Lecture 3 The design of scientific investigations

1. Lecture 3The design of scientific investigations 3.1 Considerations and terminology 3.2 Agricultural field trials 3.3 Clinical trials 3.4 General design considerations Statistical Methods in Scientific Research - Lecture 3

2. 3.1 Considerations and terminology Units of observation These are the items from which responses are recorded They may be people, human families, pots of tomatoes, agricultural field plots, samples of river water, washing machines, etc. One response is taken from each unit Statistical Methods in Scientific Research - Lecture 3

3. Factors These might be items under the control of the investigator: drugs administered to rats fertilizers administered to crops additives put into petrol or out of control but to be explored or adjusted for: ages of volunteers season of the year temperature during the experiment They might be quantitative (dose of drug, amount of additive) or qualitative (active or control, male or female) Statistical Methods in Scientific Research - Lecture 3

4. Responses These are the measurements of interest: did the rat develop cancer (yes or no)? what was the crop yield? how many miles per litre were achieved? There may be several different responses collected - number of tomatoes, total weight of tomatoes, quality of tomatoes There will be only one response of each type per unit of observation Statistical Methods in Scientific Research - Lecture 3

5. Analysis An exploration of the way in which the distribution of responses changes according to the values of the factors Exploratory: Find out what factors have an influence on the response Hypothesis testing: Find out whether one factor really does have an effect on response Estimation: Determine the magnitude of the effect of a factor or factors on response Statistical Methods in Scientific Research - Lecture 3

6. 3.2 Agricultural field trials - complete randomised block experiment direction of slope Statistical Methods in Scientific Research - Lecture 3

7. The factors are : extra nitrogen (N) or not (n) extra phosphorous (P) or not (p) extra potassium (K) or not (k) This gives 23 = 8 treatments The field is sloping from right to left, otherwise homogeneous: it is split into 3 blocks, internally homogeneous but different from one another Each block is divided into 8 plots which are the units of observation A different treatment is applied to each plot, the arrangement within blocks is at random Response will be yield of grain Statistical Methods in Scientific Research - Lecture 3

8.  Each block is a replicate of the others – the more replicates, the greater the precision of the experiment  Each block is complete, every treatment is included  There are 24 plots, 1 overall effect, 7 treatment effects and 2 block effects, leaving 14 degrees-of-freedom for the estimation of variability y = m + ti + bj + e, wheret1 = 0 andb1 = 0  The separate and combined effects of N, P and K can be explored, usually interactions with blocks are not fitted Statistical Methods in Scientific Research - Lecture 3

9. An analagous situation Statistical Methods in Scientific Research - Lecture 3

10. The factors are presence or absence of three petrol additives (A, B and C) The response is the emission of polluting chemicals over one hour of running Each of the each treatments (formed by combining the additives) is tried in each of three cars (which take the place of the blocks) The experimental structure is the same as the field experiment Here, car  treatment interactions may be of interest Statistical Methods in Scientific Research - Lecture 3

11. Variations and compromises The complete randomised block experiment is an ideal Often there are compromises • covariates at each plot to account for (eg. moisture content) • number of plots per block  number of treatments (eg tomato) • number of plots varies from block to block Design the experiment to come close to the ideal: the analysis will allow for the real situation Statistical Methods in Scientific Research - Lecture 3

12. Split plots The spraying machine covers 3 plots Three varieties are to be compared (for pest infestation) Statistical Methods in Scientific Research - Lecture 3

13. Such a structure is common: • children within classes • fruits within trees • repeated episodes within individuals (cross-over study) The analysis of such experiments is routine, but the nature of the experimental structure must be taken account of -if each split-plot is of size 2, then a paired t-test might be used Statistical Methods in Scientific Research - Lecture 3

