Choose 2 Exercises... Statististics

Module Exercise 2: Public health (large area) epidemiology

The exercise:

The Australian government Department of Health (federal) produces reports each year containing data on notifiable diseases which are of great use to those studying changes in disease distributions with space or time with the aim of planning country-wide control initiatives. To facilitate similar regional operations, states and territories produce annual Public Health Bulletins, zooming-in on the data at a higher level of resolution.

Part 1: Access a table for NSW showing disease incidence for the years 2003 to 2012, and produce labelled, computer-generated time trend graphs for giardiasis and HIV infections using an application such as Excel®.

Part 2: Briefly discuss two possible reasons why each of these diseases might have increased or decreased over this period. Reference this discussion.

Aims of the exercise:

i. To acquire skills in the extraction, presentation, analysis and use of quantitative information from a large-area epidemiological report.

ii. To develop early perspectives on risk factors for specific diseases, and insight as to how and why these might change with time.

Hints:

i. Public Health Bulletins usually include data up to the year before they were published (eg: a 2012 bulletin usually contains data up to 2011).

ii. Departments are sometimes a few years behind with their bulletins, so a bulletin for the year 2013 might not be available until 2015.

iii. For comparison of disease incidence by places or by year, rates (not absolute numbers) are always used in epidemiology. Disease notification rates are usually given per 100,000 population.

Module Exercise 3: Bivariate linear regression analysis (correlation)

Background to the exercise:

As a preliminary step in a large-scale study of asthma in Armidale, New South Wales, you are asked to carry out a study to identify the impact of ambient atmospheric general particulate pollution (PM10) on the incidence of asthmatic wheeze in primary school children. Thermal inversions can occur periodically in the Armidale basin, trapping pollutants from point and diffuse sources in the lower atmosphere.

To ensure an accurate medical diagnosis you select all primary school children attending a day clinic over a 30-day period in April. In this month, other “confounding” risk factors (such as rainfall) are at relatively low levels, and therefore to some extent controlled.

From trained clinical staff you obtain a daily record of asthmatic wheeze incidence in children presenting for all medical conditions at the clinic during the study period. The daily air quality record is obtained from the Department of the Environment and a short latency period (minutes to hours) between exposure to ambient air particulates and production of symptoms is assumed. You produce the tabulated data shown on the next page.

The exercise:

Part 1: Plot a graph showing the relationship between asthma wheeze and ambient atmospheric particulate matter (PM10) using a recognised computer application such as Excel®. Add a computer-generated line of best fit, assuming a linear relationship. Present the graph for assessment with a comment on the type of correlation (direct or inverse), its electronically-computed strength in terms of Pearson’s Product Moment Correlation Coefficient r (some versions of the graph on Excel also give this), and a qualitative interpretation of this result (eg: “low correlation”, “moderate correlation”, etc.)

Part 2: Using the formula and table given in the module notes, hand-calculate Pearson’s Product Moment Correlation Coefficient, r. Submit the tabulation used to generate values for the algebraic formula, along with your calculated value for r. Comment on the possible reason for any differences noted between the result obtained in parts 1 and 2.

Aim of the Exercise:

i. To gain an understanding of the use of bivariate linear regression analysis as a fundamental but powerful epidemiological analytical tool.

ii. To gain a conceptual idea of an industrially generated, environmental risk factor for an important health condition.

Day	Total number of children with asthmatic wheeze	Total number of children attending the clinic that day	Ambient atmospheric particulates (PM10 in µg/m3)	Blank column for calculated values
1	11	420	40
2	8	230	45
3	11	190	90
4	24	550	60
5	31	643	50
6	39	710	60
7	39	560	360
8	26	302	320
9	19	200	110
10	31	587	70
11	22	589	80
12	21	632	64
13	14	585	50
14	27	602	50
15	22	320	130
16	16	245	220
17	24	558	100
18	26	570	60
19	42	603	40
20	36	555	40
21	46	599	100
22	17	197	160
23	16	197	190
24	26	520	80
25	22	476	50
26	19	600	40
27	14	557	30
28	17	481	40
29	10	225	50
30	10	190	40

Hints:

i. If the question looks confusing and perplexing you probably need to go back to the module notes where the approach is clearly explained, and work through an example.

ii. When finished check your calculations thoroughly as marks are awarded for both method and the correct answer. With care it is relatively easy to score 100%.

iii. The first step when working with raw data is always to classify (ie: to construct a table). When in doubt, tabulate, when masses of numbers will always become clearer.

iv. Ensure accuracy by using one more decimal place in your calculations than you intend to give in your answer.

v. Use the formula in the module notes rather than the one given in text books, which is primarily for statisticians.

vi. When comparing health states (diseases and fitness) always use rates.

vii. Excel® does not do as much as SPSS and Minitab, but is probably the most user-friendly program to use, and links well with Word®. For example, values in the Word table can be cut and pasted into Excel®. Adding the line of best fit in Excel® involves highlighting the graph first by clicking on it, when the menu tab for this function will appear.

