Vascular geometry and oxygen diffusion in the vicinity of artery-vein pairs in the kidney.

Renal arterial-to-venous (AV) oxygen shunting limits oxygen delivery to renal tissue. To better understand how oxygen in arterial blood can bypass renal tissue, we quantified the radial geometry of AV pairs and how it differs according to arterial diameter and anatomic location. We then estimated diffusion of oxygen in the vicinity of arteries of typical geometry using a computational model. The kidneys of six rats were perfusion fixed, and the vasculature was filled with silicone rubber (Microfil). A single section was chosen from each kidney, and all arteries (n = 1,628) were identified. Intrarenal arteries were largely divisible into two "types," characterized by the presence or absence of a close physical relationship with a paired vein. Arteries with a close physical relationship with a paired vein were more likely to have a larger rather than smaller diameter, and more likely to be in the inner-cortex than the mid- or outer cortex. Computational simulations indicated that direct diffusion of oxygen from an artery to a paired vein can only occur when the two vessels have a close physical relationship. However, even in the absence of this close relationship oxygen can diffuse from an artery to periarteriolar capillaries and venules. Thus AV oxygen shunting in the proximal preglomerular circulation is dominated by direct diffusion of oxygen to a paired vein. In the distal preglomerular circulation, it may be sustained by diffusion of oxygen from arteries to capillaries and venules close to the artery wall, which is subsequently transported to renal veins by convection.

Telemetry-based oxygen sensor for continuous monitoring of kidney oxygenation in conscious rats.

The precise roles of hypoxia in the initiation and progression of kidney disease remain unresolved. A major technical limitation has been the absence of methods allowing long-term measurement of kidney tissue oxygen tension (Po2) in unrestrained animals. We developed a telemetric method for the measurement of kidney tissue Po2 in unrestrained rats, using carbon paste electrodes (CPEs). After acute implantation in anesthetized rats, tissue Po2 measured by CPE-telemetry in the inner cortex and medulla was in close agreement with that provided by the "gold standard" Clark electrode. The CPE-telemetry system could detect small changes in renal tissue Po2 evoked by mild hypoxemia. In unanesthetized rats, CPE-telemetry provided stable measurements of medullary tissue Po2 over days 5-19 after implantation. It also provided reproducible responses to systemic hypoxia and hyperoxia over this time period. There was little evidence of fibrosis or scarring after 3 wk of electrode implantation. However, because medullary Po2 measured by CPE-telemetry was greater than that documented from previous studies in anesthetized animals, this method is presently best suited for monitoring relative changes rather than absolute values. Nevertheless, this new technology provides, for the first time, the opportunity to examine the temporal relationships between tissue hypoxia and the progression of renal disease.

Should we use one-sided or two-sided P values in tests of significance?

'P' stands for the probability, ranging in value from 0 to 1, that results from a test of significance. It can also be regarded as the strength of evidence against the statistical null hypothesis (H0). When H0 is evaluated by statistical tests based on distributions such as t, normal or Chi-squared, P can be derived from one tail of the distribution (one-sided or one-tailed P), or it can be derived from both tails (two-sided or two-tailed P). Distinguished statisticians, the authors of statistical texts, the authors of guidelines for human and animal experimentation and the editors of biomedical journals give confusing advice, or none at all, about the choice between one- and two-sided P values. Such a choice is available only when there are no more than two groups to be compared. I argue that the choice between one- and two-sided P values depends on the alternative hypothesis (H1), which corresponds to the scientific hypothesis. If H1 is non-specific and merely states that the means or proportions in the two groups are unequal, then a two-sided P is appropriate. However, if H1 is specific and, for example, states than the mean or proportion of Group A is greater than that of Group B, then a one-sided P maybe used. The form that H1 will take if H0 is rejected must be stipulated a priori, before the experiment is conducted. It is essential that authors state whether the P values resulting from their tests of significance are one- or two-sided.

Analysing 2 × 2 contingency tables: which test is best?

