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Several sources of information suggest that human beings evolved on a diet with a ratio of omega-6 to omega-3 essential fatty acids (EFA) of approximately 1 whereas in Western diets the ratio is 15/1-16.7/1. Western diets are deficient in omega-3 fatty acids, and have excessive amounts of omega-6 fatty acids compared with the diet on which human beings evolved and their genetic patterns were established. Excessive amounts of omega-6 polyunsaturated fatty acids (PUFA) and a very high omega-6/omega-3 ratio, as is found in today's Western diets, promote the pathogenesis of many diseases, including cardiovascular disease, cancer, and inflammatory and autoimmune diseases, whereas increased levels of omega-3 PUFA (a lower omega-6/omega-3 ratio), exert suppressive effects. In the secondary prevention of cardiovascular disease, a ratio of 4/1 was associated with a 70% decrease in total mortality. A ratio of 2.5/1 reduced rectal cell proliferation in patients with colorectal cancer, whereas a ratio of 4/1 with the same amount of omega-3 PUFA had no effect. The lower omega-6/omega-3 ratio in women with breast cancer was associated with decreased risk. A ratio of 2-3/1 suppressed inflammation in patients with rheumatoid arthritis, and a ratio of 5/1 had a beneficial effect on patients with asthma, whereas a ratio of 10/1 had adverse consequences. These studies indicate that the optimal ratio may vary with the disease under consideration. This is consistent with the fact that chronic diseases are multigenic and multifactorial. Therefore, it is quite possible that the therapeutic dose of omega-3 fatty acids will depend on the degree of severity of disease resulting from the genetic predisposition. A lower ratio of omega-6/omega-3 fatty acids is more desirable in reducing the risk of many of the chronic diseases of high prevalence in Western societies, as well as in the developing countries.

Nutrient limitation (mostly N or P) is a driving force in ecosystem development. Current techniques to determine the nature of nutrient limitation use laborious fertilization experiments. It was hypothesized that the N:P ratio of'the vegetation directly indicates the nature of nutrient limitation on a community level (N vs. P limitation). This hypothesis was tested by reviewing data on fertilization studies in a variety of European freshwater wetland ecosystems (bogs, fens, wet heathlands, dune slacks, wet grasslands). In a subset of the data (dune slacks) between-site intraspecific variation and within-site interspecific variation in nutrient content and N:P ratio was studied in five plant species. A review of 40 fertilization studies reveals that an N:P ratio >16 indicates P limitation on a community level, while an N:P ratio < 14 is indicative of N limitation. At N:P ratios between 14 and 16, either N or P can be limiting or plant growth is colimited by N and P together. In only one out of 40 fertilization studies, the N:P ratio gave a false indication of the nature of nutrient limitation. Measuring the N:P ratio of the vegetation is a simple and cheap alternative to fertilization studies. The method can only be used under conditions where either N or P controls plant growth. The dataset contains a large variety of vegetation types and plant species, and 11 I of the 40 sites were near-monocultures. This suggests that interspecific differences in critical N:P ratios among species may be insignificant. However, a rigorous test of this hypothesis is required. A survey in 18 dune slacks showed large within-site variation in N:P ratio among five species (Calamagrostis epigejos, Phragmites australis, Lycopus europaeus, Mentha aquatica and Eupatorium cannabinum). The N:P ratios of the five species suggested that within plant communities species can be differentially limited by N or P. Moreover, species with an N:P ratio that suggested P-limitation were found at sites where N controlled community biomass production, and vice versa. Between-site intraspecific variation in N and P contents and N:P ratios was also large, and about equal for the five species. This illustrates the plasticity of plant species with respect to N and P contents, probably in response to differences in N and P supply ratios. The vegetation N:P ratio is of diagnostic value and its use may increase our understanding of numerous facets of physiological, population, community and ecosystem ecology.

