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Yet seeking all it finds!

My Oxford
Wherein eternall studie never faints
Still finding all, yet seeking all it finds:
How endless is your labyrinth of bliss e,
Where to be lost the sweetest finding is!
Shakespeare



SAYING WHAT WE MEAN

House of Lords
Peers have a reputation for being extremely polite to one another. Even insults are couched in language that sometimes means it is a few minutes before victims realise they have been criticised.

Given that we sometimes hide what we really mean in decorous language, ....it may be helpful to identify phrases that are variously employed and, in parenthesis, explain what is really meant. Here are some of the most utilised phrases and what they mean:

‘With all due respect….’ (That was rubbish)

‘If the noble Lord will forgive me, I will not follow him in the line that he has taken…’ (That was nothing to do with what we are talking about)

‘The noble Lord, for whom I have the greatest respect…’ (You’ve lost it this time)

‘The noble Lord makes an interesting point…’ (I have no idea what the answer is)

‘I hear what the noble Lord says….’ (I take a different view)

‘The noble Lord, who is an experienced member of the House….’ (You’ve forgotten the correct procedure)

‘I would remind the noble Lord that this is a time-limited debate’ (Shut up)

‘If the noble Lord will allow me…..’ (Sit down)

‘My Lords’, if repeated several times within the course of a few sentences (Help!)

http://lordsoftheblog.wordpress.com/2008/04/23/saying-what-we-mean/

Measure you use

The Learned World was one World, international and nondenominational, rising above the petty concerns of church and state.

Goldgar, A., (1995), İmpolite Learning (period 1680-1750)


What is trust? Trust is gained with minimum cost; but if broken – thence, no amount of money or effort can bring the level back to where it was.

Definitions of trust generally contain two components. The first is vulnerability: an act of trust involves putting oneself in a vulnerable position in the hope of gaining a positive benefit as a result. The second is expectation: the potential truster bases his decision on an expectation about whether the potential trustee will exploit his vulnerability, given that the trustee faces a ‘raw’, as Bacharach and Gambetta (1999) would call it, incentive to do so. Thus, Gambetta (1988) describes trust as ‘a threshold point, located on a probabilistic distribution’ (pg. 218).
http://www.csae.ox.ac.uk/workingpapers/pdfs/2001-12text.pdf


Do not judge, and you will not be judged. Do not condemn, and you will not be condemned. A good measure, pressed down, shaken together and running over, will be poured into your lap. For with the measure you use, it will be measured to you.

LUKE 6:9, 37

Oxford Scholarship online

Probability: Pragmatism in broad sense

For ‘explication’ of a pre-theoretical concept in terms of a scientifically precise concept a number of criteria is given to the proposed explicatum to (i) be sufficiently similar to the original concept to be recognisably an explication of it; (ii) be more exact or precise, and have clear criteria for application; (iii) play a unified and useful role in the scientific economy (so that it is not just gerrymandered and accidental); and (iv) be enmeshed in conceptual schemes simpler than any other putative explication that also meets criteria (i)–(iii). These are good constraints to keep in mind. However, this model is altogether too compressed: for it presumes that we have an independently good analysis of the scientifically precise concept (in effect, it suggests that scientific theories are not in need of conceptual clarification—that the ‘clear conditions of application’ are sufficient for conceptual understanding). It also suggests that the explicatum replace or eliminate the explicandum; and that satisfying these constraints is enough to show that the initial concept has no further importance. But clearly the relation between the scientific and pre-scientific concepts is not so one-sided; after all, the folk are the ones who accept the scientific theories, and if the theory disagrees too much with their ordinary usage, it simply won’t get accepted. I take this kind of approach to philosophical analysis to be pragmatist in some broad sense: it emphasises the conceptual needs of the users of scientific theories in understanding the aims and content of those theories.