A survey of five journals of physiology or pharmacology for 2011 showed that Fisher's exact test was used three times as frequently as Pearson's Chi-squared test. I shall argue that neither test is appropriate for analysing 2 × 2 tables of frequency in biomedical research. Pearson's test requires that random samples are taken from defined populations. The resultant 2 × 2 table is described as unconditional because neither the row nor column marginal totals are fixed in advance. Fisher's test requires the rare condition that both row and column marginal totals are fixed in advance. The resultant 2 × 2 table is described as doubly conditioned. However, the most common design of biomedical studies is that a sample of convenience is taken and divided randomly into two groups of predetermined size. The groups are then exposed to different sets of conditions. The binomial outcome is not fixed in advance, but depends on the result of the study. Thus, only the column (group) marginal totals are fixed in advance and the table is described as singly conditioned. Singly conditioned 2 × 2 tables are best analysed by tests of null hypotheses on the odds ratio (OR = 1) or by tests on proportions (p), such as the relative risk (RR = p(2)/p(1) = 1) or the difference between proportions (p(2) - p(1) = 0). One enormous advantage of these procedures is that they test specific hypotheses. They should be executed in an exact fashion by permutation.

A primer for biomedical scientists on how to execute model II linear regression analysis.

1. There are two very different ways of executing linear regression analysis. One is Model I, when the x-values are fixed by the experimenter. The other is Model II, in which the x-values are free to vary and are subject to error. 2. I have received numerous complaints from biomedical scientists that they have great difficulty in executing Model II linear regression analysis. This may explain the results of a Google Scholar search, which showed that the authors of articles in journals of physiology, pharmacology and biochemistry rarely use Model II regression analysis. 3. I repeat my previous arguments in favour of using least products linear regression analysis for Model II regressions. I review three methods for executing ordinary least products (OLP) and weighted least products (WLP) regression analysis: (i) scientific calculator and/or computer spreadsheet; (ii) specific purpose computer programs; and (iii) general purpose computer programs. 4. Using a scientific calculator and/or computer spreadsheet, it is easy to obtain correct values for OLP slope and intercept, but the corresponding 95% confidence intervals (CI) are inaccurate. 5. Using specific purpose computer programs, the freeware computer program smatr gives the correct OLP regression coefficients and obtains 95% CI by bootstrapping. In addition, smatr can be used to compare the slopes of OLP lines. 6. When using general purpose computer programs, I recommend the commercial programs systat and Statistica for those who regularly undertake linear regression analysis and I give step-by-step instructions in the Supplementary Information as to how to use loss functions.

Definition of ambulatory blood pressure targets for diagnosis and treatment of hypertension in relation to clinic blood pressure: prospective cohort study.

BACKGROUND: Twenty-four hour ambulatory blood pressure thresholds have been defined for the diagnosis of mild hypertension but not for its treatment or for other blood pressure thresholds used in the diagnosis of moderate to severe hypertension. We aimed to derive age and sex related ambulatory blood pressure equivalents to clinic blood pressure thresholds for diagnosis and treatment of hypertension. METHODS: We collated 24 hour ambulatory blood pressure data, recorded with validated devices, from 11 centres across six Australian states (n=8575). We used least product regression to assess the relation between these measurements and clinic blood pressure measured by trained staff and in a smaller cohort by doctors (n=1693). RESULTS: Mean age of participants was 56 years (SD 15) with mean body mass index 28.9 (5.5) and mean clinic systolic/diastolic blood pressure 142/82 mm Hg (19/12); 4626 (54%) were women. Average clinic measurements by trained staff were 6/3 mm Hg higher than daytime ambulatory blood pressure and 10/5 mm Hg higher than 24 hour blood pressure, but 9/7 mm Hg lower than clinic values measured by doctors. Daytime ambulatory equivalents derived from trained staff clinic measurements were 4/3 mm Hg less than the 140/90 mm Hg clinic threshold (lower limit of grade 1 hypertension), 2/2 mm Hg less than the 130/80 mm Hg threshold (target upper limit for patients with associated conditions), and 1/1 mm Hg less than the 125/75 mm Hg threshold. Equivalents were 1/2 mm Hg lower for women and 3/1 mm Hg lower in older people compared with the combined group. CONCLUSIONS: Our study provides daytime ambulatory blood pressure thresholds that are slightly lower than equivalent clinic values. Clinic blood pressure measurements taken by doctors were considerably higher than those taken by trained staff and therefore gave inappropriate estimates of ambulatory thresholds. These results provide a framework for the diagnosis and management of hypertension using ambulatory blood pressure values.