Nitrogen (N) and phosphorus (P) availability limit plant growth in most terrestrial ecosystems. This review examines how variation in the relative availability of N and P, as reflected by N : P ratios of plant biomass, influences vegetation composition and functioning. Plastic responses of plants to N and P supply cause up to 50-fold variation in biomass N : P ratios, associated with differences in root allocation, nutrient uptake, biomass turnover and reproductive output. Optimal N : P ratios - those of plants whose growth is equally limited by N and P - depend on species, growth rate, plant age and plant parts. At vegetation level, N : P ratios <10 and >20 often (not always) correspond to N- and P-limited biomass production, as shown by short-term fertilization experiments; however long-term effects of fertilization or effects on individual species can be different. N : P ratios are on average higher in graminoids than in forbs, and in stress-tolerant species compared with ruderals; they correlate negatively with the maximal relative growth rates of species and with their N-indicator values. At vegetation level, N : P ratios often correlate negatively with biomass production; high N : P ratios promote graminoids and stress tolerators relative to other species, whereas relationships with species richness are not consistent. N : P ratios are influenced by global change, increased atmospheric N deposition, and conservation managment. Contents Summary 243 I Introduction 244 II Variability of N : P ratios in response to nutrient supply 244 III Critical N : P ratios as indicators of nutrient limitation 248 IV Interspecific variation in N : P ratios 252 V Vegetation properties in relation to N : P ratios 255 VI Implications of N : P ratios for human impacts on ecosystems 258 VII Conclusions 259 Acknowledgements 259 References 260.

I describe a model of earnings and earnings growth and I demonstrate how this model may be used to obtain estimates of the expected rate of return on equity capital. These estimates are compared with estimates of the expected rate of return implied by commonly used heuristics—viz., the PEG ratio and the PE ratio. Proponents of the PEG ratio (which is the price-earnings [PE] ratio divided by the short-term earnings growth rate) argue that this ratio takes account of differences in short-run earnings growth, providing a ranking that is superior to the ranking based on PE ratios. But even though the PEG ratio may provide an improvement over the PE ratio, it is arguably still too simplistic because it implicitly assumes that the short-run growth forecast also captures the long-run future. I provide a means of simultaneously estimating the expected rate of return and the rate of change in abnormal growth in earnings beyond the (short) forecast horizon—thereby refining the PEG ratio ranking. The method may also be used by researchers interested in determining the effects of various factors (such as disclosure quality, cross-listing, etc.) on the cost of equity capital. Although the correlation between the refined estimates and estimates of the expected rate of return implied by the PEG ratio is high, supporting the use of the PEG ratio as a parsimonious way to rank stocks, the estimates of the expected rate of return based on the PEG ratio are biased downward. This correlation is much lower and the downward bias is much larger for estimates of the expected rate of return based on the PE ratio. I provide evidence that stocks for which the downward bias is higher can be identified a priori.

Abstract One of the most common descriptors of the relationship between root and shoot biomass is the root : shoot ratio, which has become a core method for estimating root biomass from the more easily measured shoot biomass. Previous reviews have examined root : shoot ratio data, but have only considered particular vegetation types and have not always critically reviewed the data used. Reliable root : shoot ratios are needed for a wide range of vegetation types in order to improve the accuracy of root biomass estimates, including those required for estimating the effects of land management and land use change in National Greenhouse Gas Inventories. This study reviewed root : shoot ratios in terrestrial biomes. A key facet of our analysis was a critical methodological review, through which unreliable data were identified and omitted on the basis of specific criteria. Of the 786 root : shoot ratio observations collated, 62% were omitted because of inadequate or unverifiable root sampling methods. When only the reliable data were examined, root : shoot ratios were found to be negatively related to shoot biomass, mean annual precipitation, mean annual temperature, forest stand age, and forest stand height. Although a single allometric equation derived in this study reliably predicted root biomass from shoot biomass for forests and woodlands, in general, the use of vegetation‐specific root : shoot ratios were found to be a more accurate method for predicting root biomass. When the root : shoot ratio data collated here were applied to an analysis of the global carbon budget, there was a 50% increase in estimated global root carbon stock, and a 12% increase in estimated total carbon stock of terrestrial vegetation. The use of the vegetation‐specific root : shoot ratios presented in this study is likely to substantially improve the accuracy of root biomass estimates for purposes such as carbon accounting and for studies of ecosystem dynamics.

