Absolute Scales Research Articles

The trouble with H0

We perform a comprehensive cosmological study of the H0 tension between the direct local measurement and the model-dependent value inferred from the Cosmic Microwave Background. With the recent measurement of H0 this tension has raised to more than 3 σ. We consider changes in the early time physics without modifying the late time cosmology. We also reconstruct the late time expansion history in a model independent way with minimal assumptions using distance measurements from Baryon Acoustic Oscillations and Type Ia Supernovae, finding that at z < 0.6 the recovered shape of the expansion history is less than 5% different than that of a standard ΛCDM model. These probes also provide a model insensitive constraint on the low-redshift standard ruler, measuring directly the combination rsh where H0 = h × 100 Mpc−1km/s and rs is the sound horizon at radiation drag (the standard ruler), traditionally constrained by CMB observations. Thus rs and H0 provide absolute scales for distance measurements (anchors) at opposite ends of the observable Universe. We calibrate the cosmic distance ladder and obtain a model-independent determination of the standard ruler for acoustic scale, rs. The tension in H0 reflects a mismatch between our determination of rs and its standard, CMB-inferred value. Without including high-ℓ Planck CMB polarization data (i.e., only considering the ``recommended baseline" low-ℓ polarisation and temperature and the high ℓ temperature data), a modification of the early-time physics to include a component of dark radiation with an effective number of species around 0.4 would reconcile the CMB-inferred constraints, and the local H0 and standard ruler determinations. The inclusion of the ``preliminary" high-ℓ Planck CMB polarisation data disfavours this solution.

Ab initio calculations of NMR shielding of Sc3+, Y3+ and La3+ ions in the water solution and 45Sc, 89Y, 138La and 139La nuclear magnetic dipole moments

Ab initio calculations of NMR shielding constants for water solvated trivalent scandium, yttrium and lanthanum cations are presented. The solvent effects of the first solvation shell are calculated explicitly using coupled cluster theory. The relativistic correction is calculated at non-correlated level. The influence of the second solvation shell is estimated at DFT level. The final NMR shielding constants define new NMR absolute shielding scales of scandium, yttrium and lanthanum and these shieldings were used for re-derivation of the nuclear magnetic dipole moments, eliminating long standing errors of ≈0.005μN.

At what scales does aggregated dispersal lead to coexistence?

Aggregation during dispersal can allow persistence of weak competitors, by creating conditions where stronger competitors are more likely to interact with conspecifics than with heterospecifics. However, aggregation mechanisms operate over a wide range of spatial scales, and species experience space in very different ways. The net effect of dispersal aggregation on coexistence will depend on how these scales interact. We show that it is possible to approximate the effects of aggregated dispersal on coexistence by considering three empirically measurable parameters: the spatial scale of interaction (how strongly competition drops off with distance), the spatial scale of aggregation (how large propagule packets are), and the temporal scale of aggregation (how frequently packets arrive). We use a novel metacommunity moment closure based on this approximation and stochastic simulations to show that aggregated dispersal allows for coexistence only when the stronger competitor is both aggregated and interacts at the same or a smaller spatial scale than the weaker competitor. When species interact and are aggregated at the same scales, coexistence outcomes are only weakly sensitive to the absolute scales of interaction and aggregation, as long as the scale of interaction is smaller than the scale of aggregation. However, coexistence is sensitive to the time‐scale of aggregation: increasing the frequency of packet arrival substantially reduces the region of fitness inequalities where both species persist. Finally, coexistence is less likely and global extinction of both competitors is more frequent when aggregation is fixed (with a constant number of propagules per packet), compared to density‐dependent (number of propagules increases with adult density).

Assessment of the Accuracy of the Bethe-Salpeter (BSE/GW) Oscillator Strengths.

Aiming to assess the accuracy of the oscillator strengths determined at the BSE/GW level, we performed benchmark calculations using three complementary sets of molecules. In the first, we considered ∼80 states in Thiel's set of compounds and compared the BSE/GW oscillator strengths to recently determined ADC(3/2) and CC3 reference values. The second set includes the oscillator strengths of the low-lying states of 80 medium to large dyes for which we have determined CC2/aug-cc-pVTZ values. The third set contains 30 anthraquinones for which experimental oscillator strengths are available. We find that BSE/GW accurately reproduces the trends for all series with excellent correlation coefficients to the benchmark data and generally very small errors. Indeed, for Thiel's sets, the BSE/GW values are more accurate (using CC3 references) than both CC2 and ADC(3/2) values on both absolute and relative scales. For all three sets, BSE/GW errors also tend to be nicely spread with almost equal numbers of positive and negative deviations as compared to reference values.