Eagle A, (2004), Twenty-One Arguments Against Propensity Analyses of Probability,
http://ora.ouls.ox.ac.uk



Null hypothesis:
“the hypothesis that the phenomenon to be demonstrated is in fact absent [Fisher, 1949, p13].”not that he hoped to “prove” this hypothesis. On the contrary, he typically hoped to “reject” this hypothesis and thus “prove” that the phenomenon in question is in fact present.
Cohen J., (1988) Statistical power analysis for the behavioural sciences, Academic Press




Data dredging, biases, and confounding
It would seem wiser to attempt a better diagnosis of the
problem before prescribing Le Fanu’s solution. Data
dredging is thought by some to be the major problem:
epidemiologists have studies with a huge number of
variables and can relate them to a large number of out­
comes, with one in 20 of the associations examined
being “statistically significant” and thus acceptable for
publication in medical journals.w6 The misinterpretation
of a P < 0.05 significance test as meaning that such find­
ings will be spurious on only 1 in 20 occasions unfortu­
nately continues. When a large number of associations
can be looked at in a dataset where only a few real asso­
ciations exist, a P value of 0.05 is compatible with the
large majority of findings still being false positives.w7
These false positive findings are the true products of
data dredging, resulting from simply looking at too
many possible associations. One solution here is to be
much more stringent with “significance” levels, moving
to P < 0.001 or beyond, rather than P < 0.05.w7

BMJ, Data dredging, bias, or confounding
access through www.oxfordjournals.org




Social Epidemiology
Commentary: Education, education, education
Eric Brunner

Department of Epidemiology & Public Health, University College London, 1–19 Torrington Place, London WC1E 6BT, UK. E-mail: e.brunner@ucl.ac.uk

There is no doubt that, broadly within a given society, poorer education is linked with poorer health. The research question is why this linkage exists, and having gained an understanding of the mechanisms, to examine what is to be done about it at policy level. Kilander et al.'s new analysis1 of 25-year mortality of men born 1920–1924 in Uppsala, Sweden, provides further valuable evidence for the education-health association, and focuses on the role of lifestyle factors as mediators between level of education and elevated risks of coronary and cancer death. Compared with those who completed high school or university education, men who had <=7 years of schooling were more . . . [Full Text of this Article]
access through:
www.oxfordjournlas.org




Instruments for Causal Inference: An Epidemiologist's Dream?

Can you guarantee that the results from your observational study are unaffected by unmeasured confounding? The only answer an epidemiologist can provide is “no.” Regardless of how immaculate the study design and how perfect the measurements, the unverifiable assumption of no unmeasured confounding of the exposure effect is necessary for causal inference from observational data, whether confounding adjustment is based on matching, stratification, regression, inverse probability weighting, or g-estimation.

Now, imagine for a moment the existence of an alternative method that allows one to make causal inferences from observational studies even if the confounders remain unmeasured. That method would be an epidemiologist's dream. Instrumental variable (IV) estimators, as reviewed by Martens et al 1 and applied by Brookhart et al 2 in the previous issue of Epidemiology, were developed to fulfill such a dream.

Instrumental variables have been defined using 4 different representations of causal effects:
1. Linear structural equations models developed in econometrics and sociology 3,4 and used by Martens et al 1
2. Nonparametric structural equations models 4
3. Causal directed acyclic graphs 4–6
4. Counterfactual causal models 7–9

A double-blind randomized trial satisfies these conditions in the following ways. Condition (i) is met because trial participants are more likely to receive treatment if they were assigned to treatment, condition (ii) is ensured by effective double-blindness, and condition (iii) is ensured by the random assignment of Z. The intention-to-treat effect (the average causal effect of Z on Y) differs from the average treatment effect of X on Y when some individuals do not comply with the assigned treatment. The greater the rate of noncompliance (eg, the smaller the effect of Z on X on the risk-difference scale), the more the intention-to-treat effect and the average treatment effect will tend to differ. Because the average treatment effect reflects the effect of X under optimal conditions (full compliance) and does not depend on local conditions, it is often of intrinsic public health or scientific interest. Unfortunately, the average effect of X on Y may be affected by unmeasured confounding.

Instrumental variables methods promise that if you collect data on the instrument Z and are willing to make some additional assumptions (see below), then you can estimate the average effect of X on Y, regardless of whether you measured the covariates normally required to adjust for the confounding caused by U. IV estimators bypass the need to adjust for the confounders by estimating the average effect of X on Y in the study population from 2 effects of Z: the average effect of Z on Y and the average effect of Z on X. These 2 effects can be consistently estimated without adjustment because Z is randomly assigned. For example, consider this well-known IV estimator: The estimated effect of X on Y is equal to an estimate of the ratio.



by Hernán, Miguel A.*; Robins, James M.*†
Issue: Volume 17(4), July 2006, pp 360-372

http://ovidsp.uk.ovid.com/spb/ovidweb.cgi

Regressive Measures

As the Oxford economist Paul Collier points out in his book The Bottom Billion, Africa has been subjected by European governments to one form of "befuddled romanticism" after another, from campaigns against GM foods and low-wage produce to "save the peasant" farm reform. Africa, says Collier, has less commercial agriculture than it did at the end of the age of empire, half a century ago.