The problem discussed in this paper is to determine whether statistics given for each county in a country are distributed at random or whether they form a pattern. The statistical instrument is the contiguity ratio c defined by formula (1.1) below, which is an obvious generalization of the Von Neumann (1941) ratio used in one-dimensional analysis, particularly time series. While the applications in the paper are confined to oneand two-dimensional problems, it is evident that the theory applies to any number of dimensions. If the figures for adjoining counties are generally closer than those for counties not adjoining, the ratio will clearly tend to be less than unity. The constants are such that when the statistics are distributed at random in the counties, the average value of the ratio is unity. The statistics will be regarded as contiguous if the actual ratio found is significantly less than unity, by reference to the standard error. The theory is discussed from the viewpoints of both randomization and classical theory. With the randomization approach, the observations themselves are the universe and no assumption need be made as to the character of the frequency distribution. In the normal case, the assumption is that the observations may be regarded as a random sample from a universe. In this case it seems certain that the ratio tends very rapidly to normality as the number of counties increases. The exact values of the first four semi-invariants are given for the case. These functions depend only on the configuration, and the calculated values for Ireland, with number of counties only 26, show that the distribution of the ratio is very close to normal. Accordingly, one can have confidence in deciding on significance from the standard error.

The hazard ratio (HR) is the main, and often the only, effect measure reported in many epidemiologic studies. For dichotomous, non–time-varying exposures, the HR is defined as the hazard in the exposed groups divided by the hazard in the unexposed groups. For all practical purposes, hazards can be thought of as incidence rates and thus the HR can be roughly interpreted as the incidence rate ratio. The HR is commonly and conveniently estimated via a Cox proportional hazards model, which can include potential confounders as covariates. Unfortunately, the use of the HR for causal inference is not straightforward even in the absence of unmeasured confounding, measurement error, and model misspecification. Endowing a HR with a causal interpretation is risky for 2 key reasons: the HR may change over time, and the HR has a built-in selection bias. Here I review these 2 problems and some proposed solutions. As an example, I will use the findings from a Women's Health Initiative randomized experiment that compared the risk of coronary heart disease of women assigned to combined (estrogen plus progestin) hormone therapy with that of women assigned to placebo.1 By using a randomized experiment as an example, the discussion can focus on the shortcomings of the HR, setting aside issues of confounding and other serious problems that arise in observational studies. The Women's Health Initiative followed over 16,000 women for an average of 5.2 years before the study was halted due to safety concerns. The primary result from the trial was a HR. As stated in the abstract1 and shown in Table 1 of the article, “Combined hormone therapy was associated with a hazard ratio of 1.24.”1 In addition, Table 2 provided the HRs during each year of follow-up: 1.81, 1.34, 1.27, 1.25, 1.45, and 0.70 for years 1, 2, 3, 4, 5, and 6+, respectively. Thus, the HR reported in the abstract and Table 1 can be viewed as some sort of weighted average of the period-specific HRs reported in Table 2. This bring us to Problem 1: although the HR may change over time, some studies report only a single HR averaged over the duration of the study's follow-up. As a result, the conclusions from the study may critically depend on the duration of the follow-up. For example, the average HR in the WHI would have been 1.8 if the study had been halted after 1 year of follow-up, 1.7 after 2 years,2 1.2 after 5 years, and—who knows—perhaps 1.0 after 10 years. The 24% increase in the rate of coronary heart disease that many researchers and journalists consider as the effect of combined hormone therapy is the result of the arbitrary choice of an average follow-up period of 5.2 years. A trial with a shorter follow-up could have reported an 80% increase, whereas a longer trial might have found little or no increase at all. The magnitude of the average HR depends on the length of follow-up because the average HR ignores the distribution of events during the follow-up. The average HR can take the value 1.0 if the hazard in the exposed is identical to the hazard in the unexposed during the entire follow-up, or if the hazard in the exposed is higher during, say, the first 5 years and lower afterward. Incidentally, the same problem arises whether the average HR is directly estimated in a cohort study, as discussed here, or estimated via the odds ratio of a properly designed case-control study with incidence density sampling. One might then conclude that we should forget about the average HR and restrict our attention to the period-specific HRs, which seem to capture the potentially time-varying magnitude of the effect. This brings us to Problem 2: the period-specific HRs have a built-in selection bias. To describe the bias, consider that the (discrete-time) hazard during period t is defined as the risk of the outcome during period t among those who reached period t free of the outcome. In the Women's Health Initiative, the calculation of the HR during year t was restricted to women who did not develop coronary heart disease—the “survivors”—between baseline and the beginning of year t. The HR after year 5 was 0.7, which means that the disease rate after year 5 was lower in the treatment arm (the hazard in the numerator of the HR) than in the placebo arm (the hazard in the denominator). However, this apparently protective effect of hormone therapy after year 5 is hardly surprising if one bears in mind that women vary in their susceptibility to heart disease. A certain proportion of all women enrolled in the trial were particularly prone to develop heart disease if they were exposed to hormone therapy or other factors (for simplicity, let's refer to them as the “susceptible women”). The proportion of susceptible women in the trial was of course unknown but, because of randomization, it was expected to be the same in both the treatment and placebo arms at baseline. However, these susceptible women were preferentially excluded from the treatment arm as they developed heart disease over time—precisely because they were assigned to a therapy with harmful effects to which they were susceptible (all other factors to which they were susceptible were expected to be equally distributed between the 2 arms). With time, the proportion of susceptible women progressively increased in the placebo arm compared with the treatment arm. The bias due to the differential selection of less susceptible women over time, because of differential depletion of