Linear regression analysis for comparing two measurers or methods of measurement: but which regression?

1. There are two reasons for wanting to compare measurers or methods of measurement. One is to calibrate one method or measurer against another; the other is to detect bias. Fixed bias is present when one method gives higher (or lower) values across the whole range of measurement. Proportional bias is present when one method gives values that diverge progressively from those of the other. 2. Linear regression analysis is a popular method for comparing methods of measurement, but the familiar ordinary least squares (OLS) method is rarely acceptable. The OLS method requires that the x values are fixed by the design of the study, whereas it is usual that both y and x values are free to vary and are subject to error. In this case, special regression techniques must be used. 3. Clinical chemists favour techniques such as major axis regression ('Deming's method'), the Passing-Bablok method or the bivariate least median squares method. Other disciplines, such as allometry, astronomy, biology, econometrics, fisheries research, genetics, geology, physics and sports science, have their own preferences. 4. Many Monte Carlo simulations have been performed to try to decide which technique is best, but the results are almost uninterpretable. 5. I suggest that pharmacologists and physiologists should use ordinary least products regression analysis (geometric mean regression, reduced major axis regression): it is versatile, can be used for calibration or to detect bias and can be executed by hand-held calculator or by using the loss function in popular, general-purpose, statistical software.

Confidence in Altman-Bland plots: a critical review of the method of differences.

1. Altman and Bland argue that the virtue of plotting differences against averages in method-comparison studies is that 95% confidence limits for the differences can be constructed. These allow authors and readers to judge whether one method of measurement could be substituted for another. 2. The technique is often misused. So I have set out, by statistical argument and worked examples, to advise pharmacologists and physiologists how best to construct these limits. 3. First, construct a scattergram of differences on averages, then calculate the line of best fit for the linear regression of differences on averages. If the slope of the regression is shown to differ from zero, there is proportional bias. 4. If there is no proportional bias and if the scatter of differences is uniform (homoscedasticity), construct 'classical' 95% confidence limits. 5. If there is proportional bias yet homoscedasticity, construct hyperbolic 95% confidence limits (prediction interval) around the line of best fit. 6. If there is proportional bias and the scatter of values for differences increases progressively as the average values increase (heteroscedasticity), log-transform the raw values from the two methods and replot differences against averages. If this eliminates proportional bias and heteroscedasticity, construct 'classical' 95% confidence limits. Otherwise, construct horizontal V-shaped 95% confidence limits around the line of best fit of differences on averages or around the weighted least products line of best fit to the original data. 7. In designing a method-comparison study, consult a qualified biostatistician, obey the rules of randomization and make replicate observations.

Estimating the risk of rare complications: is the 'rule of three' good enough?