.....While antagonism to science merely impedes progress, antagonism to economics is regressive.

Simon Jenkins, The cost of green tinkering is in famine and starvation
Guardian, April 16








..........Then we need to say what we mean by democracy. After all, everyone pays lip service to it: the Egyptians, the Chinese, Vladimir Putin, Robert Mugabe. But they mean something different. This does not and cannot imply a single rigid template. Europe is immunised against what one might call the American temptation by the simple fact that Europe's democracies are themselves so diverse: constitutional monarchies and republics, unicameral and bicameral, centralised and decentralised, with a strong executive and weaker legislature, or vice versa. We can hardly propagate a single model when we have none ourselves. All the more reason, however, to spell out the shared essentials without which there is no democracy worthy of the name. That does not just mean regular, free and fair elections. The emerging European definition of democracy will be multidimensional, including the rule of law, independent media, respect for both individual human rights and minority rights, sound public administration, civilian control over the military and a strong civil society.



Timothy Garton Ash, We need a benign European hydra to advance the cause of democracy
Guardian, 17 April

Swan-upping

Be the swans on thy bosom
still whiter than snow

Shakepeare's lives, OUP

swan-upping

• noun Brit. the annual practice of catching swans on the River Thames and marking them to indicate ownership by the Crown or a corporation.

Life in Water Environment

An ancient relative of today’s elephants lived in water, a team led by an Oxford University scientist has found.

The scientists were investigating the lifestyle of two early elephants (proboscideans) Moeritherium and Barytherium that lived in the Eocene period, over 37 million years ago. By analysing isotopes in tooth enamel from Moeritherium they were able to deduce that it was very likely a semi-aquatic mammal, spending its days in water eating freshwater plants.‘

We know from molecular data that modern elephants share a common ancestry with the sirenians - aquatic sea cows and dugongs,’ said Alexander Liu of Oxford’s Department of Earth Sciences, lead author of a report of the research published online in PNAS this week. ‘It suggests that elephants may have an ancestor which was amphibious in its mode of life and we wanted to know if Moeritherium or Barytherium was this semi-aquatic ancient relative. Unfortunately only fragments of the skeletons of these early elephants survive, so instead of looking at their bones we looked at the chemical composition of their teeth to determine what they ate and how they lived.’

Alex Liu, with colleagues Erik Seiffert from Stony Brook University (USA) and Elwyn Simons from the Duke Lemur Center (USA), analysed the oxygen and carbon isotope ratios contained within tooth enamel from both extinct proboscideans.

While carbon isotopes can give clues as to an animal’s diet, oxygen isotopes found in teeth come from local water sources - and variations in the ratios of these isotopes can indicate the type of environment the animal lived in. They compared the ratios of these isotopes to definitely terrestrial animals from the same period and these results – when combined with results from studies of embryology, molecular data, and sedimentology – lead them to believe that Moeritherium was semi-aquatic.

Alex Liu commented: ‘We now have substantial evidence to suggest that modern elephants do have ancient relatives which lived primarily in water. The next steps are to conduct similar analyses on other elephant ancestors to determine when the switch from water to land occurred, and to determine exactly when the now fully-aquatic sirenians split from their semi-aquatic proboscidean relatives.’

Related OxSciBlog story: Many faces of Moeritherium.

When does effect modification matter

When does effect modification matter?

MH methods assume that the true E - D odds ratio is the same in each stratum, an that the only reason for differences in the observed odds ratios between strata is sampling variation. We should check this assumption by applying the chi square test for heterogeneity, before reporting MH odds ratios, confidence intervals and P-values.

