SJS SDI_11 Design of Statistical Investigations Stephen Senn 1 General Introduction.
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Transcript of SJS SDI_11 Design of Statistical Investigations Stephen Senn 1 General Introduction.
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Course Outline
• General Introduction
• Experiments
• Observational studies
• Sample surveys (and other sampling schemes)
NB Each of these fields is huge and all that is attempted is a brief introduction
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General Warning
• Your lecturer is not equally experienced in these fields
• I know more about experimental design than the other two
• Examples from my personal experience tend to be drawn from pharmaceutical research and development or other medical applications
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Example Exp_1A Simple Experiment
• Four experimental p38 kinase inhibitors
• Vehicle and marketed product as controls
• Thrombaxane B2 (TXB2) is used as a marker of COX-1 activity (low values bad)
• Six rats per group were treated for a total of 36 rats
• At the end of the study rats are sacrificed and TXB2 is measured.
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a vehicle b marketed c d
Treat
0
100
200
300
txb2
Thrombaxane B2 (TXB2) inhibitionFour experimental p38 kinase inhibitors
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Specific Features of this Design• Several experimental treatments
• Two controls– active– neutral
• Six replicates per treatment
• Several tests compounds– no ordering
• No blocks– rats considered exchangeable
The meaning and relevance of these terms will be explained during the course
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Example Obs_1An Observational Study
• Case-control study (Fine et al Lancet, 1986, Quoted in Clayton and Hills)
• Does BCG protect against leprosy?
• BCG scar status in a population survey were available
• Data from 260 leprosy cases were obtained
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Fine et al
BCG Scar LeprosyCases
PopulationSurvey
TOTAL
Present 101 46028 46129
Absent 159 34594 34753
TOTAL 260 80622 80882
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Case-Control Study• Note that this is sampled by outcome
• The number of these is fixed
• Exposure is measured
• In a clinical trial, patients are assigned the exposure (the treatment)
• The outcome is measured
• An experiment involves manipulation
• Case-control does not
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Example Surv_1A Sample Survey
• Population of pharmaceutical record forms in Pembury Hospital, Tunbridge Wells
• Thousands of such forms available• A sample of 108 forms was chosen from patients
discharged between 1 July and 31 December 1976– Records chosen at fixed intervals
• Number of prescriptions recorded on each was noted
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0
10
20
30
0 2 4 6 8 10
number of prescriptions
fre
qu
en
cy
Distribution of Number of Prescriptions per Form
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Purposes of Statistical Investigations
Past/Present Future
Causal InferenceExperimentsObservational
Decision- making
DescriptionSurveys
Prediction
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Problem to Bear in Mind
• We can only study past/present
• We can construct formal theories of inference only about the past/present
• We often wish to make inference about the future
• This requires an ‘extra-statistical’ element– Most naively an assumption that the future is
like the past
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Example
• The effect of streptomycin on TB
• Trial carried out by Austin Bradford Hill and colleagues 1947
• Treatment highly effective
• Is it still as effective?
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Experimentation v Sampling
Experiments• Causal purpose• Convenient material• Allocation of
treatments crucial– Randomisation
Sampling• Descriptive purpose• Representative
material• Choice of sample
members crucial– Random sampling
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Caution
• These two are sometimes confused
• The growth of modelling approaches tends to increase the confusion
• Experiments rarely use representative material
• Surveys (and other samples) usually do.
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Basic Design CycleObjective
Tentative Design
Potential Data
Possible Analysis
Possible Conclusions
Relevant factors
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Questions 1Exp_1 Rat TXB2
• How do you decide which rat gets which treatment?
• How would you analyse these data?
• What use will be made of these data?
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Questions 2Obs_1 Fine et al
• What difference would it make to the precision of the conclusions if the population survey had been smaller?
• What difference would it make if there had been fewer leprosy cases?
• How would you test for an association between BCG and leprosy?
• What interpretations are there for an association?
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Questions 3Surv_1 Pharmaceutical Record Forms
• What is a simple random sample?
• In this specific case how would one choose such a sample?*
• Suppose that the sample of 108 forms was chosen from 5,000. What should the size of the sample have to be if there were 10,000 to choose from?
* The sample chosen in this example was not a simple random sample
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Suggested ReadingExperimental Design: Mead, R. The Design of Experiments, Cambridge University Press, Cambridge, 1988
Clarke, G.M and Kempson, R.E.Introduction to the Design and Analysis of Experiments, Arnold, London, 1997.
Case-control Studies, Breslow and Day, 1980, Statistical Method in Cancer Research, vol 1
SamplingHague and Harris, Sampling and Statistics, Kogan Page (This is a very elementary book.)
S-PLUSKrause, A and Olson, M The Basics of S and S-PLUS (2nd edition) , Springer, 2000