THE CLINICAL PROBLEM: If a surgeon has performed a particular operation on n consecutive patients without major complications, what is the long-term risk of major complications after performing many more such operations? Examples of such operations are endoscopic cholecystectomy, nephrectomy and sympathectomy. THE STATISTICAL PROBLEM AND SOLUTIONS: This general problem has exercised the minds of theoretical statisticians for more than 80 years. They agree only that the long-term risk is best expressed as the upper bound of a 95% confidence interval. We consider many proposed solutions, from those that involve complex statistical theory to the empirical 'rule of three', popular among clinicians, in which the percentage risk is given by the formula 100 x (3/n). OUR CONCLUSIONS: The 'rule of three' grossly underestimates the future risks and can be applied only when the initial complication rate is zero (that is, 0/n). If the initial complication rate is greater than zero, then no simple 'rule' suffices. We give the results of applying the more popular statistical models, including their coverage. The 'exact' Clopper-Pearson interval has wider coverage across all proportions than its nominal 95%, and is, thus, too conservative. The Wilson score confidence interval gives about 95% coverage on average overall population proportions, except very small ones, so we prefer it to the Clopper-Pearson method. Unlike all the other intervals, Bayesian intervals with uniform priors yield exactly 95% coverage at any observed proportion. Thus, we strongly recommend Bayesian intervals and provide free software for executing them.

Analysis of 2 x 2 tables of frequencies: matching test to experimental design.

BACKGROUND: Biomedical investigators often use unsuitable statistical techniques for analysing the 2 x 2 tables that result from their experimental observations. This is because they are confused by the conflicting, and sometimes inaccurate, advice they receive from statistical texts or statistical consultants. METHODS: These consist of a review of published work, and the use of five different statistical procedures to analyse a 2 x 2 table, executed by StatXact 8.0, Testimate 6.0, Stata 10.0, SAS 9.1 and SPSS 16.0. Discussion and Conclusions It is essential to classify a 2 x 2 table before embarking on its analysis. A useful classification is into (i) Independence trials (doubly conditioned). These almost never occur in biomedical research because they involve predetermining the column and row totals in a 2 x 2 table. The Fisher exact test is the best method for analysing these trials. (ii) Comparative trials (singly conditioned). These correspond to the usual experimental design in biomedical work, in which a sample of convenience is randomized into two treatment groups, so that the group (column) totals are fixed in advance. The proper tests of significance are exact tests on the odds ratio, on the ratio of proportions (relative risk and risk ratio) or on the difference between proportions. (iii) Double dichotomy trials (unconditional). In these, a genuine random sample is taken from a defined population. Thus, neither column nor row totals are fixed in advance. The only practicable test is Pearson's chi(2)-test. In analysing any of the above trials, exact tests are to be much preferred to asymptotic (approximate) tests. The different commercial software packages use different algorithms for exact tests, and can give different outcomes in terms of P-values and confidence intervals. The most useful are StatXact and Testimate.

Analysing clinical studies: principles, practice and pitfalls of Kaplan-Meier plots.

THE PROBLEM: The conventional method for estimating survival over time following an episode of disease or treatment is the Kaplan-Meier (K-M) technique, which results in a step-down survival plot, with upper and lower bounds of 1.0 and 0, respectively. The mirror image of this plot represents the cumulative incidence of an adverse event, such as death, with lower and upper bounds of 0 and 1.0, respectively. However, if there are two competing events that can occur during follow up, such as death or relapse, the K-M technique gives a false picture of the cumulative incidence of either one of these events. This occurs because patients who have died cannot subsequently relapse. THE SOLUTION: When there are two competing events, another technique must be used, which is known, variously, as cumulative incidence analysis, or 'actual' (as opposed to actuarial) incidence analysis. An example is given in which there are two competing adverse events following haemopoietic stem cell transplantation for a haematological malignancy: (i) relapse or (ii) transplant-related death. Our analysis of the example shows that the cumulative probability of relapse is progressively inflated if the traditional K-M product-limit method is used rather than actual cumulative incidence analysis. We show how K-M and actual cumulative survival or incidence analyses can be executed by a handheld calculator for small datasets or by formulae within a computer spreadsheet for large datasets. CONCLUSIONS: Surgical investigators should not use the K-M technique to predict cumulative survival or risk if there are two competing adverse events. They should use, instead, the technique of actual cumulative survival or incidence analysis.

Outlying observations and missing values: how should they be handled?

