It is argued that when it comes to nuisance parameters an assumption of ignorance is harmful. On the other hand this raises problems as to how far one should go in searching for further data when combining evidence.
What should we expect from reproducibiliryStephen Senn
Is there really a reproducibility crisis and if so are P-values to blame? Choose any statistic you like and carry out two identical independent studies and report this statistic for each. In advance of collecting any data, you ought to expect that it is just as likely that statistic 1 will be smaller than statistic 2 as vice versa. Once you have seen statistic 1, things are not so simple but if they are not so simple, it is that you have other information in some form. However, it is at least instructive that you need to be careful in jumping to conclusions about what to expect from reproducibility. Furthermore, the forecasts of good Bayesians ought to obey a Martingale property. On average you should be in the future where you are now but, of course, your inferential random walk may lead to some peregrination before it homes in on “the truth”. But you certainly can’t generally expect that a probability will get smaller as you continue. P-values, like other statistics are a position not a movement. Although often claimed, there is no such things as a trend towards significance.
Using these and other philosophical considerations I shall try and establish what it is we want from reproducibility. I shall conclude that we statisticians should probably be paying more attention to checking that standard errors are being calculated appropriately and rather less to inferential framework.
When estimating sample sizes for clinical trials there are several different views that might be taken as to what definition and meaning should be given to the sought-for treatment effect. However, if the concept of a ‘minimally important difference’ (MID) does have relevance to interpreting clinical trials (which can be disputed) then its value cannot be the same as the ‘clinically relevant difference’ (CRD) that would be used for planning them.
A doubly pernicious use of the MID is as a means of classifying patients as responders and non-responders. Not only does such an analysis lead to an increase in the necessary sample size but it misleads trialists into making causal distinctions that the data cannot support and has been responsible for exaggerating the scope for personalised medicine.
In this talk these statistical points will be explained using a minimum of technical detail.
Unfortunately, some have interpreted Numbers Needed to Treat as indicating the proportion of patients on whom the treatment has had a causal effect. This interpretation is very rarely, if ever, necessarily correct. It is certainly inappropriate if based on a responder dichotomy. I shall illustrate the problem using simple causal models.
One also sometimes encounters the claim that the extent to which two distributions of outcomes overlap from a clinical trial indicates how many patients benefit. This is also false and can be traced to a similar causal confusion.
This year marks the 70th anniversary of the Medical Research Council randomised clinical trial (RCT) of streptomycin in tuberculosis led by Bradford Hill. This is widely regarded as a landmark in clinical research. Despite its widespread use in drug regulation and in clinical research more widely and its high standing with the evidence based medicine movement, the RCT continues to attracts criticism. I show that many of these criticisms are traceable to failure to understand two key concepts in statistics: probabilistic inference and design efficiency. To these methodological misunderstandings can be added the practical one of failing to appreciate that entry into clinical trials is not simultaneous but sequential.
I conclude that although randomisation should not be used as an excuse for ignoring prognostic variables, it is valuable and that many standard criticisms of RCTs are invalid.
Minimisation is an approach to allocating patients to treatment in clinical trials that forces a greater degree of balance than does randomisation. Here I explain why I dislike it.
There are many questions one might ask of a clinical trial, ranging from what was the effect in the patients studied to what might the effect be in future patients via what was the effect in individual patients? The extent to which the answer to these questions is similar depends on various assumptions made and in some cases the design used may not permit any meaningful answer to be given at all.
A related issue is confusion between randomisation, random sampling, linear model and true multivariate based modelling. These distinctions don’t matter much for some purposes and under some circumstances but for others they do.
It is argued that when it comes to nuisance parameters an assumption of ignorance is harmful. On the other hand this raises problems as to how far one should go in searching for further data when combining evidence.
What should we expect from reproducibiliryStephen Senn
Is there really a reproducibility crisis and if so are P-values to blame? Choose any statistic you like and carry out two identical independent studies and report this statistic for each. In advance of collecting any data, you ought to expect that it is just as likely that statistic 1 will be smaller than statistic 2 as vice versa. Once you have seen statistic 1, things are not so simple but if they are not so simple, it is that you have other information in some form. However, it is at least instructive that you need to be careful in jumping to conclusions about what to expect from reproducibility. Furthermore, the forecasts of good Bayesians ought to obey a Martingale property. On average you should be in the future where you are now but, of course, your inferential random walk may lead to some peregrination before it homes in on “the truth”. But you certainly can’t generally expect that a probability will get smaller as you continue. P-values, like other statistics are a position not a movement. Although often claimed, there is no such things as a trend towards significance.
Using these and other philosophical considerations I shall try and establish what it is we want from reproducibility. I shall conclude that we statisticians should probably be paying more attention to checking that standard errors are being calculated appropriately and rather less to inferential framework.
When estimating sample sizes for clinical trials there are several different views that might be taken as to what definition and meaning should be given to the sought-for treatment effect. However, if the concept of a ‘minimally important difference’ (MID) does have relevance to interpreting clinical trials (which can be disputed) then its value cannot be the same as the ‘clinically relevant difference’ (CRD) that would be used for planning them.
A doubly pernicious use of the MID is as a means of classifying patients as responders and non-responders. Not only does such an analysis lead to an increase in the necessary sample size but it misleads trialists into making causal distinctions that the data cannot support and has been responsible for exaggerating the scope for personalised medicine.
In this talk these statistical points will be explained using a minimum of technical detail.
Unfortunately, some have interpreted Numbers Needed to Treat as indicating the proportion of patients on whom the treatment has had a causal effect. This interpretation is very rarely, if ever, necessarily correct. It is certainly inappropriate if based on a responder dichotomy. I shall illustrate the problem using simple causal models.
One also sometimes encounters the claim that the extent to which two distributions of outcomes overlap from a clinical trial indicates how many patients benefit. This is also false and can be traced to a similar causal confusion.
This year marks the 70th anniversary of the Medical Research Council randomised clinical trial (RCT) of streptomycin in tuberculosis led by Bradford Hill. This is widely regarded as a landmark in clinical research. Despite its widespread use in drug regulation and in clinical research more widely and its high standing with the evidence based medicine movement, the RCT continues to attracts criticism. I show that many of these criticisms are traceable to failure to understand two key concepts in statistics: probabilistic inference and design efficiency. To these methodological misunderstandings can be added the practical one of failing to appreciate that entry into clinical trials is not simultaneous but sequential.
I conclude that although randomisation should not be used as an excuse for ignoring prognostic variables, it is valuable and that many standard criticisms of RCTs are invalid.
Minimisation is an approach to allocating patients to treatment in clinical trials that forces a greater degree of balance than does randomisation. Here I explain why I dislike it.
There are many questions one might ask of a clinical trial, ranging from what was the effect in the patients studied to what might the effect be in future patients via what was the effect in individual patients? The extent to which the answer to these questions is similar depends on various assumptions made and in some cases the design used may not permit any meaningful answer to be given at all.
A related issue is confusion between randomisation, random sampling, linear model and true multivariate based modelling. These distinctions don’t matter much for some purposes and under some circumstances but for others they do.
Presidents' invited lecture ISCB Vigo 2017
Discusses various issues to do with how randomised clinical trials should be analysed. See also https://errorstatistics.com/2017/07/01/s-senn-fishing-for-fakes-with-fisher-guest-post/
Sample size determination in clinical trials is considered from various ethical and practical perspectives. It is concluded that cost is a missing dimension and that the value of information is key.