A global assessment of the male predominance in esophageal adenocarcinoma.

BackgroundEsophageal adenocarcinoma (EAC) is characterized by a male predominance. However, variations in the sex difference across populations and over time have not previously been thoroughly investigated.ResultsThe male-to-female ratio in EAC incidence varied greatly across continents, ranging from 1.03 in Africa to 7.64 in Northern America during 2003– 2007. The ratio was high in Europe (6.04) and Oceania (6.24), and lower in Asia (4.37) and Latin America and the Caribbean (3.94). The sex ratio remained relatively stable over time in most populations. In absolute terms, the sex difference in EAC incidence increased over time in populations of higher incidence, while it remained stable or slightly decreased in low-incidence populations.Materials and MethodsWe used data from the Cancer Incidence in Five Continents series to compute sex-specific age-standardized rates of EAC by population. The sex difference in incidence was evaluated on both absolute and relative scales, measured by the absolute difference and ratio between sexes, respectively.ConclusionsThis first global assessment of the sex ratio in EAC shows that the male predominance is particularly strong in developed countries. The underlying reasons remain to be identified, but the emerging EAC burden in men merits consideration for targeted prevention and early detection.

Radio measurements of the energy and the depth of the shower maximum of cosmic-ray air showers by Tunka-Rex

We reconstructed the energy and the position of the shower maximum of air showers with energies E ≳ 100 PeV applying a method using radio measurements performed with Tunka-Rex. An event-to-event comparison to air-Cherenkov measurements of the same air showers with the Tunka-133 photomultiplier array confirms that the radio reconstruction works reliably. The Tunka-Rex reconstruction methods and absolute scales have been tuned on CoREAS simulations and yield energy and Xmax values consistent with the Tunka-133 measurements. The results of two independent measurement seasons agree within statistical uncertainties, which gives additional confidence in the radio reconstruction. The energy precision of Tunka-Rex is comparable to the Tunka-133 precision of 15%, and exhibits a 20% uncertainty on the absolute scale dominated by the amplitude calibration of the antennas. For Xmax, this is the first direct experimental correlation of radio measurements with a different, established method. At the moment, the Xmax resolution of Tunka-Rex is approximately 40 g/cm2. This resolution can probably be improved by deploying additional antennas and by further development of the reconstruction methods, since the present analysis does not yet reveal any principle limitations.

K+-nucleon amplitudes in the medium below 800 MeV/c

Simple in-medium meson-nucleon kinematics has been applied recently in calculations of strong interaction effects in kaonic atoms, pionic atoms and elastic scattering of low energy pions by nuclei. More sensitive tests of this approach are possible with K + -nucleus interactions below 800 MeV/c because of the superior penetration of kaons into nuclei. The energy dependence of calculated reaction and total cross sections for K + on 6 Li, C, Si and Ca agrees better with experiment when this approach is used. Calculated absolute scales are in full agreement with experiment for the very low density nucleus 6 Li whereas calculations are 23±4 % too low for C, Si and Ca, thus quantifying phenomenologically the enhancement in the nuclear medium observed before.

Future trends and inequalities in premature coronary deaths in England: Modelling study

BackgroundCoronary heart disease (CHD) is a major cause of premature mortality, particularly in deprived groups. Might recent declines in overall mortality obscure different rates of decline among social strata, creating potentially misleading views on inequalities? MethodsWe used a Bayesian analysis of an age–period–cohort model for the English population. We projected age-specific premature CHD mortality (ages 35–74) by gender and area-based deprivation status for the period 2007–2035, using 1982–2006 as the input. Deprivation status was measured by Index of Multiple Deprivation quintiles, which aggregate seven types of deprivation, including health and income.We analysed inequality in premature CHD mortality. We investigated the annual changes in inequality and the contributions of changes in each IMDQ to the overall annual changes, using both absolute (probability) and relative (logit) scales. We quantified inequality using the statistical variance in the probability of premature death among deprivation quintiles. ResultsThe overall premature CHD mortality trends conceal marked heterogeneities. Our models predict more rapid declines in premature CHD mortality for the most affluent quintiles than for the most deprived (annualized rate of decline 2006–2025, 7.5% [95% Credible Interval 4.3–10.5%] versus 5.4% [2.2–8.7%] for men, and 6.3% [3.0–9.9%] versus 5.9% [1.5–10.8%] for women). For men, the posterior probability that the rate of decline is greater for the most affluent was 82%.Variance in premature CHD mortality across deprivation quintiles was projected to decrease by approximately 81% [28–95%] among men and by 89% [30–99%] among women. This decrease was particularly driven by the most deprived groups due to their higher premature death rates. However, relative inequality was projected to rise by 93% among men [81–125%] and rise by 13% [−25–58%] among women. These increases are also mostly influenced by the most deprived, reflecting their slower declines in premature deaths. ConclusionsOverall, premature coronary death rates in England continue to decline steeply. Absolute inequalities are decreasing, reflecting declines in the high premature mortality in deprived groups. However, relative inequalities are projected to widen further, reflecting slower mortality declines in the most deprived groups. More aggressive and progressive prevention policies are urgently needed.

