Answers to these exercises can be found in Part 4, at the end of the chapters.
1 1.9.1 Rounding and significant digitsRound the following numbers to two decimal places. Use the rules plus common sense.12.2345144.567373.66513.665299.4545Round the same numbers to three significant digits.
2 1.9.2 Interpreting data: does screening save lives?62 000 women in a health insurance scheme were randomly allocated to either a screening programme for breast cancer, or no screening. After 5 years, the following results were observed (Table 1.4):Does screening save lives? Which numbers tell you so?Among the women in the screening group, the death rate from all other causes in the ‘Refused’ group was almost twice that in the ‘Examined’ group. Did screening cut the death rate in half? Explain briefly.Was the study blind?
3 1.9.3 Hypothesis and null hypothesisIn a study designed to assess whether undernutrition is a cause of short stature in poor inner‐city children:State the hypothesis (H1)State the null hypothesis (H0)Consider:confounding factorssources of systematic biasConsider ways to minimize the effects of confounding and systematic bias
REFERENCES
1 1. Popper Karl R. Conjectures and Refutations. The Growth of Scientific Knowledge. 5th edition. Routledge. London. 2002.
2 2. Fisher RA. Design of Experiments. 7th edition. Oliver and Boyd. London. 1960.
3 3. Juster Norton. The Phantom Tollbooth. Random House. New York. 2000.
4 4. Bradford Hill A. The environment and disease: association or causation? Proc R Soc Med. 1965 May; 58(5): 295–300.
5 5. Bradford Hill A. A Short Textbook of Medical Statistics. 11th edition. Hodder and Stoughton. London. 1985.
6 6. Fedak KM, Bernal A, Capshaw ZA, Gross S. Applying the Bradford Hill criteria in the 21st century: how data integration has changed causal inference in molecular epidemiology. Emerg Themes Epidemiol. 2015; 12: 14. doi: https://doi.org/10.1186/s12982‐015‐0037‐4 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4589117/
7 7. Shein‐Chung Chow, Jen‐Pei Liu. Design and Analysis of Clinical Trials: Concepts and Methodologies. 3rd edition. Wiley.London. ISBN: 978‐0‐470‐88765‐3. 892. January 2014
8 8. Medical Research Council. Developing and Evaluating Complex Interventions: New Guidance. Medical Research Council. London. 2008. https://mrc.ukri.org/documents/pdf/developing‐and‐evaluating‐complex‐interventions/
9 9. Rothman K. Epidemiology: An Introduction. 2nd edition. Oxford University Press. 2012.
10 10. Margetts B and Nelson M. Design Concepts in Nutritional Epidemiology. 2nd edition. Oxford University Press. 1997.
11 11. IBM SPSS Statistics. Version 24. © Copyright IBM Corporation and others, 1989, 2016.
Notes
1 1 As you can see, I am already beginning to hedge my bets. I am not saying that we will never find absolute truths or wholly objective observations. I am saying that it is unlikely. How unlikely is the basis for another discussion.
2 2 My favourite description of the world is Proposition 1 from Wittgenstein’s Tractatus Logico‐Philosophicus: ‘The world is everything that is the case’. The Propositions get better and better. Have a look at:http://en.wikipedia.org/wiki/Tractatus_Logico‐Philosophicus, or Wittgenstein for Beginners by John Heaton and Judy Groves (1994), Icon Books Ltd., if you want to get more serious.
3 3 Sherlock Holmes to Watson in: The Scandal in Bohemia
4 4 The term ‘population’ is defined in Chapter 2. It is not limited to the lay definition of all people living in a country. Instead, we can define our ‘population’. In the example above, we are talking about the population of all animals (from yeast to elephants). But we could equally well define a population as all women between 35 and 54 years of age living in London, or all GP surgeries in Liverpool. More to come in Chapter 2.
5 5 I presume he means men and women. And children. Or ‘humans’. Use of the term ‘men’ was common to his time of writing. Don’t take offence. The point he is making is important.
6 6 You will see that I keep putting the word ‘truth’ in single quotes. This is because although we want to test whether or not our hypothesis is true – it is, after all, a statement of what we believe to be true – we will never be able to collect measures that are wholly accurate. Hence, the truth is illusory, not an absolute. This is what the single quotes are intended to convey.
7 7 ‘The term “belief” is taken to cover our critical acceptance of scientific theories – a tentative acceptance combined with an eagerness to revise the theory if we succeed in designing a test which it cannot pass’ [1, p. 51]. It is important to get used to the idea that any ‘truth’ which we hope to observe is likely to be superseded by a more convincing ‘truth’ based on a more robust experiment or set of observations using better measuring instruments, and which takes into account some important details which we did not observe the first time.
8 8 This is the hypothesis – short and sweet. The study protocol will specify which subjects we choose, the dosage of the supplement, how often it is administered over what period, how walking distance is measured in a standardized way, what we mean by ‘improve,’ whether we measure blood parameters to confirm compliance with the protocol, etc.
9 9 The word ‘data’ is plural, by the way – she should have said ‘I have collected all these data’ – but we will come to that later.
10 10 The UK rules governing labelling and packaging can be found here: https://www.gov.uk/food‐labelling‐and‐packaging/nutrition‐health‐claims‐and‐supplement‐labelling. Two things are immediately apparent: there are lots of exceptions; and the EU has a lot to say.
11 11 Randomization is usually carried out by computer. You could do it equally well by simply tossing a coin, but if the coin is not tossed in exactly the same way for every pair, the randomization may be biased by the way in which the coin was tossed from one matched pair to the next. This introduces additional ‘noise’ in the system and is easily avoided by using the computer to generate the random numbers needed.
12 12 On the other hand, keep all the significant digits when doing your calculations. We will see how this works in later chapters.
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