susceptibles, is the built-in selection bias of period-specific HRs. This bias may explain that the HR after year 5 is less than 1.0 even if hormone therapy has no truly preventive effect in any woman at any time. This built-in selection bias of the HR has also been described using causal diagrams.3,4 In short, the average HR may be uninformative because of potentially time-varying period-specific HRs, and because the period-specific HRs may be time-varying because of built-in selection bias. These problems can be overcome by summarizing the study findings as appropriately adjusted survival curves, where the survival at time t is defined as the proportion of individuals who are free of disease through time t. Another alternative not discussed here is the comparison of the distribution of survival times between the exposed and the unexposed, which can be accomplished by using accelerated failure time models5 rather than Cox models. Because of the shortcomings of the HR, the analysis of randomized experiments routinely include Kaplan-Meier survival curves—or their complement, the cumulative risk curve (see Figure 2 of the Women's Health Initiative trial report1). In contrast (and despite multiple warnings in the epidemiologic literature3–6), the analysis of observational follow-up studies are commonly summarized by HRs only. A possible explanation for this practice in observational studies is the need to deal with confounding. The HRs presented in observational studies are not simply the hazard in the exposed divided by the hazard in the unexposed. Rather, these HRs are adjusted for measured confounders by using regression models, inverse probability weighting, or other methods. Unadjusted HRs would be of little use for causal inference from observational data, as would unadjusted survival curves. It is not unexpected that most epidemiologic articles include HRs only, because epidemiology students are traditionally taught to estimate adjusted HRs but not adjusted survival curves.7 The next paragraph sketches a general procedure to obtain survival curves adjusted for baseline confounders. First, fit a discrete-time hazards model (eg, a pooled logistic model with relatively short periods) that estimates, at each time and for each person, the conditional probability of remaining free of the outcome given exposure, baseline covariates, and time of follow-up. Allow for time-varying hazards by modeling the variable “time of follow-up,” using a flexible functional form (eg, cubic splines), and for time-varying HRs by adding product terms between exposure and “time of follow-up.” Second, for each subject, multiply the model's predicted values through time t to estimate the survival at t for subjects with their same combination of covariate values. One can then construct conditional (adjusted) survival curves under the conditions of exposure and no exposure for each observed combination of values of the baseline covariates (in randomized trials, the survival curves are unconditional or marginal, ie, averaged over all the individuals irrespective of their covariate values). Third, predict the survival at time t for each subject both under exposure and under no exposure, regardless of the subject's exposure status. Fourth, separately average the conditional survivals under exposure and under no exposure, over all subjects. This last step effectively standardizes the curves to the empirical distribution of the covariates in the study, and results in 2 marginal survival curves: one under exposure, another under no exposure. The above procedure can be extended in a number of ways. In settings with time-varying exposures and confounders, the procedure can be combined with inverse probability weighting of the hazards model. This procedure has been used to present adjusted survival curves under continuous use (“always exposed”) and no use of hormone therapy (“never exposed”) in the analysis of both observational studies8 and randomized experiments9 in which time-varying exposures arise when considering adherence-adjusted analyses. In settings with continuous rather than dichotomous exposures, the procedure requires the choice of a finite number of levels of exposure to be compared (“always versus never exposed” will not do).10 One may then construct as many survival curves as there are exposure levels of interest. For continuous and time-varying exposures one needs to be especially careful about dose-response assumptions. Sensitivity analyses can be used to evaluate the possibility of model extrapolation beyond the observed data. Confidence intervals for the survival curves can be obtained by bootstrapping. So should we outlaw the use of HRs in epidemiologic studies? Of course not. A single average HR through t may be misleading, as explained above, but a single survival probability at t could be as misleading because both measures ignore the distribution of events between baseline and t. On the other hand, a series of average HRs for increasingly longer periods of follow-up is informative. For example, in the WHI the average HRs for 1, 2, and 5 years were approximately 1.8, 1.7, and 1.2, which indicates that hormone therapy increases the cumulative risk of heart disease in the early part of the follow-up but probably not much over longer periods. The same conclusion is drawn from the survival curves for the treatment and placebo groups, which converge after 8 years. In mortality studies with sufficiently long follow-up, the survival probabilities in both groups are ensured to reach the value 0, and the average HR is ensured to reach the value 1. An advantage of the survival curves over a series of average HRs is that the survival curves provide information about the absolute risks. For example, in the Women's Health Initiative, the average HR of 1.8 during year 1 means that the one-year risk was about 0.49% in the treatment group and 0.28% in the placebo group rather than, say, 49% versus 28%. An advantage of the average HRs over the survival curves is the readiness with which confidence intervals can be computed in standard software. What about period-specific HRs? Their built-in selection bias makes them difficult to interpret as a measure of time-varying effect. For example, in the Women's Health Initiative, the HR goes from greater than 1.0 to less than 1.0 after year 5—that is, the hazards of the treatment and the placebo groups cross at about year 5. However, this crossing of hazards is essentially meaningless from a practical standpoint. What really matters is that the survival is lower in the placebo group compared with the treatment group until at least year 8. Hazards may cross at some point during the follow-up because of depletion of susceptibles even if the survival curves never cross. Cumulative measures, such as a series of average HRs or survival curves, are needed to summarize the data in a meaningful way. On the other hand, period-specific HRs are useful as an intermediate step to estimate survival curves in the procedure described above. In summary, survival curves are more informative than HRs and can be easily generated. It would not be a bad thing to see them more widely used in observational studies.