Overcoming Stagnation in the Levels and Distribution of Child Mortality: The Case of the Philippines.

BackgroundHealth-related within-country inequalities continue to be a matter of great interest and concern to both policy makers and researchers. This study aims to assess the level and the distribution of child mortality outcomes in the Philippines across geographical and socioeconomic indicators.MethodologyData on 159,130 children ever borne were analysed from five waves of the Philippine Demographic and Health Survey. Direct estimation was used to construct under-five and neonatal mortality rates for the period 1980–2013. Rate differences and ratios, and where possible, slope and relative indices of inequality were calculated to measure disparities on absolute and relative scales. Stratification was undertaken by levels of rural/urban location, island groups and household wealth.FindingsNational under-five and neonatal mortality rates have shown considerable albeit differential reductions since 1980. Recently released data suggests that neonatal mortality has declined following a period of stagnation. Declines in under-five mortality have been accompanied by decreases in wealth and geography-related absolute inequalities. However, relative inequalities for the same markers have remained stable over time. For neonates, mixed evidence suggests that absolute and relative inequalities have remained stable or may have risen.ConclusionIn addition to continued reductions in under-five mortality, new data suggests that the Philippines have achieved success in addressing the commonly observed stagnated trend in neonatal mortality. This success has been driven by economic improvement since 2006 as well as efforts to implement a nationwide universal health care campaign. Yet, such patterns, nonetheless, accorded with persistent inequalities, particularly on a relative scale. A continued focus on addressing universal coverage, the influence of decentralisation and armed conflict, and issues along the continuum of care is advocated.

Mechanistic and Kinetic Study of Singlet O2 Oxidation of Methionine by On-Line Electrospray Ionization Mass Spectrometry.

We report a reaction apparatus developed to monitor singlet oxygen ((1)O2) reactions in solution using on-line ESI mass spectrometry and spectroscopy measurements. (1)O2 was generated in the gas phase by the reaction of H2O2 with Cl2, detected by its emission at 1270 nm, and bubbled into aqueous solution continuously. (1)O2 concentrations in solution were linearly related to the emission intensities of airborne (1)O2, and their absolute scales were established based on a calibration using 9,10-anthracene dipropionate dianion as an (1)O2 trapping agent. Products from (1)O2 oxidation were monitored by UV-Vis absorption and positive/negative ESI mass spectra, and product structures were elucidated using collision-induced dissociation-tandem mass spectrometry. To suppress electrical discharge in negative ESI of aqueous solution, methanol was added to electrospray via in-spray solution mixing using theta-glass ESI emitters. Capitalizing on this apparatus, the reaction of (1)O2 with methionine was investigated. We have identified methionine oxidation intermediates and products at different pH, and measured reaction rate constants. (1)O2 oxidation of methionine is mediated by persulfoxide in both acidic and basic solutions. Persulfoxide continues to react with another methionine, yielding methionine sulfoxide as end-product albeit with a much lower reaction rate in basic solution. Density functional theory was used to explore reaction potential energy surfaces and establish kinetic models, with solvation effects simulated using the polarized continuum model. Combined with our previous study of gas-phase methionine ions with (1)O2, evolution of methionine oxidation pathways at different ionization states and in different media is described.

Absolute shielding scales for Al, Ga, and In and revised nuclear magnetic dipole moments of (27)Al, (69)Ga, (71)Ga, (113)In, and (115)In nuclei.