1. The problems of, and best solutions for, outlying observations and missing values are very dependent on the sizes of the experimental groups. For original articles published in Clinical and Experimental Pharmacology and Physiology during 2006-2007, the range of group sizes ranged from three to 44 ('small groups'). In surveys, epidemiological studies and clinical trials, the group sizes range from 100s to 1000s ('large groups'). 2. How can one detect outlying (extreme) observations? The best methods are graphical, for instance: (i) a scatterplot, often with mean+/-2 s; and (ii) a box-and-whisker plot. Even with these, it is a matter of judgement whether observations are truly outlying. 3. It is permissable to delete or replace outlying observations if an independent explanation for them can be found. This may be, for instance, failure of a piece of measuring equipment or human error in operating it. If the observation is deleted, it can then be treated as a missing value. Rarely, the appropriate portion of the study can be repeated. 4. It is decidedly not permissable to delete unexplained extreme values. Some of the acceptable strategies for handling them are: (i) transform the data and proceed with conventional statistical analyses; (ii) use the mean for location, but use permutation (randomization) tests for comparing means; and (iii) use robust methods for describing location (e.g. median, geometric mean, trimmed mean), for indicating dispersion (range, percentiles), for comparing locations and for regression analysis. 5. What can be done about missing values? Some strategies are: (i) ignore them; (ii) replace them by hand if the data set is small; and (iii) use computerized imputation techniques to replace them if the data set is large (e.g. regression or EM (conditional Expectation, Maximum likelihood estimation) methods). 6. If the missing values are ignored, or even if they are replaced, it is essential to test whether the individuals with missing values are otherwise indistinguishable from the remainder of the group. If the missing values have not occurred at random, but are associated with some property of the individuals being studied, the subsequent analysis may be biased.

Statistics in biomedical laboratory and clinical science: applications, issues and pitfalls.

This review is directed at biomedical scientists who want to gain a better understanding of statistics: what tests to use, when, and why. In my view, even during the planning stage of a study it is very important to seek the advice of a qualified biostatistician. When designing and analyzing a study, it is important to construct and test global hypotheses, rather than to make multiple tests on the data. If the latter cannot be avoided, it is essential to control the risk of making false-positive inferences by applying multiple comparison procedures. For comparing two means or two proportions, it is best to use exact permutation tests rather then the better known, classical, ones. For comparing many means, analysis of variance, often of a complex type, is the most powerful approach. The correlation coefficient should never be used to compare the performances of two methods of measurement, or two measures, because it does not detect bias. Instead the Altman-Bland method of differences or least-products linear regression analysis should be preferred. Finally, the educational value to investigators of interaction with a biostatistician, before, during and after a study, cannot be overemphasized.

Writing intelligible English prose for biomedical journals.

1. I present a combination of semi-objective and subjective evidence that the quality of English prose in biomedical scientific writing is deteriorating. 2. I consider seven possible strategies for reversing this apparent trend. These refer to a greater emphasis on good writing by students in schools and by university students, consulting books on science writing, one-on-one mentoring, using 'scientific' measures to reveal lexical poverty, making use of freelance science editors and encouraging the editors of biomedical journals to pay more attention to the problem. 3. I conclude that a fruitful, long-term, strategy would be to encourage more biomedical scientists to embark on a career in science editing. This strategy requires a complementary initiative on the part of biomedical research institutions and universities to employ qualified science editors. 4. An immediately realisable strategy is to encourage postgraduate students in the biomedical sciences to undertake the service courses provided by many universities on writing English prose in general and scientific prose in particular. This strategy would require that heads of departments and supervisors urge their postgraduate students to attend such courses. 5. Two major publishers of biomedical journals, Blackwell Publications and Elsevier Science, now provide lists of commercial editing services on their web sites. I strongly recommend that authors intending to submit manuscripts to their journals (including Blackwell's Clinical and Experimental Pharmacology and Physiology) make use of these services. This recommendation applies especially to those for whom English is a second language.