Kirkwood et al, 2003, Medical Statistics, Blackwell, p.187

Statistics Tests

1. Paired-sample t test is based on the assumption of normality of distribution – Although no particular distribution needed for the paired sample but certain level of symmetry is assumed for the population distribution of the paired differences.
2. Wilcoxon signed rank sum test- When we work on small samples with probability of non-normality of the paired observation differences, it is best to use Wilcoxon matched pairs signed ranks test, which yields the test statistics that uses ranking with no concern about normality of distribution. As with the paired sample t-test, we are interested in measuring the differences before and after the treatment. The procedure for the Wilcoxon signed rank sum test is as follows:

- The differences are calculated and then ranked in ascending order, ignoring the sign of the difference.
- Zeroes are ignored (and the sample size is adjusted accordingly).
- Those with the same difference are given an average ranking. (For example, if the eighth and ninth values are the same, they are ranked as 8.5.)
- The ranks are then given the sign of the difference.
- Ranks are summed for all those with negative differences and those with positive differences.
- "The smallest value is then looked up in the appropriate table for the number of pairs included in the sign ranking.

Two Way Analysis of Variance-Two Way Analysis of Variance is a way of studying the effects of two factors separately (their main effects) and (sometimes) together (their interaction effect)

3. Wilcoxon rank sums test: This test compares two different sample distributions to see if they come from the same non-normal population probability distribution. This is the non-parametric equivalent of the t-test.

4. Mann-Whitney U test: this is a non-parametric test identical to the above (No. 2) but with more complex calculation.the non-parametric analogue of the independent two-sample t-test is the Mann-Whitney test. For both the general test and its two-sample version, the null hypothesis is that the medians (and not the means) are equal, against the general alternative that at least one differs from the others. We compare the medians, rather than the means, because the data will probably not be symmetric if we are using a non-parametric test, so the value of the mean will be artificially inflated or deflated. The Mann-Whitney test test this null hypothesis by transforming the data into pooled ranks (that is, they start by assigning rank 1 to the smallest observation in the pooled sample, and so on) and then calculating a test statistic from these ranks. Both tests appear in the non-parametric sub-menu of SPSS.

5. Sign test available in SPSS also calculate similar significant points when we apply non-parametric test on two independent sample. This tests hypotheses regarding the median of a distribution and is independent of distribution type.

6. Kolmogorov-Smirnov test: This test is used to compare two different samples to see if they could be from the the same population or to see if a sample distribution is of a certain hypothesized type.

7. Tukey's method depends on equal sample sizes and so is less widely applicable.

8. Scheffe's method uses a generalised procedure for all of the possible linear combinations of treatment means (called contrasts) but these results in wider confidence levels than the other two methods. Scheffé’s (1953) method of simultaneous inference construct bands called Scheffé confidence bands to be distinct from the usual s.e. bands which is representing a shift from the mean of the distribution in proportion to its variance.

9. while individual coefficients may be imprecisely estimated (low t-statistics), the joint effect could still be quite precisely estimated (high F-statistics).

10. Welsh test correction is applied to t test, when the assumption of normality is not supported. The Welch function on t-tests corrects for unequal variances

11. Kruskal-Wallis H-test: The non-parametric equivalent of ANOVA F-test is the Kruskal-Wallis test, which is a generalisation of the Mann-Whitney test for more than two groups. If the assumptions regarding normality and the variances being equal break-down then the appropriate non-parametric test is the Kruskal-Wallis H-test.

12. The non-parametric equivalent of Anova test where the assumptions of normality and similar variance is absent - called Friedman test. Friedman’s Test compare observations repeated on the same subjects. Unlike the parametric repeated measures ANOVA or paired t-test, this non-parametric makes no assumptions about the distribution of the data (e.g., normality).

13. Bonferroni, uses t tests to perform pair-wise comparisons between group means, but controls overall error rate by setting the error rate for each test to the experiment-wise error rate divided by the total number of tests. Hence, the observed significance level is adjusted for the fact that multiple comparisons are being made.

14. Non-parametric two related sample test: Stratification in case control studies- the results may then be pooled across the strata to arrive at conclusive evidence for any association. This can be achieved by using the Mantel-Haenszel χ2 test.

PARAMETRIC TESTS:
Two Way Analysis of Variance: Two Way Analysis of Variance is a way of studying the effects of two factors separately (their main effects) and (sometimes) together (their interaction effect).