Module Exercise 4: Association analysis

The exercise:

As a consultant health scientist with an engineering group you are contracted by the local authority of a small rural Australian town to investigate a recent outbreak among the residents of cramps and diarrhoea producing frequent loose and pale, malodorous, greasy stools.

You inspect the water supply and find it is pumped from a local creek directly into a large concrete reservoir without filtration, where it undergoes a 24-hour settlement before being subject to in-line chlorine gas disinfection and pumping to a gravity distribution tank on a hill, from which it enters the local reticulation to 1,900 residences. The chlorine residual in the reticulation has been checked by the district water chemist as 1 mg/l at the typical house standpipe, and the creek is able to supply the volume of water needed while other supplies tend to become unreliable in the dry season. Tests carried out four times a year show the water supplied to the houses to be free of E coli faecal indicator, and low in chemical pollutants such as heavy metals, BTEX and pesticides.

You take water samples at five of the houses for E coli (EC) and enterococci (Ent) indicator and while waiting for the results from a laboratory in a capital city initiate a health survey, receiving forms back from 630 of the 5,000 residents. Of the 400 residents who chose to drink town water, 220 became ill. However 87 of those who drank alternative water only (tank, borehole or bottled water) also reported becoming ill. Some residents comment that the town water sometimes has a “bad” taste and odour whereas others say they have always drunk the water and have never experienced any health problems.

Part 1:

Apply a non-parametric test of association to the survey data in order to decide whether there is a statistically significant association between drinking water from the piped water supply, and the incidence of diarrhoea. Here calculation of rates is not necessary as the appropriate statistical test automatically generates ratios (a basic type of rate).

Perform the test based on the method shown in the notes, using a calculator and any statistical tables needed, and present the results showing all tabulations and working. For those who wish to check their answer using Excel®, please note that this application gives the result as a statistical probability, p, and this will be a different value to that produced in your hand-worked answer.

Part 2: With regard to your survey result, describe one important short-term (immediate) recommendation and one important long-term recommendation you would make to Council.

Aim of exercise: To gain an insight as to the use of association analysis in the solution of a health problem with a single health state and one suspect risk factor, and to gain skills in using epidemiological results to develop important short- and long-term solutions to a public health problems.

Hints:

i. A good starting point in a public health investigation is to use the symptoms to identify what type of disease might be involved, then develop an initial hypothesis of how it might have spread.

ii. Next look at the environmental circumstances to see if known risk factors for the identified disease are present to support your hypothesis.

iii. finally carry out statistical analysis to support your hypothesis and to produce some figures to enable managers to motivate for resources in order to take action.

iv. Finally send of laboratory samples for pathogens to confirm your hypothesis.

Values of chi-squared to act as a standard for comparison.

Module Exercise 5: Relative risk analysis

Exercise:

146 cyclists attended a convention dinner at a hotel and on returning to their rooms a few hours afterwards 84 started to feel nauseous and began vomiting, without accompanying fever or diarrhoea. With a team of trained interviewers you visit all of the players and collect the following information:

Food eaten	Cyclists ill	Cyclists not ill
Bruschetta with liver pate	38	82
Corn chowder	18	44
Thai fish cakes	22	43
Chicken in aspic	79	31
Greek salad	70	70
Fruit flan	38	6
Coffee	29	31
Tea	33	30

Part1:

Showing full tabulations and working, calculate the relative risk associated with each food eaten, and finally provide a ranked table of foods eaten, showing relative risks.

Part2:

Identify the type of food poisoning, the common food ingredient (if any) which might have caused it, and briefly describe the circumstances under which the agent might have been introduced and the toxin developed in the food.

Aim of exercise:

i. To gain an insight as to the use of epidemiological risk analysis in identifying the most likely environmental source of disease from a number of potential co-sources.

ii. To use qualitative knowledge to support quantitative information generated by risk analysis, in order to reach sensible conclusions which can be applied to successful, early intervention.

Hints:

i. When confronted with analysis, always start by constructing tables with totals, in this case, one for each food type so that you can compare results from each table.

ii. Each item in the above table is a “mixed food”. Ultimately you need to know what ingredients are in each to carry out a proper investigation. Consult recipes.

iii. Identify the most likely food poisoning type from the symptoms, then identify likely sources and growth factors for the relevant food poisoning bacterium from the literature.

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