The Rothamsted school meets Lord's paradoxStephen Senn
Lords ‘paradox’ is a notoriously difficult puzzle that is guaranteed to provoke discussion, dissent and disagreement. Two statisticians analyse some observational data and come to radically different conclusions, each of which has acquired defenders over the years since Lord first proposed his puzzle in 1967. It features in the recent Book of Why by Pearl and McKenzie, who use it to demonstrate the power of Pearl’s causal calculus, obtaining a solution they claim is unambiguously right. They also claim that statisticians have failed to get to grips with causal questions for well over a century, in fact ever since Karl Pearson developed Galton’s idea of correlation and warned the scientific world that correlation is not causation.
However, only two years before Lord published his paradox John Nelder outlined a powerful causal calculus for analyzing designed experiments based on a careful distinction between block and treatment structure. This represents an important advance in formalizing the approach to analysing complex experiments that started with Fisher 100 years ago, when he proposed splitting variability using the square of the standard deviation, which he called the variance, continued with Yates and has been developed since the 1960s by Rosemary Bailey, amongst others. This tradition might be referred to as The Rothamsted School. It is fully implemented in Genstat® but, as far as I am aware, not in any other package.
With the help of Genstat®, I demonstrate how the Rothamsted School would approach Lord’s paradox and come to a solution that is not the same as the one reached by Pearl and McKenzie, although given certain strong but untestable assumptions it would reduce to it. I conclude that the statistical tradition may have more to offer in this respect than has been supposed.
Views of the role of hypothesis falsification in statistical testing do not divide as cleanly between frequentist and Bayesian views as is commonly supposed. This can be shown by considering the two major variants of the Bayesian approach to statistical inference and the two major variants of the frequentist one.
A good case can be made that the Bayesian, de Finetti, just like Popper, was a falsificationist. A thumbnail view, which is not just a caricature, of de Finetti’s theory of learning, is that your subjective probabilities are modified through experience by noticing which of your predictions are wrong, striking out the sequences that involved them and renormalising.
On the other hand, in the formal frequentist Neyman-Pearson approach to hypothesis testing, you can, if you wish, shift conventional null and alternative hypotheses, making the latter the strawman and by ‘disproving’ it, assert the former.
The frequentist, Fisher, however, at least in his approach to testing of hypotheses, seems to have taken a strong view that the null hypothesis was quite different from any other and there was a strong asymmetry on inferences that followed from the application of significance tests.
Finally, to complete a quartet, the Bayesian geophysicist Jeffreys, inspired by Broad, specifically developed his approach to significance testing in order to be able to ‘prove’ scientific laws.
By considering the controversial case of equivalence testing in clinical trials, where the object is to prove that ‘treatments’ do not differ from each other, I shall show that there are fundamental differences between ‘proving’ and falsifying a hypothesis and that this distinction does not disappear by adopting a Bayesian philosophy. I conclude that falsificationism is important for Bayesians also, although it is an open question as to whether it is enough for frequentists.
The Seven Habits of Highly Effective StatisticiansStephen Senn
If you know why the title of this talk is extremely stupid, then you clearly know something about control, data and reasoning: in short, you have most of what it takes to be a statistician. If you have studied statistics then you will also know that a large amount of anything, and this includes successful careers, is luck.
In this talk I shall try share some of my experiences of being a statistician in the hope that it will help you make the most of whatever luck life throws you, In so doing, I shall try my best to overcome the distorting influence of that easiest of sciences hindsight. Without giving too much away, I shall be recommending that you read, listen, think, calculate, understand, communicate, and do. I shall give you some example of what I think works and what I think doesn’t
In all of this you should never forget the power of negativity and also the joy of being able to wake up every day and say to yourself ‘I love the small of data in the morning’.
Talk given at ISCB 2016 Birmingham
For indications and treatments where their use is possible, n-of-1 trials represent a promising means of investigating potential treatments for rare diseases. Each patient permits repeated comparison of the treatments being investigated and this both increases the number of observations and reduces their variability compared to conventional parallel group trials.
However, depending on whether the framework for analysis used is randomisation-based or model- based produces puzzling difference in inferences. This can easily be shown by starting on the one hand with the randomisation philosophy associated with the Rothamsted school of inference and building up the analysis through the block + treatment structure approach associated with John Nelder’s theory of general balance (as implemented in GenStat®) or starting on the other hand with a plausible variance component approach through a mixed model. However, it can be shown that these differences are related not so much to modelling approach per se but to the questions one attempts to answer: ranging from testing whether there was a difference between treatments in the patients studied, to predicting the true difference for a future patient, via making inferences about the effect in the average patient.
This in turn yields interesting insight into the long-run debate over the use of fixed or random effect meta-analysis.
Some practical issues of analysis will also be covered in R and SAS®, in which languages some functions and macros to facilitate analysis have been written. It is concluded that n-of-1 hold great promise in investigating chronic rare diseases but that careful consideration of matters of purpose, design and analysis is necessary to make best use of them.
Acknowledgement
This work is partly supported by the European Union’s 7th Framework Programme for research, technological development and demonstration under grant agreement no. 602552. “IDEAL”
Clinical trials: quo vadis in the age of covid?Stephen Senn
A discussion of the role of clinical trials in the age of COVID. My contribution to the phastar 2020 life sciences summit https://phastar.com/phastar-life-science-summit
There are many valid criticisms of P-values but the criticism that they are largely responsible for the reproducibility crisis has been accepted rather lightly in some quarters. Whatever the inferential statistic that is used, it is quite illogical to assume that as the sample size increases it will tend to show more evidence against the null hypothesis. This applies to Bayesian posterior probabilities as much as it does to P-values. In the context of P-values it can be referred to as the trend towards significance fallacy but more generally, for reasons I shall explain, it could be referred to as the anticipated evidence fallacy.
The anticipated evidence fallacy is itself an example of the overstated evidence fallacy. I shall also discuss this fallacy and other relevant matters affecting reproducible science including the problem of false negatives.
The history of p-values is covered to try and shed light on a mystery: why did Student and Fisher agree numerically but disagree in terms of interpretation.?
How to combine results from randomised clinical trials on the additive scale with real world data to provide predictions on the clinically relevant scale for individual patients
Personalised medicine a sceptical viewStephen Senn
Some grounds for believing that the current enthusiasm about personalised medicine is exaggerated, founded on poor statistics and represents a disappointing loss of ambition.
There are many questions one might ask of a clinical trial, ranging from what was the effect in the patients studied to what might the effect be in future patients via what was the effect in individual patients? The extent to which the answer to these questions is similar depends on various assumptions made and in some cases the design used may not permit any meaningful answer to be given at all.
A related issue is confusion between randomisation, random sampling, linear model and true multivariate based modelling. These distinctions don’t matter much for some purposes and under some circumstances but for others they do.
A yet further issue is that causal analysis in epidemiology, which has brought valuable insights in many cases, has tended to stress point estimates and ignore standard errors. This has potentially misleading consequences.
An understanding of components of variation is key. Unfortunately, the development of two particular topics in recent years, evidence synthesis by the evidence based medicine movement and personalised medicine by bench scientists has either paid scant attention to components of variation or to the questions being asked or both resulting in confusion about many issues.