Hardened truth about immunity

Call it an immune system double-cross. The same proteins that fight germs may also help fat and cholesterol clog our arteries, new research shows. Understanding this deadly duality could eventually lead to new drugs to ward off heart disease.

http://www.oxfordjournal.com


HOW IS OUR WORLD CHANGING?

An answer to this question is not simply that we now face global competition and hence have to work harder to educate more people. My reading of the innovation literature [8-11] suggests that the major factor to address is the increasing rate of change.

Not so many years ago, companies could come up with an innovative idea for a product or service and gradually refine it for 25 years or more. People could develop particular kinds of expertise and be successful for a lifetime. This made it possible for educational institutions (e.g., community colleges, four-year institutions) to teach job-specific skills and knowledge and know that most of this would still be useful in the workplace.

Today, innovation cycles are often very short and educational systems are often insufficiently nimble. As educators, we may end up training students in specifics that are no longer useful once they reach the workplace. Some suggest that preparing people for change highlights the need to emphasize the adaptive features of expertise.


Oxford journals, The crisis of human survival
http://www.oxfordjournal.com/html/diary/showlog.vm?sid=66&log_id=237

Methodological insights

In some way every biomedical researcher is searching for a kind of ultimate explanation of disease. So, we have been told that all cancers were due to mutations in p53 (some years ago), then it was the turn of epigenetics, and so on. It seems
that looking for a single and simple explanation of things—and an ensuing unambiguous classification— is inherent in human psychology. However, we should also be aware that at least sometimes it is not possible to find such an explanation and such a classification. For example, people have struggled for years but still an unambiguous
classification of viruses is not available.2 When we adopt a classification of disease (for example, International Classification of Diseases, tenth revision, ICD-10), or when we refer to the diagnostic criteria for disease, or when we think
of causes, we usually imply that such activities are based on unequivocal criteria that sharply distinguish one disease from another one, or that relate a cause to its effect. This is very clear in the paradigm of ‘‘necessary and sufficient’’ causes.
However, reality is very far from such interpretation.....

Vineis P., Methodological insights: fuzzy sets in medicine
doi:10.1136/jech.2007.063644
J. Epidemiol. Community Health 2008;62;273-278
http://jech.bmj.com/cgi/content/full/62/3/273

you can respond to this article through this:
http://jech.bmj.com/cgi/eletter-submit/62/3/273

source: British Medical Journal
http://jech.bmj.com/cgi/reprint/62/3/273

Cumulative Distribution

Cumulative Distribution Function

All random variables (discrete and continuous) have a cumulative distribution function. It is a function giving the probability that the random variable X is less than or equal to x, for every value x.

*********************

Formally, the cumulative distribution function F(x) is defined to be:

F(x) = P(X >= x) for infinite < x < infinite c.d.f.

For a discrete random variable, the cumulative distribution function is found by summing up the probabilities.

For a continuous random variable, the cumulative distribution function is the integral of its probability density function.



Probability Density Function

The probability density function of a continuous random variable is a function which can be integrated to obtain the probability that the random variable takes a value in a given interval.

*********************

More formally, the probability density function, f(x), of a continuous random variable X is the derivative of the cumulative distribution function F(x):

f(x) = d / dx * F(x)