PURPOSE: The proportional reporting ratio (PRR) is the proportion of spontaneous reports for a given drug that are linked to a specific adverse outcome, divided by the corresponding proportion for all or several other drugs. The PRR is similar to the proportional mortality ratio (PMR), an old epidemiologic measure calculated from death registries and constructed in similar fashion to the PRR. The PMR has important deficiencies, however, which the PRR shares. Miettinen and Wang demonstrated that the PMR could be improved by reformulating it as an odds ratio and applying the principles of a case-control study to the measure. In this paper, we review the problem with the PRR and show how the corresponding odds ratio represents an improvement over the PRR. METHODS: The method used is discussion and illustration by way of a hypothetical example. RESULTS: The PRR does not estimate relative risk. If, however, a spontaneous report database is viewed as source data for a case-control study, the reporting odds ratio (ROR) can be used to estimate relative risk. Treating the data as source data for a case-control study allows for further reduction of bias by the judicious choice of controls. CONCLUSIONS: Calculating the ROR in spontaneous report databases offers advantages over the PRR. It allows for estimation of the relative risk, and focuses attention on which people or reports should be included or excluded from the control series, permitting more deliberate elimination of biases. It also highlights the inherent weaknesses in spontaneous report data, which become more evident in light of the usual principles of control selection in case-control studies.

BACKGROUND: Cross-sectional studies with binary outcomes analyzed by logistic regression are frequent in the epidemiological literature. However, the odds ratio can importantly overestimate the prevalence ratio, the measure of choice in these studies. Also, controlling for confounding is not equivalent for the two measures. In this paper we explore alternatives for modeling data of such studies with techniques that directly estimate the prevalence ratio. METHODS: We compared Cox regression with constant time at risk, Poisson regression and log-binomial regression against the standard Mantel-Haenszel estimators. Models with robust variance estimators in Cox and Poisson regressions and variance corrected by the scale parameter in Poisson regression were also evaluated. RESULTS: Three outcomes, from a cross-sectional study carried out in Pelotas, Brazil, with different levels of prevalence were explored: weight-for-age deficit (4%), asthma (31%) and mother in a paid job (52%). Unadjusted Cox/Poisson regression and Poisson regression with scale parameter adjusted by deviance performed worst in terms of interval estimates. Poisson regression with scale parameter adjusted by chi2 showed variable performance depending on the outcome prevalence. Cox/Poisson regression with robust variance, and log-binomial regression performed equally well when the model was correctly specified. CONCLUSIONS: Cox or Poisson regression with robust variance and log-binomial regression provide correct estimates and are a better alternative for the analysis of cross-sectional studies with binary outcomes than logistic regression, since the prevalence ratio is more interpretable and easier to communicate to non-specialists than the odds ratio. However, precautions are needed to avoid estimation problems in specific situations.