For instance, it is often claimed that numbers needed to treat indicate the proportion of patients for whom treatments work, that inclusion criteria determine the generalisability of results and that heterogeneity means that a random effects meta-analysis is required. None of these is true. The scope for personalised medicine has very plausibly been exaggerated and an important cause of variation in the healthcare system, physicians, is often overlooked.
I shall argue that thinking about questions is important.
The Rothamsted School & The analysis of designed experimentsStephenSenn2
A historical account is given of the approach of "The Rothamsted School" to the analysis of designed experiments. The link between the way that experiments are designed and how they should be analysed is fundamental to this approach. The key figures are RA Fisher, Frank Yates and John Nelder
Presidents' invited lecture ISCB Vigo 2017
Discusses various issues to do with how randomised clinical trials should be analysed. See also https://errorstatistics.com/2017/07/01/s-senn-fishing-for-fakes-with-fisher-guest-post/
Sample size determination in clinical trials is considered from various ethical and practical perspectives. It is concluded that cost is a missing dimension and that the value of information is key.
The Rothamsted school meets Lord's paradoxStephen Senn
Lords ‘paradox’ is a notoriously difficult puzzle that is guaranteed to provoke discussion, dissent and disagreement. Two statisticians analyse some observational data and come to radically different conclusions, each of which has acquired defenders over the years since Lord first proposed his puzzle in 1967. It features in the recent Book of Why by Pearl and McKenzie, who use it to demonstrate the power of Pearl’s causal calculus, obtaining a solution they claim is unambiguously right. They also claim that statisticians have failed to get to grips with causal questions for well over a century, in fact ever since Karl Pearson developed Galton’s idea of correlation and warned the scientific world that correlation is not causation.
However, only two years before Lord published his paradox John Nelder outlined a powerful causal calculus for analyzing designed experiments based on a careful distinction between block and treatment structure. This represents an important advance in formalizing the approach to analysing complex experiments that started with Fisher 100 years ago, when he proposed splitting variability using the square of the standard deviation, which he called the variance, continued with Yates and has been developed since the 1960s by Rosemary Bailey, amongst others. This tradition might be referred to as The Rothamsted School. It is fully implemented in Genstat® but, as far as I am aware, not in any other package.
With the help of Genstat®, I demonstrate how the Rothamsted School would approach Lord’s paradox and come to a solution that is not the same as the one reached by Pearl and McKenzie, although given certain strong but untestable assumptions it would reduce to it. I conclude that the statistical tradition may have more to offer in this respect than has been supposed.
Views of the role of hypothesis falsification in statistical testing do not divide as cleanly between frequentist and Bayesian views as is commonly supposed. This can be shown by considering the two major variants of the Bayesian approach to statistical inference and the two major variants of the frequentist one.
A good case can be made that the Bayesian, de Finetti, just like Popper, was a falsificationist. A thumbnail view, which is not just a caricature, of de Finetti’s theory of learning, is that your subjective probabilities are modified through experience by noticing which of your predictions are wrong, striking out the sequences that involved them and renormalising.
On the other hand, in the formal frequentist Neyman-Pearson approach to hypothesis testing, you can, if you wish, shift conventional null and alternative hypotheses, making the latter the strawman and by ‘disproving’ it, assert the former.
The frequentist, Fisher, however, at least in his approach to testing of hypotheses, seems to have taken a strong view that the null hypothesis was quite different from any other and there was a strong asymmetry on inferences that followed from the application of significance tests.
Finally, to complete a quartet, the Bayesian geophysicist Jeffreys, inspired by Broad, specifically developed his approach to significance testing in order to be able to ‘prove’ scientific laws.
By considering the controversial case of equivalence testing in clinical trials, where the object is to prove that ‘treatments’ do not differ from each other, I shall show that there are fundamental differences between ‘proving’ and falsifying a hypothesis and that this distinction does not disappear by adopting a Bayesian philosophy. I conclude that falsificationism is important for Bayesians also, although it is an open question as to whether it is enough for frequentists.
The Seven Habits of Highly Effective StatisticiansStephen Senn
If you know why the title of this talk is extremely stupid, then you clearly know something about control, data and reasoning: in short, you have most of what it takes to be a statistician. If you have studied statistics then you will also know that a large amount of anything, and this includes successful careers, is luck.
In this talk I shall try share some of my experiences of being a statistician in the hope that it will help you make the most of whatever luck life throws you, In so doing, I shall try my best to overcome the distorting influence of that easiest of sciences hindsight. Without giving too much away, I shall be recommending that you read, listen, think, calculate, understand, communicate, and do. I shall give you some example of what I think works and what I think doesn’t
In all of this you should never forget the power of negativity and also the joy of being able to wake up every day and say to yourself ‘I love the small of data in the morning’.
Talk given at ISCB 2016 Birmingham
For indications and treatments where their use is possible, n-of-1 trials represent a promising means of investigating potential treatments for rare diseases. Each patient permits repeated comparison of the treatments being investigated and this both increases the number of observations and reduces their variability compared to conventional parallel group trials.
However, depending on whether the framework for analysis used is randomisation-based or model- based produces puzzling difference in inferences. This can easily be shown by starting on the one hand with the randomisation philosophy associated with the Rothamsted school of inference and building up the analysis through the block + treatment structure approach associated with John Nelder’s theory of general balance (as implemented in GenStat®) or starting on the other hand with a plausible variance component approach through a mixed model. However, it can be shown that these differences are related not so much to modelling approach per se but to the questions one attempts to answer: ranging from testing whether there was a difference between treatments in the patients studied, to predicting the true difference for a future patient, via making inferences about the effect in the average patient.
This in turn yields interesting insight into the long-run debate over the use of fixed or random effect meta-analysis.
Some practical issues of analysis will also be covered in R and SAS®, in which languages some functions and macros to facilitate analysis have been written. It is concluded that n-of-1 hold great promise in investigating chronic rare diseases but that careful consideration of matters of purpose, design and analysis is necessary to make best use of them.
Acknowledgement
This work is partly supported by the European Union’s 7th Framework Programme for research, technological development and demonstration under grant agreement no. 602552. “IDEAL”
Clinical trials: quo vadis in the age of covid?Stephen Senn
A discussion of the role of clinical trials in the age of COVID. My contribution to the phastar 2020 life sciences summit https://phastar.com/phastar-life-science-summit
There are many valid criticisms of P-values but the criticism that they are largely responsible for the reproducibility crisis has been accepted rather lightly in some quarters. Whatever the inferential statistic that is used, it is quite illogical to assume that as the sample size increases it will tend to show more evidence against the null hypothesis. This applies to Bayesian posterior probabilities as much as it does to P-values. In the context of P-values it can be referred to as the trend towards significance fallacy but more generally, for reasons I shall explain, it could be referred to as the anticipated evidence fallacy.
The anticipated evidence fallacy is itself an example of the overstated evidence fallacy. I shall also discuss this fallacy and other relevant matters affecting reproducible science including the problem of false negatives.
The history of p-values is covered to try and shed light on a mystery: why did Student and Fisher agree numerically but disagree in terms of interpretation.?
How to combine results from randomised clinical trials on the additive scale with real world data to provide predictions on the clinically relevant scale for individual patients
Personalised medicine a sceptical viewStephen Senn
Some grounds for believing that the current enthusiasm about personalised medicine is exaggerated, founded on poor statistics and represents a disappointing loss of ambition.