source: http://techniques.geog.ox.ac.uk/mod_2/glossary/prob.html#cdf

www.stats.ox.ac.uk/~dalby/statistics.html

the prevalence, incidence, co-morbidities and therapeutic objectives

A retrospective study was performed based on data from patients attended for stroke, aged > 30 years, from five Spanish primary care centres and two hospitals in 2006. Comparative group: patients without stroke. Main analysed variables were: age, sex, co-morbidity (cardiovascular/others), clinical parameters and direct costs (pharmacy, derivations, visits, emergencies, procurement, and hospitalisation). An ANCOVA analysis and logistic regression were used to fit the model. RESULTS: A 4.5% of 57.026 patients (n = 2.585; CI 95% = 4.3-4.7%) suffered stroke. The incidence of stroke was 220 new-cases/100.000 populations. Main differences between patients suffering stroke/control group were: age (72.5 vs. 53.5), men (58.2% vs. 44.6%), episodes/year (7,9 vs. 4,8), visits/year (15,8 vs. 8,1), p < 0,001. Stroke had an independent relation with age (OR = 1,4), male (OR = 2,3), diabetes (OR = 1,6), hypertension (OR = 1,5), smoking (OR = 1,5), alcohol (OR = 1,4), depression (OR = 1,4), dyslipidemia (OR = 1,3) and dementia (OR = 1,2). Some of the results were: systolic pressure (134.1 vs. 127.6 mmHg) and LDL-cholesterol (116.4 vs. 126.2 mg/dL), in presence/absence of stroke, p < 0,001. The average of annual costs of stroke was 2,590.36 vs. 985.26 euros, p < 0.001. After the correction of the logistic model results did not change: 1,774.33 (CI 95% = 1,720.10-1.828.55) vs. 1,021.98 euros (CI 95% = 1,010.92-1,033.03), p < 0,001. All components of costs were higher in the stroke group. CONCLUSIONS: Patients that demanded assistance for stroke had a higher number of co-morbidities and a higher total cost/patient/year. Therapeutic objectives could be improved, mainly in primary prevention of cardiovascular risk factors.

http://ora.ouls.ox.ac.uk/access/detail.php?pid=ora:810

Confidence Intervals

Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model



A simultaneous confidence band provides a variety of inferences on the unknown components of a regression model. Construction of simultaneous confidence bands for a simple linear regression model has a rich history, going back to(1929). The purpose of this article is to consolidate the disparate modern literature on simultaneous confidence bands in linear regression, and to provide expressions for the construction of exact 1−αlevel simultaneous confidence bands for a simple linear regression model of either one-sided or two-sided form.We center attention on the three most recognized shapes:hyperbolic, two-segment, and three-segment (which is also referred to as a trapezoidal shape and includes a constant-width band as a special case). Some of these expressions have already appeared in
the statistics literature, and some are newly derived in this article. The derivations typically involve a standard bivariate t random vector and its polar coordinate transformation.

Key words: Simple linear regression; simultaneous inferences; bivariate normal; bivariate t; polar coordinators.

www.blackwell-synergy.com/j

Symmetry Definitions

The issue of symmetry is now widely recognised as of fundamental importance in constraint satisfaction problems (CSPs). It seems self-evident that in order to deal with symmetry we should first agree what we mean by symmetry. Surprisingly, this appears not to be true: researchers in this area have defined symmetry in fundamentally different ways, whilst often still identifying the same collection of symmetries in a given problem and dealing with them in the same way. In this paper, we first survey the various symmetry definitions that have appeared in the literature. We show that the existing definitions reflect two distinct views of symmetry: that symmetry is a property of the solutions, i.e., that any mapping that preserves the solutions is a symmetry; or that symmetry preserves the constraints, and therefore as a consequence also preserves the solutions. We propose two new definitions of solution symmetry and constraint symmetry to capture these two distinct views, and show that they are indeed different: although any constraint symmetry is also a solution symmetry, there can be many solution symmetries that are not constraint symmetries. We discuss the relationship between the symmetry groups identified by these definitions and show that each is the automorphism group of a hypergraph, derived from either the solutions or the constraints of the CSP.


Symmetry Definitions for Constraint Satisfaction Problems
David Cohen & Peter Jeavons & Christopher Jefferson &
Karen E. Petrie & Barbara M. Smith

http://web.comlab.ox.ac.uk/people/Peter.Jeavons/

Risk, Chance and Probability

Dr. Price, of Llangeinor in Glamorgan, pioneered the gathering of information on death, thus becoming at the same time a founder of both epidemiology and the insurance industry. Price organised Thomas Bayes' papers after his death, and wrote up the work on prior probability we know today as Bayes' Theorem; some think it should be Price's Theorem. He was also an economist (the younger Pitt used his ideas to manage government debt), a dabbler in science (Joseph Priestly and Benjamin Franklin bounced ideas about electricity off him), and he was an ethicist and thinker about individual liberty. Some of his thoughts were incorporated into the American Declaration of Independence. Other friends and correspondents included Adam Smith, John Quincey Adams, and John Howard.