BACKGROUND: Inflammation may play an important role in cancer progression, and a high neutrophil-to-lymphocyte ratio (NLR) has been reported to be a poor prognostic indicator in several malignancies. Here we quantify the prognostic impact of this biomarker and assess its consistency in solid tumors. METHODS: A systematic review of electronic databases was conducted to identify publications exploring the association of blood NLR and clinical outcome in solid tumors. Overall survival (OS) was the primary outcome, and cancer-specific survival (CSS), progression-free survival (PFS), and disease-free survival (DFS) were secondary outcomes. Data from studies reporting a hazard ratio and 95% confidence interval (CI) or a P value were pooled in a meta-analysis. Pooled hazard ratios were computed and weighted using generic inverse-variance and random-effect modeling. All statistical tests were two-sided. RESULTS: One hundred studies comprising 40559 patients were included in the analysis, 57 of them published in 2012 or later. Median cutoff for NLR was 4. Overall, NLR greater than the cutoff was associated with a hazard ratio for OS of 1.81 (95% CI = 1.67 to 1.97; P < .001), an effect observed in all disease subgroups, sites, and stages. Hazard ratios for NLR greater than the cutoff for CSS, PFS, and DFS were 1.61, 1.63, and 2.27, respectively (all P < .001). CONCLUSIONS: A high NLR is associated with an adverse OS in many solid tumors. The NLR is a readily available and inexpensive biomarker, and its addition to established prognostic scores for clinical decision making warrants further investigation.

The gut microbiota is emerging as a promising target for the management or prevention of inflammatory and metabolic disorders in humans. Many of the current research efforts are focused on the identification of specific microbial signatures, more particularly for those associated with obesity, type 2 diabetes, and cardiovascular diseases. Some studies have described that the gut microbiota of obese animals and humans exhibits a higher Firmicutes/Bacteroidetes ratio compared with normal-weight individuals, proposing this ratio as an eventual biomarker. Accordingly, the Firmicutes/Bacteroidetes ratio is frequently cited in the scientific literature as a hallmark of obesity. The aim of the present review was to discuss the validity of this potential marker, based on the great amount of contradictory results reported in the literature. Such discrepancies might be explained by the existence of interpretative bias generated by methodological differences in sample processing and DNA sequence analysis, or by the generally poor characterization of the recruited subjects and, more particularly, the lack of consideration of lifestyle-associated factors known to affect microbiota composition and/or diversity. For these reasons, it is currently difficult to associate the Firmicutes/Bacteroidetes ratio with a determined health status and more specifically to consider it as a hallmark of obesity.

Meta-analysis provides formal statistical techniques for summarizing the results of independent experiments and is increasingly being used in ecology. The response ratio (the ratio of mean outcome in the experimental group to that in the control group) and closely related measures of proportionate change are often used as measures of effect magnitude in ecology. Using these metrics for meta-analysis requires knowledge of their statistical properties, but these have not been previously derived. We give the approximate sampling distribution of the log response ratio, discuss why it is a particularly useful metric for many applications in ecology, and demonstrate how to use it in meta-analysis. The meta-analysis of response-ratio data is illustrated using experimental data on the effects of increased atmospheric CO2 on plant biomass responses.

The empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken. In this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions. It is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean, for a class of M-estimates that includes quantiles, and for differentiable statistical functionals. The results are nonpara-metric extensions of Wilks's (1938) theorem for parametric likelihood ratios. The intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on Student's t statistic. A hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced.