There are many questions one might ask of a clinical trial, ranging from what was the effect in the patients studied to what might the effect be in future patients via what was the effect in individual patients? The extent to which the answer to these questions is similar depends on various assumptions made and in some cases the design used may not permit any meaningful answer to be given at all.
A related issue is confusion between randomisation, random sampling, linear model and true multivariate based modelling. These distinctions don’t matter much for some purposes and under some circumstances but for others they do.
A yet further issue is that causal analysis in epidemiology, which has brought valuable insights in many cases, has tended to stress point estimates and ignore standard errors. This has potentially misleading consequences.
An understanding of components of variation is key. Unfortunately, the development of two particular topics in recent years, evidence synthesis by the evidence based medicine movement and personalised medicine by bench scientists has either paid scant attention to components of variation or to the questions being asked or both resulting in confusion about many issues.
For instance, it is often claimed that numbers needed to treat indicate the proportion of patients for whom treatments work, that inclusion criteria determine the generalisability of results and that heterogeneity means that a random effects meta-analysis is required. None of these is true. The scope for personalised medicine has very plausibly been exaggerated and an important cause of variation in the healthcare system, physicians, is often overlooked.
I shall argue that thinking about questions is important.
The Rothamsted School & The analysis of designed experimentsStephenSenn2
A historical account is given of the approach of "The Rothamsted School" to the analysis of designed experiments. The link between the way that experiments are designed and how they should be analysed is fundamental to this approach. The key figures are RA Fisher, Frank Yates and John Nelder
Whatever happened to design based inferenceStephenSenn2
Given as the Sprott lecture, University of Waterloo September 2022
Abstract
What exactly should we think about appropriate analyses for designed experiments and why? If conditional inference trumps marginal inference, why should we care about randomisation? Isn’t everything just modelling? The Rothamsted School held that design matters. Taking an example of applying John Nelder’s general balance approach to a notorious problem, Lord’s paradox, I shall show that there may be some lessons for two fashionable topics: causal analysis and big data. I shall conclude that if we want not only to make good estimates but estimate how good our estimates are, design does matter.
The statistical revolution of the 20th century was largely concerned with developing methods for analysing small datasets. Student’s paper of 1908 was the first in the English literature to address the problem of second order uncertainty (uncertainty about the measures of uncertainty) seriously and was hailed by Fisher as heralding a new age of statistics. Much of what Fisher did was concerned with problems of what might be called ‘small data’, not only as regards efficient analysis but also as regards efficient design and in addition paying close attention to what was necessary to measure uncertainty validly.
I shall consider the history of some of these developments, in particular those that are associated with what might be called the Rothamsted School, starting with Fisher and having its apotheosis in John Nelder’s theory of General Balance and see what lessons they hold for the supposed ‘big data’ revolution of the 21st century.
The importance of measurements of uncertainty is explained and illustrated with the help of a famous experiment in nutrition from 1930 and a complex cross-over trial from the 1990s,
This powerpoint presentation gives a brief explanation about the biostatic data .this is quite helpful to individuals to understand the basic research methodology terminologys
P Values and Replication: the problem is not what you think
Lecture at MRC Brain Science & Cognition, Cambridge 16 December 2015
Abstract
It has been claimed that there is a crisis of replication in science. Prominent amongst the many factors that have been fingered as being responsible is the humble and ubiquitous P-value. One journal has even gone so far as to ban all inferential statistics. However, it is one thing to banish measures of uncertainty and another to banish uncertainty from your measures. I shall claim that the apparent discrepancy between P-values and posterior probabilities is as much a discrepancy between two approaches to Bayesian inference as it is between frequentist and Bayesian frameworks and that a further problem has been misunderstandings regarding predictive probabilities. I conclude that banning P-values won’t make all published results repeatable and that it is possible undesirable that it should.
The response to the COVID-19 crisis by various vaccine developers has been extraordinary, both in terms of speed of response and the delivered efficacy of the vaccines. It has also raised some fascinating issues of design, analysis and interpretation. I shall consider some of these issues, taking as my example, five vaccines: Pfizer/BioNTech, AstraZeneca/Oxford, Moderna, Novavax, and J&J Janssen but concentrating mainly on the first two. Among matters covered will be concurrent control, efficient design, issues of measurement raised by two-shot vaccines and implications for roll-out, and the surprising effectiveness of simple analyses. Differences between the five development programmes as they affect statistics will be covered but some essential similarities will also be discussed.
An early and overlooked causal revolution in statistics was the development of the theory of experimental design, initially associated with the "Rothamstead School". An important stage in the evolution of this theory was the experimental calculus developed by John Nelder in the 1960s with its clear distinction between block and treatment factors in designed experiments. This experimental calculus produced appropriate models automatically from more basic formal considerations but was, unfortunately, only ever implemented in Genstat®, a package widely used in agriculture but rarely so in medical research. In consequence its importance has not been appreciated and the approach of many statistical packages to designed experiments is poor. A key feature of the Rothamsted School approach is that identification of the appropriate components of variation for judging treatment effects is simple and automatic.
The impressive more recent causal revolution in epidemiology, associated with Judea Pearl, seems to have no place for components of variation, however. By considering the application of Nelder’s experimental calculus to Lord’s Paradox, I shall show that this reveals that solutions that have been proposed using the more modern causal calculus are problematic. I shall also show that lessons from designed clinical trials have important implications for the use of historical data and big data more generally.
In Search of Lost Infinities: What is the “n” in big data?Stephen Senn
In designing complex experiments, agricultural scientists, with the help of their statistician collaborators, soon came to realise that variation at different levels had very different consequences for estimating different treatment effects, depending on how the treatments were mapped onto the underlying block structure. This was a key feature of the Rothamsted approach to design and analysis and a strong thread running through the work of Fisher, Yates and Nelder, being expressed in topics such as split-pot designs, recovering inter-block information and fractional factorials. The null block-structure of an experiment is key to this philosophy of design and analysis. However modern techniques for analysing experiments stress models rather than symmetries and this modelling approach requires much greater care in analysis, with the consequence that you can easily make mistakes and often will.
In this talk I shall underline the obvious, but often unintentionally overlooked, fact that understanding variation at the various levels at which it occurs is crucial to analysis. I shall take three examples, an application of John Nelder’s theory of general balance to Lord’s Paradox, the use of historical data in drug development and a hybrid randomised non-randomised clinical trial, the TARGET study, to show that the data that many, including those promoting a so-called causal revolution, assume to be ‘big’ may actually be rather ‘small’. The consequence is that there is a danger that the size of standard errors will be underestimated or even that the appropriate regression coefficients for adjusting for confounding may not be identified correctly.
I conclude that an old but powerful experimental design approach holds important lessons for observational data about limitations in interpretation that mere numbers cannot overcome. Small may be beautiful, after all.
History of how and why a complex cross-over trial was designed to prove the equivalence of two formulations of a beta-agonist and what the eventual results were. Presented at the Newton Institute 28 July 2008. Warning: following the important paper by Kenward & Roger Biostatistics, 2010, I no longer think the random effects analysis is appropriate, although, in fact the results are pretty much the same as for the fixed effects analysis.