We present coupled cluster calculations of NMR shielding constants of aluminum, gallium, and indium in water-ion clusters. In addition, relativistic and dynamical corrections and the influence of the second solvation shell are evaluated. The final NMR shielding constants define new absolute shielding scales, 600.0 ± 4.1 ppm, 2044.4 ± 31.4 ppm, and 4507.7 ± 63.7 ppm for aluminum, gallium, and indium, respectively. The nuclear magnetic dipole moments for (27)Al, (69)Ga, (71)Ga, (113)In, and (115)In isotopes are corrected by combining the computed shielding constants with experimental NMR frequencies. The absolute magnitude of the correction increases along the series and for indium isotopes it reaches approximately -8.0 × 10(-3) of the nuclear magneton.

Kramer and Casper Respond to "A-P-C... It's Easy as 1-2-3!".

We appreciate Dr. Harper's thoughtful and thorough commentary (1) on our paper (2). From our vantage point, there are more areas of agreement than disagreement. Although we do not deny being intrigued by the “buried epidemiologic treasure” of an observed cohort effect, our motivation was not to champion age-period-cohort (APC) analysis as a faultless method but instead to use the APC toolbox to examine another elusive process: the temporal evolution of a population health disparity. The ubiquity of racial disparities in health can make them seem inevitable. However, trends in black-white disparities in heart disease mortality suggest that such inequity is not a fixed constant but a time-varying phenomenon. Instead of examining why disparities arose, we focused on when they arose. As a descriptive tool, the APC toolbox—consisting of nonparametric graphical tools in addition to the 3-factor regression on which Dr. Harper primarily focused attention—offers a set of analytical approaches for describing the time components conflated in secular trends. Regrettably, several assumptions underpinning our analysis were left unclear. Our decision to constrain the first 2 periods in order to make the 3-factor regression identifiable reflected our somewhat unorthodox approach to APC analysis, which primarily examined rate ratios rather than rates. While the first 2 periods saw substantial secular declines in death rates, these periods also had relatively stable rate ratios. Regarding the scale for reporting disparity trends, Dr. Harper correctly notes that our reliance on the relative scale needed explanation (1), and we are grateful for his effort in producing complementary absolute measures. In general, we agree that both ratios and differences provide valuable information about the nature of health disparities, but in this setting we suggest that the relative scale measures fundamental mechanisms hypothesized in the evolution of health disparities. The dramatic declines in heart disease mortality rates for all groups over a period of 4 decades in the United States are impressive and meaningful. However, the “rising tide lifts all boats” perspective—all race-sex groups have lower rates now than in 1973—may obscure persistent patterns of unequal access to novel heart disease prevention efforts. One explanation for emerging disparities in the face of overall declines is that as new knowledge of heart disease prevention arises, economically advantaged groups gain access to the new knowledge and treatments before groups with less economic advantage (3). The result is not a complete exclusion from “progress” but instead delayed or incomplete access to its benefits. Because absolute rates are declining, the absolute difference may look good, while the relative gap more sensitively marks a disparity in the diffusion of progress. As we discussed (2) and Dr. Harper elaborated on (1), there are many pitfalls in APC analysis and the underlying assumptions necessary to gain useful information. However, we do not fully agree that there are “wildly differing” results among studies concerning the influence of period and cohort effects on racial differences in heart disease mortality. In contrast, we find a great deal of qualitative if not exact numerical agreement. Considering the question of when racial disparities emerge, Dr. Harper's analyses on both the relative and absolute scales are generally supportive of our conclusion (and the conclusion of Masters et al. (4), whom he cites) that cohort differences contributed more to racial disparities in heart disease mortality than did period differences. The largest difference in conclusions between our analysis and Harper's rate difference analysis is on the age scale: We reported large disparities among younger adults on the relative scale (2), but given lower rates at younger ages, these differences are quite small on the absolute scale. We argue that both truths are relevant. Ultimately, the APC toolbox accomplished the task for which it is suited: not making causal inferences but instead describing aspects of the temporal dynamics which make up secular trends. As with many descriptive tools, the results are hypothesis-generating, and the discussion engendered here has indeed raised several questions worthy of further study.

High-accuracy X-ray absorption spectra from mM solutions of nickel (II) complexes with multiple solutions using transmission XAS.

