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

Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations— e.g., random noise—cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being ''suboptimal''. Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significant- ly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the ''neural code''. Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise—via stochastic resonance or otherwise—than if it did. We also challenge neurosci- entists and biologists, both computational and experi- mental, to embrace a very broad definition of stochastic resonance in terms of signal-processing ''noise benefits'', and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology.

/pdf/what-is-stochastic-resonance-definitions-misconceptions-2wpsnjdehd.pdf

What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology

Sensitivity analysis (SA) can aid in identifying influential model parameters and optimizing model structure, yet infectious disease modelling has yet to adopt advanced SA techniques that are capable of providing considerable insights over traditional methods. We investigate five global SA methods—scatter plots, the Morris and Sobol’ methods, Latin hypercube sampling-partial rank correlation coefficient and the sensitivity heat map method—and detail their relative merits and pitfalls when applied to a microparasite (cholera) and macroparasite (schistosomaisis) transmission model. The methods investigated yielded similar results with respect to identifying influential parameters, but offered specific insights that vary by method. The classical methods differed in their ability to provide information on the quantitative relationship between parameters and model output, particularly over time. The heat map approach provides information about the group sensitivity of all model state variables, and the parameter sensitivity spectrum obtained using this method reveals the sensitivity of all state variables to each parameter over the course of the simulation period, especially valuable for expressing the dynamic sensitivity of a microparasite epidemic model to its parameters. A summary comparison is presented to aid infectious disease modellers in selecting appropriate methods, with the goal of improving model performance and design.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2012.1018

Sensitivity analysis of infectious disease models: methods, advances and their application.

The past decade has seen rapid advances in the development of new methods for the design and analysis of split-plot experiments. Unfortunately, the value of these designs for industrial experimentation has not been fully appreciated. In this paper, we review recent developments and provide guidelines for the use of split-plot designs in industrial applications.

/pdf/split-plot-designs-what-why-and-how-1jn16oxokm.pdf

Split-Plot Designs - What, Why, and How

Fractional factorial designs are among the most important statistical contributions to the efficient exploration of the effects of several controllable factors on a response of interest. Fractional factorials are widely used in experiments in fields as diverse as agriculture, industry, and medical research. A key feature of fractional factorials that is not shared by more ad hoc methods for reducing the size of experiments is that the statistical properties are known in advance of experimentation. Consequently, an experimenter can investigate alternatives that enable the goals of the experiment to be met with the least cost, shortest time, or most effective use of resources. On occasion, an experimenter might decide not to conduct an experiment as originally planned once the statistical properties of the design are known. This article highlights the fundamental concepts, design strategies, and statistical properties of fractional factorial designs. Copyright © 2009 John Wiley & Sons, Inc.



For further resources related to this article, please visit the WIREs website.

Fractional factorial design

This paper presents a statistical study of a deterministic model for the transmission dynamics and control of severe acute respiratory syndrome (SARS). The effect of the model parameters on the dynamics of the disease is analyzed using sensitivity and uncertainty analyses. The response (or output) of interest is the control reproduction number, which is an epidemiological threshold governing the persistence or elimination of SARS in a given population. The compartmental model includes parameters associated with control measures such as quarantine and isolation of asymptomatic and symptomatic individuals. One feature of our analysis is the incorporation of time-dependent functions into the model to reflect the progressive refinement of these SARS control measures over time. Consequently, the model contains continuous time-varying inputs and outputs. In this setting, sensitivity and uncertainty analytical techniques are used in order to analyze the impact of the uncertainty in the parameter estimates on the results obtained and to determine which parameters have the largest impact on driving the disease dynamics.

Sensitivity and uncertainty analyses for a sars model with time-varying inputs and outputs.

Mechanical ventilators breathe for you when you cannot or when your lungs are too sick to do their job. Most ventilators monotonously deliver the same-sized breaths, like clockwork; however, healthy people do not breathe this way. This has led to the development of a biologically variable ventilator—one that incorporates noise. There are indications that such a noisy ventilator may be beneficial for patients with very sick lungs. In this paper we use a probabilistic argument, based on Jensen's inequality, to identify the circumstances in which the addition of noise may be beneficial and, equally important, the circumstances in which it may not be beneficial. Using the local convexity of the relationship between airway pressure and tidal volume in the lung, we show that the addition of noise at low volume or low pressure results in higher mean volume (at the same mean pressure) or lower mean pressure (at the same mean volume). The consequence is enhanced gas exchange or less stress on the lungs, both clinically desirable. The argument has implications for other life support devices, such as cardiopulmonary bypass pumps. This paper illustrates the benefits of research that takes place at the interface between mathematics and medicine.