Tom Selleck Health: A Comprehensive Look at the Iconic Actor’s Wellness Journeygreendigital
Tom Selleck, an enduring figure in Hollywood. has captivated audiences for decades with his rugged charm, iconic moustache. and memorable roles in television and film. From his breakout role as Thomas Magnum in Magnum P.I. to his current portrayal of Frank Reagan in Blue Bloods. Selleck's career has spanned over 50 years. But beyond his professional achievements. fans have often been curious about Tom Selleck Health. especially as he has aged in the public eye.
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Introduction
Many have been interested in Tom Selleck health. not only because of his enduring presence on screen but also because of the challenges. and lifestyle choices he has faced and made over the years. This article delves into the various aspects of Tom Selleck health. exploring his fitness regimen, diet, mental health. and the challenges he has encountered as he ages. We'll look at how he maintains his well-being. the health issues he has faced, and his approach to ageing .
Early Life and Career
Childhood and Athletic Beginnings
Tom Selleck was born on January 29, 1945, in Detroit, Michigan, and grew up in Sherman Oaks, California. From an early age, he was involved in sports, particularly basketball. which played a significant role in his physical development. His athletic pursuits continued into college. where he attended the University of Southern California (USC) on a basketball scholarship. This early involvement in sports laid a strong foundation for his physical health and disciplined lifestyle.
Transition to Acting
Selleck's transition from an athlete to an actor came with its physical demands. His first significant role in "Magnum P.I." required him to perform various stunts and maintain a fit appearance. This role, which he played from 1980 to 1988. necessitated a rigorous fitness routine to meet the show's demands. setting the stage for his long-term commitment to health and wellness.
Fitness Regimen
Workout Routine
Tom Selleck health and fitness regimen has evolved. adapting to his changing roles and age. During his "Magnum, P.I." days. Selleck's workouts were intense and focused on building and maintaining muscle mass. His routine included weightlifting, cardiovascular exercises. and specific training for the stunts he performed on the show.
Selleck adjusted his fitness routine as he aged to suit his body's needs. Today, his workouts focus on maintaining flexibility, strength, and cardiovascular health. He incorporates low-impact exercises such as swimming, walking, and light weightlifting. This balanced approach helps him stay fit without putting undue strain on his joints and muscles.
Importance of Flexibility and Mobility
In recent years, Selleck has emphasized the importance of flexibility and mobility in his fitness regimen. Understanding the natural decline in muscle mass and joint flexibility with age. he includes stretching and yoga in his routine. These practices help prevent injuries, improve posture, and maintain mobilit
These lecture slides, by Dr Sidra Arshad, offer a quick overview of physiological basis of a normal electrocardiogram.
Learning objectives:
1. Define an electrocardiogram (ECG) and electrocardiography
2. Describe how dipoles generated by the heart produce the waveforms of the ECG
3. Describe the components of a normal electrocardiogram of a typical bipolar leads (limb II)
4. Differentiate between intervals and segments
5. Enlist some common indications for obtaining an ECG
Study Resources:
1. Chapter 11, Guyton and Hall Textbook of Medical Physiology, 14th edition
2. Chapter 9, Human Physiology - From Cells to Systems, Lauralee Sherwood, 9th edition
3. Chapter 29, Ganong’s Review of Medical Physiology, 26th edition
4. Electrocardiogram, StatPearls - https://www.ncbi.nlm.nih.gov/books/NBK549803/
5. ECG in Medical Practice by ABM Abdullah, 4th edition
6. ECG Basics, http://www.nataliescasebook.com/tag/e-c-g-basics
- Video recording of this lecture in English language: https://youtu.be/lK81BzxMqdo
- Video recording of this lecture in Arabic language: https://youtu.be/Ve4P0COk9OI
- Link to download the book free: https://nephrotube.blogspot.com/p/nephrotube-nephrology-books.html
- Link to NephroTube website: www.NephroTube.com
- Link to NephroTube social media accounts: https://nephrotube.blogspot.com/p/join-nephrotube-on-social-media.html
Title: Sense of Smell
Presenter: Dr. Faiza, Assistant Professor of Physiology
Qualifications:
MBBS (Best Graduate, AIMC Lahore)
FCPS Physiology
ICMT, CHPE, DHPE (STMU)
MPH (GC University, Faisalabad)
MBA (Virtual University of Pakistan)
Learning Objectives:
Describe the primary categories of smells and the concept of odor blindness.
Explain the structure and location of the olfactory membrane and mucosa, including the types and roles of cells involved in olfaction.
Describe the pathway and mechanisms of olfactory signal transmission from the olfactory receptors to the brain.
Illustrate the biochemical cascade triggered by odorant binding to olfactory receptors, including the role of G-proteins and second messengers in generating an action potential.
Identify different types of olfactory disorders such as anosmia, hyposmia, hyperosmia, and dysosmia, including their potential causes.
Key Topics:
Olfactory Genes:
3% of the human genome accounts for olfactory genes.
400 genes for odorant receptors.
Olfactory Membrane:
Located in the superior part of the nasal cavity.
Medially: Folds downward along the superior septum.
Laterally: Folds over the superior turbinate and upper surface of the middle turbinate.
Total surface area: 5-10 square centimeters.
Olfactory Mucosa:
Olfactory Cells: Bipolar nerve cells derived from the CNS (100 million), with 4-25 olfactory cilia per cell.
Sustentacular Cells: Produce mucus and maintain ionic and molecular environment.
Basal Cells: Replace worn-out olfactory cells with an average lifespan of 1-2 months.
Bowman’s Gland: Secretes mucus.
Stimulation of Olfactory Cells:
Odorant dissolves in mucus and attaches to receptors on olfactory cilia.
Involves a cascade effect through G-proteins and second messengers, leading to depolarization and action potential generation in the olfactory nerve.
Quality of a Good Odorant:
Small (3-20 Carbon atoms), volatile, water-soluble, and lipid-soluble.
Facilitated by odorant-binding proteins in mucus.
Membrane Potential and Action Potential:
Resting membrane potential: -55mV.
Action potential frequency in the olfactory nerve increases with odorant strength.
Adaptation Towards the Sense of Smell:
Rapid adaptation within the first second, with further slow adaptation.
Psychological adaptation greater than receptor adaptation, involving feedback inhibition from the central nervous system.
Primary Sensations of Smell:
Camphoraceous, Musky, Floral, Pepperminty, Ethereal, Pungent, Putrid.
Odor Detection Threshold:
Examples: Hydrogen sulfide (0.0005 ppm), Methyl-mercaptan (0.002 ppm).
Some toxic substances are odorless at lethal concentrations.
Characteristics of Smell:
Odor blindness for single substances due to lack of appropriate receptor protein.
Behavioral and emotional influences of smell.
Transmission of Olfactory Signals:
From olfactory cells to glomeruli in the olfactory bulb, involving lateral inhibition.