14. 3.3 Clinical trials - randomised intervention studies An experimental drug (E) is to be compared with a control treatment (C) in a population of patients diagnosed with the condition in question Units of observation: individual patients Factors: treatment -experimental or control baseline prognostic factors -such as age, severity of condition Response: a measure of efficacy -reduction in blood pressure after one month - measure of functionality 90 days after a stroke - time from entry of trial to death Statistical Methods in Scientific Research - Lecture 3

15. Analysis Straightforward: Compare the patients receiving E with those receiving C in terms of the efficacy response while adjusting for baseline prognostic factors Typical strategy:  Fit a linear model (for normally distributed, binary, ordinal or survival data)  Include prognostic factors first, then add treatment: significant effect  Check whether prognostic factor  treatment interactions are important Statistical Methods in Scientific Research - Lecture 3

16. Hard part Ensuring that any differences found between E and C really are due to treatment Strategies:  randomisation  blindness Note: In agricultural field trials, all plots are to be sown and then harvested at the same time In clinical trials, patients enter one by one over a period of time, as they are diagnosed and they are treated immediately Statistical Methods in Scientific Research - Lecture 3

17. Randomisation When each patient is diagnosed, first assess eligibility and obtain consent then allocate to treatment  toss a coin (heads  E, tails  C) -completely random allocation  throw a die to allocate next four patients 1  EECC, 2  ECEC, 3  ECCE 4 CEEC, 5  CECE, 6  CCEE - random permuted blocks  phone up an Interactive Voice Recognition System (IVRS): random allocation will be made to favour comparability of the two groups in terms of prognostic factors -minimisation Statistical Methods in Scientific Research - Lecture 3

18. Randomisation Each method would be implemented by computer, either in advance (giving allocations in sealed envelopes) or on-line The random element ensures that the two treatment groups are as comparable as possible -no choosing the treatment having met the patient -no predicting the next allocation when assessing eligibility By chance, some imbalance between treatment groups may remain, so still a need to adjust for prognostic factors Statistical Methods in Scientific Research - Lecture 3

19. Blindness The patient should not know whether they are on E or C -the control group receives a placebo identical to E -this avoids bias in subjective assessments and decisions such as withdrawal from the study The treating clinician should not know patients’ treatments -this also avoids bias in subjective assessments and decisions such as withdrawal from the study Not always possible: for example surgery versus drug treatment -could use a blind assessor Statistical Methods in Scientific Research - Lecture 3

20. Analogous situations • Psychological interventions in human subjects • Educational interventions in children • Animal experiments Cluster randomised trials Clusters of units of observation are randomised to treatment • Classes of children are taught in different ways • Groups of prisoners are supervised in different ways The analysis follows the split-plot pattern Statistical Methods in Scientific Research - Lecture 3

21. The randomised clinical trial as a gold standard John Snow’s cholera study of 1854: Snow (1855), see also MacMahon and Pugh (1970) Statistical Methods in Scientific Research - Lecture 3

22. Choice of controls Neither subjects nor households could be randomised to water company, but Snow writes: In the sub-districts enumerated ... the mixing of the supply is of the most intimate kind. The pipes of each company go down all the streets, and into nearly all of the courts and alleys. A few houses are supplied by one Company and a few by the other, according to the decision of the owner or occupier when the Water Companies were in active competition. In many cases a single house has a supply different from that on either side. Each company supplies both rich and poor, both large houses and small: there is no difference either in the condition or occupation of the persons receiving the water of the different companies. In other words: nearly as good as randomisation Statistical Methods in Scientific Research - Lecture 3

23. 3.4 General design considerations  Decide on the objectives of your investigation -exploratory, hypothesis testing, estimation?  Identify the units of observation, the factors of interest -both those under your control and those outside it  Determine the responses to be collected from each unit of observation  Work out how the data will be analysed when they have been collected  Determine an appropriate sample size (next lecture)  Write a protocol for your study, recording both the considerations above and the relevant details from your own subject (and any ethical considerations)  Check with your supervisor and with a statistician Statistical Methods in Scientific Research - Lecture 3