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SJS SDI_11 Design of Statistical Investigations Stephen Senn 1 General Introduction

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SJS SDI_12 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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SJS SDI_13 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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SJS SDI_14 Example Exp_1 A 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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SJS SDI_15

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6 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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SJS SDI_17 Example Obs_1 An 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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SJS SDI_18 Fine et al

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SJS SDI_19 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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SJS SDI_110 Example Surv_1 A 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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SJS SDI_111

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SJS SDI_112 Purposes of Statistical Investigations

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SJS SDI_113 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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SJS SDI_114 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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SJS SDI_115 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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SJS SDI_116 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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SJS SDI_117 Basic Design Cycle Objective Tentative Design Potential Data Possible Analysis Possible Conclusions Relevant factors

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SJS SDI_118 Questions 1 Exp_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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SJS SDI_119 Questions 2 Obs_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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SJS SDI_120 Questions 3 Surv_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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SJS SDI_121 Suggested Reading Experimental 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 Sampling Hague and Harris, Sampling and Statistics, Kogan Page (This is a very elementary book.) S-PLUS Krause, A and Olson, M The Basics of S and S-PLUS (2nd edition), Springer, 2000

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SJS SDI_111 Design of Statistical Investigations Stephen Senn 11 Nested Factors.

SJS SDI_111 Design of Statistical Investigations Stephen Senn 11 Nested Factors.

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