Price was a Fellow of the Royal Society of London, and given the Freedom of the city of London. He was also honoured by Yale University (alongside George Washington), and invited by the young USA to assist in its financial administration. Price was also highly regarded in France, where he was made a Freeman of the city of Paris, and an honorary member of the National Assembly. On his death, France had a day of mourning. Curiously, in Wales, where he was born, he is almost unknown.

http://www.jr2.ox.ac.uk/bandolier/booth/booths/risk.html

Fisher 's Exact test

Arguably, Fisher’s towering contribution to statistics was his initiating a recasting of statistical induction from ‘induction by enumeration’ (see Pearson, 1920) to ‘model-based induction’. The key to his recasting was the notion of a statistical model providing an idealized description of the data generating process and specified in terms of probabilistic assumptions concerning ‘a hypothetical infinite population’.

..This included a formalization of a ‘random sample’ in the form of the Independence and Identically Distributed (IID) assumptions, to replace the ‘uniformity’ and ‘representativeness’ stipulations, and the explicitly introduction of a distributional assumption, such as Normality. The latter assumption was crucial for Fisher’s frequentist error probabilities, which are deductively derived from the statistical model for any sample size n, and provide a measure of the ‘trustworthiness’ of the inference procedure: how often a certain method will give rise to reliable inferences concerning the underlying actual data generating process. The form of induction envisaged by Fisher is one where the reliability of the inference is emanating from the ‘trustworthiness’ of the procedure used to arrive at the inference. In summary, an inference is reached by an inductive procedure which, with high probability, will reach true conclusions (estimation, testing, prediction) from true (or approximately true) premises (statistical model); see Mayo (1996). Fisher’s crucial contributions to the built-in deductive component, known as ‘sampling theory’, in the form of deriving the finite sampling distributions of several estimators and test statistics, pioneered the recasting of statistical induction in terms of ‘reliable procedures’ based on ‘ascertainable error probabilities’. Fisher envisaged the modeling process as revolving around a prespecified parametric statistical model Mθ(y), chosen so as to ensure that the observed data y0 can be realistically viewed as a truly typical realization of the stochastic mechanism (process) described by Mθ(y) :

“The postulate of randomness thus resolves itself into the question, "Of what population is this a random sample?" which must frequently be asked by every practical statistician.” (Fisher, 1922, p. 313)

Aris Spanos,Testing the Validity of a Statistical Model, 2007
http://www.economics.ox.ac.uk/hendryconference/Papers/Spanos_DFHVol.pdf

Risk perception

Figure 1: How graduates and professionals label the same adverse event presented in different ways


Risk perception and presentation

A study [1] was carried out on two groups, 38 graduate students and 47 healthcare professionals. A hypothetical situation about adverse events of an influenza vaccine was presented to them in either a probability format (5%), or a frequency format (1 in 20). Randomisation was by alternation in questionnaire handouts.

The questionnaire asked whether they would be prepared to receive a vaccine if the risk of fever and headache within seven days was either 5% (one group) or 1 in 20 (the other). A second question asked participants to match frequency with one of six phrases, from very common to very rare.

Results

There was no difference between occupation, age, or sex of the groups receiving information as probability or frequency. About 60% of participants would have elected to have the influenza vaccine, without any significant difference between a probability format (67% electing to receive it) and the frequency format (55%).

There were differences between the way in which the risk was matched to phrases (Figure 1). In both presentations, the same risk was labelled as very common, through to rare. Presentation as frequency (1 in 20) resulted in much greater consensus, with 84% happy that this could be called common or occasional, and only 9% considering it either rare or very common.


source:
www.jr2.ox.ac.uk/bandolier/band144/b144-3.html#Heading2

P values between 0.04 and 0.06

The study to compare the distribution of P values in abstracts of randomised controlled trials with that in observational studies, and checks on P values between 0.04 and 0.06, looked into the Design Cross sectional study of 260 abstracts in PubMed of articles published in 2003 that contained "relative risk" or "odds ratio" and reported results from a randomised trial, and random samples of 130 abstracts from cohort studies and 130 from case-control studies. P values were noted or calculated if unreported. Main outcome measured Prevalence of significant P values in abstracts and distribution of P values between 0.04 and 0.06.