Primitive, less old, and new olfactory systems with different path
Lung Cancer: Artificial Intelligence, Synergetics, Complex System Analysis, S...Oleg Kshivets
RESULTS: Overall life span (LS) was 2252.1±1742.5 days and cumulative 5-year survival (5YS) reached 73.2%, 10 years – 64.8%, 20 years – 42.5%. 513 LCP lived more than 5 years (LS=3124.6±1525.6 days), 148 LCP – more than 10 years (LS=5054.4±1504.1 days).199 LCP died because of LC (LS=562.7±374.5 days). 5YS of LCP after bi/lobectomies was significantly superior in comparison with LCP after pneumonectomies (78.1% vs.63.7%, P=0.00001 by log-rank test). AT significantly improved 5YS (66.3% vs. 34.8%) (P=0.00000 by log-rank test) only for LCP with N1-2. Cox modeling displayed that 5YS of LCP significantly depended on: phase transition (PT) early-invasive LC in terms of synergetics, PT N0—N12, cell ratio factors (ratio between cancer cells- CC and blood cells subpopulations), G1-3, histology, glucose, AT, blood cell circuit, prothrombin index, heparin tolerance, recalcification time (P=0.000-0.038). Neural networks, genetic algorithm selection and bootstrap simulation revealed relationships between 5YS and PT early-invasive LC (rank=1), PT N0—N12 (rank=2), thrombocytes/CC (3), erythrocytes/CC (4), eosinophils/CC (5), healthy cells/CC (6), lymphocytes/CC (7), segmented neutrophils/CC (8), stick neutrophils/CC (9), monocytes/CC (10); leucocytes/CC (11). Correct prediction of 5YS was 100% by neural networks computing (area under ROC curve=1.0; error=0.0).
CONCLUSIONS: 5YS of LCP after radical procedures significantly depended on: 1) PT early-invasive cancer; 2) PT N0--N12; 3) cell ratio factors; 4) blood cell circuit; 5) biochemical factors; 6) hemostasis system; 7) AT; 8) LC characteristics; 9) LC cell dynamics; 10) surgery type: lobectomy/pneumonectomy; 11) anthropometric data. Optimal diagnosis and treatment strategies for LC are: 1) screening and early detection of LC; 2) availability of experienced thoracic surgeons because of complexity of radical procedures; 3) aggressive en block surgery and adequate lymph node dissection for completeness; 4) precise prediction; 5) adjuvant chemoimmunoradiotherapy for LCP with unfavorable prognosis.
micro teaching on communication m.sc nursing.pdfAnurag Sharma
Microteaching is a unique model of practice teaching. It is a viable instrument for the. desired change in the teaching behavior or the behavior potential which, in specified types of real. classroom situations, tends to facilitate the achievement of specified types of objectives.
The prostate is an exocrine gland of the male mammalian reproductive system
It is a walnut-sized gland that forms part of the male reproductive system and is located in front of the rectum and just below the urinary bladder
Function is to store and secrete a clear, slightly alkaline fluid that constitutes 10-30% of the volume of the seminal fluid that along with the spermatozoa, constitutes semen
A healthy human prostate measures (4cm-vertical, by 3cm-horizontal, 2cm ant-post ).
It surrounds the urethra just below the urinary bladder. It has anterior, median, posterior and two lateral lobes
It’s work is regulated by androgens which are responsible for male sex characteristics
Generalised disease of the prostate due to hormonal derangement which leads to non malignant enlargement of the gland (increase in the number of epithelial cells and stromal tissue)to cause compression of the urethra leading to symptoms (LUTS
Anti ulcer drugs and their Advance pharmacology ||
Anti-ulcer drugs are medications used to prevent and treat ulcers in the stomach and upper part of the small intestine (duodenal ulcers). These ulcers are often caused by an imbalance between stomach acid and the mucosal lining, which protects the stomach lining.
||Scope: Overview of various classes of anti-ulcer drugs, their mechanisms of action, indications, side effects, and clinical considerations.
Report Back from SGO 2024: What’s the Latest in Cervical Cancer?bkling
Are you curious about what’s new in cervical cancer research or unsure what the findings mean? Join Dr. Emily Ko, a gynecologic oncologist at Penn Medicine, to learn about the latest updates from the Society of Gynecologic Oncology (SGO) 2024 Annual Meeting on Women’s Cancer. Dr. Ko will discuss what the research presented at the conference means for you and answer your questions about the new developments.
Flu Vaccine Alert in Bangalore Karnatakaaddon Scans
As flu season approaches, health officials in Bangalore, Karnataka, are urging residents to get their flu vaccinations. The seasonal flu, while common, can lead to severe health complications, particularly for vulnerable populations such as young children, the elderly, and those with underlying health conditions.
Dr. Vidisha Kumari, a leading epidemiologist in Bangalore, emphasizes the importance of getting vaccinated. "The flu vaccine is our best defense against the influenza virus. It not only protects individuals but also helps prevent the spread of the virus in our communities," he says.
This year, the flu season is expected to coincide with a potential increase in other respiratory illnesses. The Karnataka Health Department has launched an awareness campaign highlighting the significance of flu vaccinations. They have set up multiple vaccination centers across Bangalore, making it convenient for residents to receive their shots.
To encourage widespread vaccination, the government is also collaborating with local schools, workplaces, and community centers to facilitate vaccination drives. Special attention is being given to ensuring that the vaccine is accessible to all, including marginalized communities who may have limited access to healthcare.
Residents are reminded that the flu vaccine is safe and effective. Common side effects are mild and may include soreness at the injection site, mild fever, or muscle aches. These side effects are generally short-lived and far less severe than the flu itself.
Healthcare providers are also stressing the importance of continuing COVID-19 precautions. Wearing masks, practicing good hand hygiene, and maintaining social distancing are still crucial, especially in crowded places.
Protect yourself and your loved ones by getting vaccinated. Together, we can help keep Bangalore healthy and safe this flu season. For more information on vaccination centers and schedules, residents can visit the Karnataka Health Department’s official website or follow their social media pages.
Stay informed, stay safe, and get your flu shot today!
1. Seven Myths of Randomisation
in Clinical Trials
Stephen Senn
1(c)Stephen Senn 2011-2015
2. Why this talk
• I had begun to notice that there were a
number of published criticisms of
randomisation in the methodology of science
literature of randomisation
• These seemed to be accepted as valid by
others
• I felt a refutation was called for
2(c)Stephen Senn 2011-2015
3. The Magnificent Seven
• Patients are treated simultaneously
• Balance is necessary for valid inference
• Observed covariates can be ignored
• Randomisation is not necessary for blinding
• Randomisation is inefficient
• Randomisation precludes balancing
• Large trials have better balance
3(c)Stephen Senn 2011-2015
4. Outline
• A game of chance
• The seven myths
• My philosophy of randomisation and analysis
4(c)Stephen Senn 2011-2015
5. Game of Chance
• Two dice are rolled
– Red die
– Black die
• You have to call correctly the odds of a total score of 10
• Three variants
– Game 1 You call the odds and the dice are rolled together
– Game 2 the red die is rolled first, you are shown the score
and then must call the odds
– Game 3 the Game 2 the red die is rolled first, you are not
shown the score and then must call the odds
5(c)Stephen Senn 2011-2015
6. Total Score when Rolling Two Dice
Variant 1. Three of 36 equally likely results give a 10. The probability is 3/36=1/12.
6(c)Stephen Senn 2011-2015
7. Variant 2: If the red die score is 1,2 or 3, probability of a total of10 is 0. If
the red die score is 4,5 or 6 the probability of a total of10 is 1/6.
Variant 3: The probability = (½ x 0) + (½ x 1/6) = 1/12
Total Score when Rolling Two Dice
7(c)Stephen Senn 2011-2015
8. The Morals
• You can’t treat game 2 like game 1.