/pdf/convexity-jensen-s-inequality-and-benefits-of-noisy-1ets3qr5a6.pdf

Convexity, Jensen's inequality and benefits of noisy mechanical ventilation

Programming a mechanical ventilator with a biologically variable or fractal breathing pattern (an example of 1/f noise) improves gas exchange and respiratory mechanics Here we show that fractal ventilation increases respiratory sinus arrhythmia (RSA) – a mechanism known to improve ventilation/perfusion matching Pigs were anaesthetised with propofol/ketamine, paralysed with doxacurium, and ventilated in either control mode (CV) or in fractal mode (FV) at baseline and then following infusion of oleic acid to result in lung injury Mean RSA and mean positive RSA were nearly double with FV, both at baseline and following oleic acid At baseline, mean RSA = 186 msec with CV and 368 msec with FV (n = 10; p = 0043); post oleic acid, mean RSA = 111 msec with CV and 218 msec with FV (n = 9, p = 0028); at baseline, mean positive RSA = 208 msec with CV and 381 msec with FV (p = 0047); post oleic acid, mean positive RSA = 132 msec with CV and 244 msec with FV (p = 0026) Heart rate variability was also greater with FV At baseline the coefficient of variation for heart rate was 22% during CV and 40% during FV Following oleic acid the variation was 21 vs 56% respectively These findings suggest FV enhances physiological entrainment between respiratory, brain stem and cardiac nonlinear oscillators, further supporting the concept that RSA itself reflects cardiorespiratory interaction In addition, these results provide another mechanism whereby FV may be superior to conventional CV

/pdf/fractal-ventilation-enhances-respiratory-sinus-arrhythmia-2xxflgflm2.pdf

Fractal ventilation enhances respiratory sinus arrhythmia

In industrial screening experiments, if some factors are hard to vary and others are easy to vary, randomization restrictions may lead to the use of fractional factorial split-plot (FFSP) designs. Blocked FFSP (BFFSP) designs arise when all runs cannot be performed under homogeneous conditions. This article introduces three approaches for blocking FFSP designs. A catalog of designs is presented in which BFFSP designs are ranked according to the minimum aberration criterion. In addition, additional optimality criteria are used to assist in the ranking procedure. The case study that motivated this research is also discussed in detail.

/pdf/the-design-of-blocked-fractional-factorial-split-plot-kqv1hco4il.pdf

The Design of Blocked Fractional Factorial Split-Plot Experiments

With biologically variable ventilation [BVV – using a computer-controller to add breath-to-breath variability to respiratory frequency (f) and tidal volume (VT)] gas exchange and respiratory mechanics were compared using the ARDSNet low VT algorithm (Control) versus an approach using mathematical modelling to individually optimise VT at the point of maximal compliance change on the convex portion of the inspiratory pressure-volume (P-V) curve (Experimental). Pigs (n = 22) received pentothal/midazolam anaesthesia, oleic acid lung injury, then inspiratory P-V curve fitting to the four-parameter logistic Venegas equation F(P) = a + b[1 + e
-(P-c)/d
]-1 where: a = volume at lower asymptote, b = the vital capacity or the total change in volume between the lower and upper asymptotes, c = pressure at the inflection point and d = index related to linear compliance. Both groups received BVV with gas exchange and respiratory mechanics measured hourly for 5 hrs. Postmortem bronchoalveolar fluid was analysed for interleukin-8 (IL-8). All P-V curves fit the Venegas equation (R2 > 0.995). Control VT averaged 7.4 ± 0.4 mL/kg as compared to Experimental 9.5 ± 1.6 mL/kg (range 6.6 – 10.8 mL/kg; p F(E(P))." In both groups the inequality applied, since F(P) defines volume in the Venegas equation and (P) pressure and the range of VTs varied within the convex interval for individual P-V curves. Over 5 hrs, there were no significant differences between groups in minute ventilation, airway pressure, blood gases, haemodynamics, respiratory compliance or IL-8 concentrations. No difference between groups is a consequence of BVV occurring on the convex interval for individualised Venegas P-V curves in all experiments irrespective of group. Jensen's inequality provides theoretical proof of why a variable ventilatory approach is advantageous under these circumstances. When using BVV, with VT centred by Venegas P-V curve analysis at the point of maximal compliance change, some leeway in low VT settings beyond ARDSNet protocols may be possible in acute lung injury. This study also shows that in this model, the standard ARDSNet algorithm assures ventilation occurs on the convex portion of the P-V curve.

/pdf/mathematical-modelling-to-centre-low-tidal-volumes-following-32m0zganf6.pdf

John F. Brewster

Papers

Sensitivity and uncertainty analyses for a sars model with time-varying inputs and outputs.

Convexity, Jensen's inequality and benefits of noisy mechanical ventilation

Fractal ventilation enhances respiratory sinus arrhythmia

The Design of Blocked Fractional Factorial Split-Plot Experiments

Mathematical modelling to centre low tidal volumes following acute lung injury: A study with biologically variable ventilation