The first result in the abstract was statistically significant in 70% of the trials, 84% of cohort studies, and 84% of case-control studies. Although many of these results were derived from subgroup or secondary analyses, or biased selection of results, they were presented without reservations in 98% of the trials. P values were more extreme in observational studies (P < 0.001) and in cohort studies than in case-control studies (P = 0.04). The distribution of P values around P = 0.05 was extremely skewed. Only five trials had 0.05 ≤ P < 0.06, whereas 29 trials had 0.04 ≤ P < 0.05. I could check the calculations for 27 of these trials. One of four non-significant results was significant. Four of the 23 significant results were wrong, five were doubtful, and four could be discussed. Nine cohort studies and eight case-control studies reported P values between 0.04 and 0.06, but in all 17 cases P < 0.05. Because the analyses had been adjusted for confounders, these results could not be checked.

Conclusions = Significant results in abstracts are common but should generally be disbelieved.

Believability of relative risks and odds ratios in abstracts: cross sectional study, BMJ 2006;333:231-234 (29 July), doi:10.1136/bmj.38895.410451.79 (published 19 July 2006)

Creating Fantasy Communities

Ersatz "communities" were declared open by politicians cutting ribbons. Each generation of towns prayed in aid some planning maxim. Those of the 1960s and 1970s, over-engineered by their architects, not only damaged the social fabric of urban Britain but induced an alienation, a "new town blues", recounted in every analysis from Lionel Esher's Broken Wave to Lynsey Hanley's recent Estates. Though rooted in the genteel Edwardian garden suburb, the movement grew brutalist and dark, and its other half was a depopulated and demoralised inner city.

Throughout history, nothing has appealed to the authoritarian mind so much as creating fantasy communities.

Simon Jenkins, Guardian, Eco-towns are the greatest try-on in the history of property speculation.

Intention to treat

A key complication in drawing inference about causal effects in any trial is that compliance is rarely perfect. A standard approach is to estimate the intention-to-treat (ITT) effect. The ITT effect describes the benefit of being randomized to treatment. ITT can be used, for example, to determine the impact that
recommending (or encouraging; Hirano and others, 2000) a particular treatment over an alternative treatment would have, on average, in the population. However, one treatment might appear superior because it is better tolerated. For example, one could imagine a treatment that fewer people would comply with but that has superior results among those that do comply. If this information was known, the recommended
treatment could potentially be tailored to individual subjects. Thus, in addition to knowing the ITT effect, it would be useful to know which treatment would result in better outcomes among subjects who would comply with and receive either intervention and which characteristics are predictive of compliance.
In trials of an active treatment versus placebo (or no treatment), it is possible to recover causal effects under some reasonably mild assumptions. For all-or-none compliance situations, the method of instrumental variables can be particularly useful (Angrist and others, 1996). Causal effects among compliers (subjects who would take treatment if offered) are identifiable under the assumption that there are no
subjects who would take the active treatment if randomized to the control arm but not to the treatment arm (no defiers). This assumption is reasonable in trials where the control group does not have access to the active treatment. In such settings, the instrumental variables estimator is equivalent to the estimator from certain structural mean models (Robins, 1994; Goetghebeur and Lapp, 1997; Robins and Rotznitzky,(2004). Structural mean models can also be used when compliance is continuous and if there are interactions between the causal effect and the baseline covariates. However, if it is unreasonable to assume there are no defiers, the causal parameters are generally not identifiable without structural assumptions; several
authors have derived bounds on the causal effects (Robins, 1989; Manski, 1990; Balke and Pearl, 1997; Joffe, 2001). For comparisons of 2 active treatments, the principal stratification framework (Frangakis and Rubin, 2002) can be used to define and infer causal parameters of interest, such as the effect of the exercise intervention
compared with standard therapy among subjects who would comply with either intervention.
Direct implementation of the principal stratification approach has several limitations. First, causal effects of interest would not be point identified (Cheng and Small, 2006). Further, it would not provide information about characteristics of subjects in each subpopulation (stratum). To address these issues, we identify
causal parameters of interest, up to a sensitivity parameter, through the use of baseline covariates that are predictive of compliance. Including covariates in the model is not straightforward as care has to be taken to ensure the marginal compliance distributions are compatible with the joint distribution. In addition, our
model clearly separates parameters that can be identified from the data from those that cannot. Finally, we illustrate how a constraint on the joint distribution of the potential compliance variables can be integrated into the methodology. This approach provides investigators with additional useful information, beyond just the ITT effect.
Principal stratification with predictors of compliance for randomized trials with 2 active treatments, Biostatistics (2008), 9, 2, pp. 277–289, Oxford Univ Press Journals