many
patients should be recruited to the study to detect this difference with 90%
power, assuming a two sided significance level of 5%? [5 marks]
(d) A randomised control trial was conducted to investigate the benefit of a test
treatment compared to placebo in the treatment of patients with an aggressive
form of incurable cancer. A total of 48 patients were recruited to the trial with
complete follow-up for the first nine months. The numbers at risk and the
number of deaths per month in group are presented in the table below:
Use a log-rank test to determine if there is a significant difference between
these two treatments. Estimate the hazard ratio, giving approximate 95%
confidence limits for the true value. Interpret your results. [10 marks]
Total for Q2: 25 marks
M342/U20732 final examination 2018/2019
Q3. (a) In the context of Randomised Control Trials briefly explain what is meant by:
parallel trial, cross-over trial, double-blind, intention to treat (ITT) analysis.
[4 marks]
(b) In a population of patients being treated for angina 20% can be expected to
experience a heart attack or death within 12 months. A new treatment is to be
compared to placebo with the main aim of reducing this risk from 20% down
to 10%. How many subjects need to be recruited to a parallel Randomised
Control Trial to detect a 10% difference with 80% power?
The same study is planned to investigate Quality of Life (QoL), measured using
the short form SF-36 questionnaire. A SD of approximately 27.0 is anticipated
based on previous studies in similar patients. Will the sample size determined
above be sufficient to detect a mean difference of 10 points in QOL with
power 90%? [6 marks]
(c) A randomised double blind parallel group trial compared cannabis extract to
placebo in the treatment of neuropathic pain in patients with multiple sclerosis.
The data below record the reduction in pain scores, measured on a Visual
Analogue Scale, following 12 weeks of treatment:

Using a parametric test, determine if these data provide evidence that cannabis
extract has an effect on neuropathic pain in patients with multiple sclerosis. [6 marks]
(d) A randomised control trial was conducted to compare the use of 50 mg Ginkgo
biloba extract LI 1370 to placebo in treating patients with memory loss. A total
of 116 patients were randomly divided into two groups of 58 by individually
matching for age (to within three years), gender and disease severity. After 6
months of treatment patients were given a task to perform which was classified
a success or failure. The following data record the outcome for the 58 matched
pairs:

Use an appropriate a test to determine if there is evidence of a significant
difference between treatments in the probability of successfully completing the
task. Give a 95% confidence interval for the difference in success rates. [9 marks]
Total for Q3: 25 marks
M342/U20732 final examination 2018/2019
Q4. (a) Briefly outline the main difference(s) between a screening test and a diagnostic
test.
Two mnemonics, SPin” and SNout”, associated with testing for disease
refer to the specificity and sensitivity of a test. Briefly explain what SPin”
stands for and the property it describes.
Patients admitted to hospital with suspected Myocardial Infarct (Heart attack)
do not always turn out to have suffered from an MI.
Creatine kinase is a biochemical marker which can give an indication of whether
someone with a suspected MI is a real MI case or has some other condition.
Blood samples taken from 220 cases of MI and 180 patients with other conditions and tested using the marker. The following results were obtained:

Calculate the Specificity of the biomarker as a predictor of an MI, giving
approximate 95% confidence limits for the true value.
Compute the Kappa statistic and comment on the agreement between the test
result and true status of a patient. [13 marks]
Question 4 continued on the next page.
M342/U20732 final examination 2018/2019
(b) Briefly explain the difference between Indirect Standardisation and Direct
Standardisation.
The data below record the number of deaths following a particular form of
surgery at hospital A stratified by age of patients together with the corresponding figures for all hospitals in the UK during one particular year.
The crude death rate for hospital A is 0.0612 (6.12%) compared to 0.0441
(4.41%) for all hospitals, suggesting that patients at hospital A experience
higher mortality rates. Briefly explain why it might be incorrect to conclude
this.
Compute the Standardised Mortality Ratio (SMR) for this hospital giving approximate 95% confidence limits. Interpret your findings. [12 marks]
Total for Q4: 25 marks
M342/U20732 final examination 2018/2019
Q5. (a) Briefly explain the main purpose of Principal Components Analysis (PCA).
Students at a south coast university study six modules during their first year.
Summary Statistics for the final percentage marks are tabulated below:
For these data discuss whether it might be appropriate to extract Principal
Components from the Covariance matrix or the Correlation matrix.
The output below summaries a PCA based on the Correlation matrix.
What criteria might you use to determine how many components to retain?
How many components should be retained in this study?
How much of the total variability in the data is explained by the first component?
How much of the total variability in the data is explained by the first two
components?
Briefly interpret the first and second components derived from these data. [12 marks]
Question 5 continued on the next page.
M342/U20732 final examination 2018/2019
(b) Describe the main difference between Cluster Analysis and Discriminant
Analysis.
Briefly outline two decisions that need to be made when performing a Cluster
Analysis.
Three measurements, X1; X2 & X3 are made on each of six objects and
the pairwise City-Block” (Manhattan) distances tabulated below: Summary
Statistics for the final percentage marks are tabulated below:
Compute the missing city-block distance between individual 3 & 4.
Apply a Single Linkage (nearest neighbour) cluster analysis to these distances
and sketch the associated dendrogram.
Discuss whether there is a clear cluster structure to these six individuals. [13 marks]
Total for Q5: 25 marks
M342/U20732 final examination 2018/2019