– You must condition on the information you receive in order to act
wisely
– You must use the actual data from the red die
• You can treat game 3 like game 1.
– You can use the distribution in probability that the red die has
• You can’t ignore an observed prognostic covariate in analysing
a clinical trial just because you randomised
– That would be to treat game 2 like game 1
• You can ignore an unobserved covariate precisely because you
did randomise
– Because you are entitled to treat game 3 like game 1
8(c)Stephen Senn 2011-2015
9. Trialists continue to use their
randomization as an excuse for ignoring
prognostic information (myth 3), and they
continue to worry about the effect of
factors they have not measured (myth 2).
Neither practice is logical.
The Reality
9(c)Stephen Senn 2011-2015
10. Myth 1: Patients are treated
simultaneously
If, having created groups matched with respect to those ‘known’
factors, one then goes on to decide which will be the
experimental and which the control group by some random
process—in the simplest case by tossing a fair coin—then one
can do no epistemic harm, though one also does no further
epistemic good. Worrall 2007, p463.
For example, one could arrange for the matching to be
performed by a panel of doctors representing a spectrum of
opinion on the likely value of the drugs and whose criteria of
selection have been made explicit. Urbach, 1985, p272
10(c)Stephen Senn 2011-2015
11. All this is pretty obvious
• The point is that it is obvious to us
• It is not obvious to them
– Critics of randomisation writing on clinical trials
• You need to tell them to abandon the deep-
freeze microwave theory of clinical trials
• You can’t thaw patients out just when it suits
you
11(c)Stephen Senn 2011-2015
12. Myth 2:
Balance is necessary for validity
• It is generally held as being self evident that a
trial which is not balanced is not valid.
• Trials are examined at baseline to establish
their validity.
• In fact the matter is not so simple...........
12(c)Stephen Senn 2011-2015
13. A Tale of Two Tables
Trial 1 Treatment
Sex Verum Placebo Total
Male 34 26 60
Female 15 25 40
Total 49 51 100
Trial 2 Treatment
Sex Verum Placebo
Male 26 26 52
Female 15 15 30
Total 41 41 82
• Trial two balanced
but trial one not
• Surely trial two
must be more
reliable
• Things are not so
simple
13(c)Stephen Senn 2011-2015
14. A Tale of Two Tables
Trial 1 Treatment
Sex Verum Placebo Total
Male 26+8 26 60
Female 15 15+10 40
Total 49 51 100
Trial 2 Treatment
Sex Verum Placebo
Male 26 26 52
Female 15 15 30
Total 41 41 82
• Trial two contains trial
one
• How can more
information be worse
than less
• If statistical theory could
not deal with Trial 1
there would be
something wrong with it
14(c)Stephen Senn 2011-2015
15. Stratification
All we need to do is compare like with like.
If we compare males with males and females with females we
shall obtain two unbiased estimators of the treatment effects.
These can then be combined in some appropriate way. This
technique is called stratification.
A similar approach called analysis of covariance is available to deal
with continuous covariates such as height, age or a baseline
measurement.
15(c)Stephen Senn 2011-2015
16. What you learn in your first regression
course
1 11 1 0 1
2 12 2 1 2
1
1
1 ...
1 ...
k
k
n n kn k n
Y X X
Y X X
Y X X
X β ε
Y = Xβ +ε
L
M M M O M M M
Y
ˆ
-1
β = X X X Y
1 2ˆ ˆ( ) , ( ) .E V
β β β XX
16(c)Stephen Senn 2011-2015
17. 1 2
11 12 1
12 22 2
1
22
ˆvar( ) ( )
2/
k
k kk
X X
a a a
a a
a a
a n
The value of 2 depends on the
model.
For a given model, the value of
a22 depends on the design and
this only achieves its lower
bound when covariates are
balanced.
The Value of Balance
Variance multiplier for the treatment
effect
17(c)Stephen Senn 2011-2015
18. Myth 3
Observed covariates can be ignored
• This is wrong whether or not covariates are imbalanced
• Nobody would analyse a matched pairs design like a
completely randomised design
• However two classes of statisticians are implicitly signing up
to this
– Those who minimise
– Those who use the propensity score
18(c)Stephen Senn 2011-2015
19. The Problem with Minimisation
• Many public sector trials are minimised but
not strictly randomised
– That is to say a dynamic form of balancing is
employed
• Often the covariates used for balancing are
not fitted in the model
19(c)Stephen Senn 2011-2015
20. Typical MRC Stuff
‘The central telephone randomisation system used a minimisation algorithm to
balance the treatment groups with respect to eligibility criteria and other major
prognostic factors.’ (p24)
‘All comparisons involved logrank analyses of the first occurrence of particular
events during the scheduled treatment period after randomisation among all those
allocated the vitamins versus all those allocated matching placebo capsules (ie,
they were “intention-to treat” analyses).’ (p24)
1. (2002) MRC/BHF Heart Protection Study of cholesterol lowering
with simvastatin in 20,536 high-risk individuals: a randomised placebo-
controlled trial. Lancet 360:7-22
20(c)Stephen Senn 2011-2015
21. Corollary – unobserved covariates can
be ignored if you have randomised
• The error is to assume that because you can’t use
randomisation as a justification for ignoring
information it is useless
• It is useful for what you don’t see
• Knowing that the two-dice game is fairly run is
important even though the average probability is not
relevant to game two
• Average probabilities are important for calibrating your
inferences
o Your conditional probabilities must be coherent with your
marginal ones
See the relationship between the games
(C) Stephen Senn 2014 21
22. A Red Herring
• One sometimes hears that the fact that there are
indefinitely many covariates means that
randomisation is useless
• This is quite wrong
• It is based on a misunderstanding that variant 3 of
our game should not be analysed like variant 1
• I showed you that it should
(c)Stephen Senn 2013 22
23. You are not free to imagine anything
at all
• Imagine that you are in
control of all the thousands
and thousands of covariates
that patients will have
• You are now going to allocate
the covariates and their
effects to patients
o As in a simulation
• If you respect the actual
variation in human health that
there can be you will find that
the net total effect of these
covariates is bounded
𝑌 = 𝛽0 + 𝑍 + 𝛽1 𝑋1 + ⋯ 𝛽 𝑘 𝑋 𝑘 + ⋯
Where Z is a treatment indicator and the
X are covariates. You are not free to
arbitrarily assume any values you like for
the Xs and the 𝛽𝑠 because the variance of
Y must be respected.
(c)Stephen Senn 2013 23
24. The importance of ratios
• In fact from one point of view there is only one covariate that
matters
o potential outcome
If you know this, all other covariates are irrelevant
• And just as this can vary between groups in can vary within
• The t-statistic is based on the ratio of differences between to
variation within
• Randomisation guarantees (to a good approximation) the
unconditional behaviour of this ratio and that is all that
matters for what you can’t see (game 3)
• An example follows
(c)Stephen Senn 2013 24
25. Hills andArmitageEneuresis Data
10
8
14
2
12
6 1210
6
4
2
0
40 8
Drynights placebo
Line of equality
Sequence Drug Placebo
Sequence placebo drug
Cross-over trial in
Eneuresis
Two treatment periods of
14 days each
1. Hills, M, Armitage, P. The two-period
cross-over clinical trial, British Journal of Clinical
Pharmacology 1979; 8: 7-20.
