THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Many scientific phenomena are now investigated by complex computer models or codes A computer experiment is a number of runs of the code with various inputs A feature of many computer experiments is that the output is deterministic--rerunning the code with the same inputs gives identical observations Often, the codes are computationally expensive to run, and a common objective of an experiment is to fit a cheaper predictor of the output to the data Our approach is to model the deterministic output as the realization of a stochastic process, thereby providing a statistical basis for designing experiments (choosing the inputs) for efficient prediction With this model, estimates of uncertainty of predictions are also available Recent work in this area is reviewed, a number of applications are discussed, and we demonstrate our methodology with an example

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The design and analysis of computer experiments

Statistics for Spatial Data.

Measuring Health: A Guide to Rating Scales and Questionnaires

Elicitation is the process of extracting expert knowledge about some unknown quantity or quantities, and formulating that information as a probability distribution. Elicitation is important in situations, such as modelling the safety of nuclear installations or assessing the risk of terrorist attacks, where expert knowledge is essentially the only source of good information. It also plays a major role in other contexts by augmenting scarce observational data, through the use of Bayesian statistical methods. However, elicitation is not a simple task, and practitioners need to be aware of a wide range of research findings in order to elicit expert judgements accurately and reliably. Uncertain Judgements introduces the area, before guiding the reader through the study of appropriate elicitation methods, illustrated by a variety of multi-disciplinary examples.

Uncertain Judgements: Eliciting Experts' Probabilities

Summary. In many areas of science and technology, mathematical models are built to simulate complex real world phenomena. Such models are typically implemented in large computer programs and are also very complex, such that the way that the model responds to changes in its inputs is not transparent. Sensitivity analysis is concerned with understanding how changes in the model inputs influence the outputs. This may be motivated simply by a wish to understand the implications of a complex model but often arises because there is uncertainty about the true values of the inputs that should be used for a particular application. A broad range of measures have been advocated in the literature to quantify and describe the sensitivity of a model's output to variation in its inputs. In practice the most commonly used measures are those that are based on formulating uncertainty in the model inputs by a joint probability distribution and then analysing the induced uncertainty in outputs, an approach which is known as probabilistic sensitivity analysis. We present a Bayesian framework which unifies the various tools of prob- abilistic sensitivity analysis. The Bayesian approach is computationally highly efficient. It allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than standard Monte Carlo methods. Furthermore, all measures of interest may be computed from a single set of runs.

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Probabilistic sensitivity analysis of complex models: a Bayesian approach

We consider a problem of inference for the output of a computationally expensive computer model. We suppose that the model is to be used in a context where the values of one or more inputs are uncertain, so that the input configuration is a random variable. We require to make inference about the induced distribution of the output. This distribution is called the uncertainty distribution, and the general problem is known to users of computer models as uncertainty analysis. To be specific, we develop Bayesian inference for the distribution and density functions of the model output. Modelling the output, as a function of its inputs, as a Gaussian process, we derive expressions for the posterior mean and variance of the distribution and density functions, based on data comprising observed outputs at a sample of input configurations. We show that direct computation of these expressions may encounter numerical difficulties. We develop an alternative approach based on simulating approximate realisations from the posterior distribution of the output function. Two examples are given to illustrate our methods.

Bayesian inference for the uncertainty distribution of computer model outputs

Objectives: To establish the clinical effectiveness and cost-effectiveness of selective oestrogen receptor modulators, bisphosphonates and parathyroid hormone (subject to licensing) for the prevention and treatment of osteoporosis and the prevention of osteoporotic fractures in postmenopausal women.

Data sources: Electronic databases.

Review methods: Studies that met the review’s entry criteria were eligible for inclusion in the meta-analyses provided that they reported fracture incidence in terms of the number of patients suffering fractures. Meta-analysis was carried out using the random-effects model. A model was constructed to estimate the cost-effectiveness of osteoporosis interventions. The model calculated the number of fractures that occurred and provided the costs associated with osteoporotic fractures, and the quality-adjusted life-years (QALYs). In addition, the conditions of breast cancer and coronary heart disease (CHD) were modelled, as some interventions have been shown to affect the risk of these conditions.

Results: Ninety randomised controlled trials (RCTs) met the inclusion criteria. They related to the five interventions (alendronate, etidronate, risedronate, raloxifene and teriparatide) and to five comparators (calcium, calcium plus vitamin D, calcitriol, hormone replacement therapy and exercise), as well as placebo or no treatment. All five interventions have been shown to reduce the risk of vertebral fracture in women with severe osteoporosis with adequate calcium intakes. However, none of these drugs has been demonstrated, by direct comparison, to be significantly more effective than either each other or the other active interventions reviewed in this report. The intervention costs of treating all osteoporotic women, for a period of 5 years, were in the region of £900–1500 million for alendronate, etidronate, risedronate and raloxifene. The cost per QALY ratios fell dramatically with age. Assuming the risks of a woman with severe osteoporosis at the threshold of osteoporosis, no treatment had a cost per QALY below £35,000 at 50 years of age. At 60 years of age, the cost per QALY of raloxifene was £26,000 assuming no impact on hip fractures, and £31,000 assuming an adverse effect. However, these results are driven by the effect on breast cancer and the assumptions made regarding this disease state. No other intervention had a cost per QALY below £35,000. When analyses were conducted assuming that the fracture risk is doubled at each site, alendronate and risedronate had cost per QALY ratios below £30,000 at all ages. For women at the threshold of osteoporosis, without a prior fracture and aged 70 years, the cost per QALY of the three bisphosphonates ranged from £34,000 to £41,000. Raloxifene had a cost per QALY of £23,000, assuming no effect on hip fracture, given assumptions regarding breast cancer. At 80 years of age, the cost per QALY of alendronate and risedronate was below £20,000. This was true for etidronate when incorporating observational data, but the value rose to £69,000 when only RCT data were used. No other intervention had a cost per QALY below £35,000. It was assumed that doubling the risk of fracture for women without a prior fracture would give results similar to patients at the threshold of osteoporosis with a prior fracture.

Conclusions: Of the five interventions, only raloxifene appeared to reduce the risk of vertebral fracture in postmenopausal women unselected for low bone mineral density (BMD). However, as the full data have not been made public, there is some uncertainty regarding this result. None of the five interventions has been shown to reduce the risk of non-vertebral fracture in women unselected for low BMD. All of the proposed interventions provided gains in QALYs compared with no treatment in women with sufficient calcium and vitamin D intakes. The size of the QALY gain for each intervention was strongly related to the age of the patient. The estimated costs varied widely for the interventions. These net costs were markedly different by age, with some interventions becoming cost-saving at higher age ranges in patients with a prior fracture. Areas for future research include: the evidence base for the efficacy of fracture prevention in the very elderly, reanalysis of raloxifene using a dedicated breast cancer and CHD model, and more trials considering the cost-effectiveness of teriparatide.

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A systematic review and economic evaluation of alendronate, etidronate, risedronate, raloxifene and teriparatide for the prevention and treatment of postmenopausal osteoporosis

http://www.yaroslavvb.com/papers/epistemic.pdf

Jeremy E. Oakley

Papers

Uncertain Judgements: Eliciting Experts' Probabilities

Probabilistic sensitivity analysis of complex models: a Bayesian approach

Bayesian inference for the uncertainty distribution of computer model outputs

A systematic review and economic evaluation of alendronate, etidronate, risedronate, raloxifene and teriparatide for the prevention and treatment of postmenopausal osteoporosis

Probability is Perfect, but We Can't Elicit it Perfectly