We would like to make the readership aware that risk or prevalence ratios and differences, when they are the parameter of interest, can be directly calculated by using SAS software (SAS Institute, Inc., Cary, North Carolina). There is no longer any good justification for fitting logistic regression models and estimating odds ratios when the odds ratio is not a good approximation of the risk or prevalence ratio. Instead, SAS PROC GENMOD's log-binomial regression (1) capability can be used for estimation and inference about the parameter of interest. Here is an example of the code required to analyze the breast cancer survival data discussed by Greenland (2):

A linearization of a rational expectations present value model for corporate stock prices produces a simple relation between the log dividend-price ratio and mathematical expectations of future log real dividend changes and future real discount rates. This relation can be tested using vector autoregressive methods. Three versions of the linearized model, differing in the measure of discount rates, are tested for U. S. time series 1871-1986: versions using real interest rate data, aggregate real consumption data, and return variance data. The results yield a metric to judge the relative importance of real dividend growth, measured real discount rates and unexplained factors in determining the dividend-price ratio.

Visual analogue scales (VAS) of sensory intensity and affective magnitude were validated as ratio scale measures for both chronic and experimental pain. Chronic pain patients and healthy volunteers made VAS sensory and affective responses to 6 noxious thermal stimuli (43, 45, 47, 48, 49 and 51 degrees C) applied for 5 sec to the forearm by a contact thermode. Sensory VAS and affective VAS responses to these temperatures yielded power functions with exponents 2.1 and 3.8, respectively; these functions were similar for pain patients and for volunteers. The power functions were predictive of estimated ratios of sensation or affect produced by pairs of standard temperatures (e.g. 47 and 49 degrees C), thereby providing direct evidence for ratio scaling properties of VAS. Vas sensory intensity responses to experimental pain, VAS sensory intensity responses to different levels of chronic pain, and direct temperature (experimental pain) matches to 3 levels of chronic pain were all internally consistent, thereby demonstrating the valid use of VAS for the measurement of and comparison between chronic pain and experimental heat pain.

Gold nanorods with aspect ratios of 4.6 ± 1.2, 13 ± 2, and 18 ± 2.5 (all with 16 ± 3 nm short axis) are prepared by a seeding growth approach in the presence of an aqueous miceller template. Citrate-capped 3.5 nm diameter gold particles, prepared by the reduction of HAuCl 4 with borohydride, are used as the seed. The aspect ratio of the nanorods is controlled by varying the ratio of seed to metal salt. The long rods are isolated from spherical particles by centrifugation.

BACKGROUND: In humans, the intestinal microbiota plays an important role in the maintenance of host health by providing energy, nutrients, and immunological protection. Applying current molecular methods is necessary to surmount the limitations of classical culturing techniques in order to obtain an accurate description of the microbiota composition. RESULTS: Here we report on the comparative assessment of human fecal microbiota from three age-groups: infants, adults and the elderly. We demonstrate that the human intestinal microbiota undergoes maturation from birth to adulthood and is further altered with ageing. The counts of major bacterial groups Clostridium leptum, Clostridium coccoides, Bacteroidetes, Bifidobacterium, Lactobacillus and Escherichia coli were assessed by quantitative PCR (qPCR). By comparing species diversity profiles, we observed age-related changes in the human fecal microbiota. The microbiota of infants was generally characterized by low levels of total bacteria. C. leptum and C. coccoides species were highly represented in the microbiota of infants, while elderly subjects exhibited high levels of E. coli and Bacteroidetes. We observed that the ratio of Firmicutes to Bacteroidetes evolves during different life stages. For infants, adults and elderly individuals we measured ratios of 0.4, 10.9 and 0.6, respectively. CONCLUSION: In this work we have confirmed that qPCR is a powerful technique in studying the diverse and complex fecal microbiota. Our work demonstrates that the fecal microbiota composition evolves throughout life, from early childhood to old age.

In this paper, we develop a classical approach to model selection. Using the Kullback-Leibler Information Criterion to measure the closeness of a model to the truth, we propose simple likelihood-ratio based statistics for testing the null hypothesis that the competing models are equally close to the true data generating process against the alternative hypothesis that one model is closer. The tests are directional and are derived successively for the cases where the competing models are non-nested, overlapping, or nested and whether both, one, or neither is misspecified. As a prerequisite, we fully characterize the asymptotic distribution of the likelihood ratio statistic under the most general conditions. We show that it is a weighted sum of chi-square distribution or a normal distribution depending on whether the distributions in the competing models closest to the truth are observationally identical. We also propose a test of this latter condition.