25(c)Stephen Senn 2011-2015
26. 0.7
4
0.5
2
0.3
0
0.1
-2-4
0.6
0.2
0.4
0.0
Permutatedtreatment effect
Blue diamond shows
treatment effect whether or
not we condition on patient
as a factor.
It is identical because the
trial is balanced by patient.
However the permutation
distribution is quite different
and our inferences are
different whether we
condition (red) or not
(black) and clearly
balancing the randomisation
by patient and not
conditioning the analysis by
patient is wrong
26(c)Stephen Senn 2011-2015
27. The two permutation* distributions
summarised
Summary statistics for Permuted
difference no blocking
Number of observations = 10000
Mean = 0.00561
Median = 0.0345
Minimum = -3.828
Maximum = 3.621
Lower quartile = -0.655
Upper quartile = 0.655
P-value for observed difference 0.0340
*Strictly speaking randomisation
distributions
Summary statistics for Permuted
difference blocking
Number of observations = 10000
Mean = 0.00330
Median = 0.0345
Minimum = -2.379
Maximum = 2.517
Lower quartile = -0.517
Upper quartile = 0.517
P-value for observed difference 0.0014
27(c)Stephen Senn 2011-2015
28. Two Parametric Approaches
Not fitting patient effect
Estimate s.e. t(56) t pr.
2.172 0.964 2.25 0.0282
(P-value for permutation is 0.034)
Fitting patient effect
Estimate s.e. t(28) t pr
.
2.172 0.616 3.53 0.00147
(P-value for Permutation is 0.0014)
28(c)Stephen Senn 2011-2015
29. What happens if you balance but
don’t condition?
Approach Variance of estimated
treatment effect over all
randomisations*
Mean of variance of
estimated treatment
effect over all
randomisations*
Completely randomised
Analysed as such
0.987 0.996
Randomised within-
patient
Analysed as such
0.534 0.529
Randomised within-
patient Analysed as
completely randomised
0.534 1.005
*Based on 10000 random permutations
(c)Stephen Senn 2011-2015 29
That is to say, permute values respecting the fact that they come from a cross-
over but analysing them as if they came from a parallel group trial
30. In terms of t-statistics
Approach Observed variance
of t-statistic over all
randomisations*
Predicted
theoretical variance
Completely
randomised
Analysed as such
1.027 1.037
Randomised within-
patient
Analysed as such
1.085 1.077
Randomised within-
patient Analysed as
completely
randomised
0.534 1.037@
*Based on 10000 random permutations
@ Using the common falsely assumed theory
(c)Stephen Senn 2011-2015 30
31. The Shocking Truth
• The validity of conventional analysis of randomised
trials does not depend on covariate balance
• It is valid because they are not perfectly balanced
• If they were balanced the standard analysis would
be wrong
(c)Stephen Senn 2011-2015 31
32. Myth 4
Randomisation is Not Necessary for Blinding
Fisher, in a letter to Jeffreys, explained the dangers of using a
haphazard method thus
… if I want to test the capacity of the human race for
telepathically perceiving a playing card, I might choose the
Queen of Diamonds, and get thousands of radio listeners to
send in guesses. I should then find that considerably more
than one in 52 guessed the card right... Experimentally this
sort of thing arises because we are in the habit of making
tacit hypotheses, e.g. ‘Good guesses are at random except for
a possible telepathic influence.’ But in reality it appears that
red cards are always guessed more frequently than
black(Bennett, 1990).(pp268-269)
…if the trial was, and remained, double-blind then
randomization could play no further role in this respect.
(Worrall, 2007)(P454)
32(c)Stephen Senn 2011-2015
33. Avoiding Double Guessing
• If you don’t randomise you have to assume
that your strategy has not been guessed by
the investigator
• You are using ‘the argument from the
stupidity of others’
• Not publishing the block size in your protocol
is a classic example
33(c)Stephen Senn 2011-2015
34. Myth 5
Randomisation is Inefficient
• There is a sense in which this is no myth
• Randomisation is not fully efficient
• Theory shows that there is a loss of about one
patient per factor fitted compared to a
completely balanced design
– Such completely balanced designs are not usually
possible, however
• In any case, the loss is small
34(c)Stephen Senn 2011-2015
35. An Example
Linear Trend in Prognosis
The figures refer to the difference in position between B and A. Of course
alternation means that the Bs are on average one place beyond the As. The other
schemes are ‘unbiased’. Since alternation and the double sandwich are
deterministic the have no variance.
It is assumed that there are 2n patients in total and that n is an even number.
35(c)Stephen Senn 2011-2015
36. Myth 6
Randomisation precludes balancing
• Of course we know this is
not true
• We can build strata and
randomise within them
• ‘Balance what you can
and randomise what you
can’t’ was Fisher’s recipe
36(c)Stephen Senn 2011-2015
37. Myth 7
Large trials are more balanced than small ones
Measure of balance Comparison large v
small (on average)
Mean difference at
baseline
Large trial is more
balanced
Total difference at
baseline
Small trial is more
balanced
Standardised
difference at
baseline
Large and small trial
equally balanced
• Large trials have narrower
confidence intervals for the
treatment effect
• The advantage of increased mean
balance in covariates has already
been consumed in the form of
narrower limits
• There is no further insurance to
be given by size
– Only increase in validity is
because closer to asymptotic
limit that guarantees Normality
37(c)Stephen Senn 2011-2015
38. My Philosophy of Clinical Trials
• Your (reasonable) beliefs dictate the model
• You should try measure what you think is important
• You should try fit what you have measured
– Caveat : random regressors and the Gauss-Markov theorem
• If you can balance what is important so much the better
– But fitting is more important than balancing
• Randomisation deals with unmeasured covariates
– You can use the distribution in probability of unmeasured covariates
– For measured covariates you must use the actual observed distribution
• Claiming to do ‘conservative inference’ is just a convenient
way of hiding bad practice
– Who thinks that analysing a matched pairs t as a two sample t is acceptable?
38(c)Stephen Senn 2011-2015
39. What’s out and What’s in
Out In
• Log-rank test
• T-test on change scores
• Chi-square tests on 2 x 2
tables
• Responder analysis and
dichotomies
• Balancing as an excuse for
not conditioning
• Proportional hazards
• Analysis of covariance
fitting baseline
• Logistic regression fitting
covariates
• Analysis of original values
• Modelling as a guide for
designs
39(c)Stephen Senn 2011-2015
40. Unresolved Issue
• In principle you should never be worse off by
having more information
• The ordinary least squares approach has two
potential losses in fitting covariates
– Loss of orthogonality
– Losses of degrees of freedom
• This means that eventually we lose by fitting
more covariates
40(c)Stephen Senn 2011-2015
41. Resolution?
• The Gauss-Markov theorem does not apply to
stochastic regressors
• In theory we can do better by having random effect
models
• However there are severe practical difficulties
• Possible Bayesian resolution in theory
• A pragmatic compromise of a limited number of
prognostic factors may be reasonable
41(c)Stephen Senn 2011-2015
42. To sum up
• There are a lot of people out there who fail to
understand what randomisation can and
cannot do for you
• We need to tell them firmly and clearly what
they need to understand
42(c)Stephen Senn 2011-2015
43. Finally
I leave you with
this thought
Statisticians are always
tossing coins but do not
own many
43(c)Stephen Senn 2011-2015