A new approach is introduced for determining X-ray absorption spectroscopy (XAS) spectra on absolute and relative scales using multiple solutions with different concentrations by the characterization and correction of experimental systematics. This hybrid technique is a development of standard X-ray absorption fine structure (XAFS) along the lines of the high-accuracy X-ray extended range technique (XERT) but with applicability to solutions, dilute systems and cold cell environments. This methodology has been applied to determining absolute XAS of bis(N-n-propyl-salicylaldiminato) nickel(II) and bis(N-i-propyl-salicylaldiminato) nickel(II) complexes with square planar and tetrahedral structures in 15 mM and 1.5 mM dilute solutions. It is demonstrated that transmission XAS from dilute systems can provide excellent X-ray absorption near-edge structure (XANES) and XAFS spectra, and that transmission measurements can provide accurate measurement of subtle differences including coordination geometries. For the first time, (transmission) XAS of the isomers have been determined from low-concentration solutions on an absolute scale with a 1-5% accuracy, and with relative precision of 0.1% to 0.2% in the active XANES and XAFS regions after inclusion of systematic corrections.

Genetic parameters for different growth scales in GIFT strain of Nile tilapia (Oreochromis niloticus).

Body weight, length, width and depth at two growth stages were observed for a total of 5015 individuals of GIFT strain, along with a pedigree including 5588 individuals from 104 sires and 162 dams was collected. Multivariate animal models and a random regression model were used to genetically analyse absolute and relative growth scales of these growth traits. In absolute growth scale, the observed growth traits had moderate heritabilities ranging from 0.321 to 0.576, while pairwise ratios between body length, width and depth were lowly inherited and maximum heritability was only 0.146 for length/depth. All genetic correlations were above 0.5 between pairwise growth traits and genetic correlation between length/width and length/depth varied between both growth stages. Based on those estimates, selection index of multiple traits of interest can be formulated in future breeding program to improve genetically body weight and morphology of the GIFT strain. In relative growth scale, heritabilities in relative growths of body length, width and depth to body weight were 0.257, 0.412 and 0.066, respectively, while genetic correlations among these allometry scalings were above 0.8. Genetic analysis for joint allometries of body weight to body length, width and depth will contribute to genetically regulate the growth rate between body shape and body weight.

Communication: The absolute shielding scales of oxygen and sulfur revisited.

We present an updated semi-experimental absolute shielding scale for the (17)O and (33)S nuclei. These new shielding scales are based on accurate rotational microwave data for the spin-rotation constants of H2(17)O [Puzzarini et al., J. Chem. Phys. 131, 234304 (2009)], C(17)O [Cazzoli et al., Phys. Chem. Chem. Phys. 4, 3575 (2002)], and H2(33)S [Helgaker et al., J. Chem. Phys. 139, 244308 (2013)] corrected both for vibrational and temperature effects estimated at the CCSD(T) level of theory as well as for the relativistic corrections to the relation between the spin-rotation constant and the absolute shielding constant. Our best estimate for the oxygen shielding constants of H2(17)O is 328.4(3) ppm and for C(17)O -59.05(59) ppm. The relativistic correction for the sulfur shielding of H2(33)S amounts to 3.3%, and the new sulfur shielding constant for this molecule is 742.9(4.6) ppm.

Growing social inequality in the prevalence of type 2 diabetes in Canada, 2004-2012.

The prevalence of diabetes in Canada has nearly doubled since 2000. Trends in social inequalities in diabetes across Canada and its different regions have not been assessed. We estimated relative and absolute social inequalities in type 2 diabetes prevalence in Canada between 2004 and 2012. We used the relative (RII) and slope (SII) indices of inequality to measure relative and absolute education-based inequalities respectively in type 2 diabetes prevalence in a sample of 413,453 men and women surveyed as part of the Canadian Community Health Survey between 2004 and 2012. Across regions and time periods, inequalities were more pronounced for women than for men, both on the absolute and relative scales. The difference in the prevalence of type 2 diabetes between individuals with the highest level of educational attainment compared to the lowest, as reflected by the SII, expanded from approximately 2.5% to 4.5% for women and 1.4% to 2.3% for men between 2004 and 2012. Monitoring and tracking social inequalities in the burden of diabetes over time can help to assess whether Canadian diabetes strategies are effective at reaching marginalized populations and mitigating inequalities. Our results signal the need for interventions to address growing social inequalities in Canada with regard to type 2 diabetes, particularly among women.

Positive computational modelling of the dynamics of active and inert biomass with extracellular polymeric substances

Departing from a complex system of nonlinear partial differential equations that models the growth dynamics of biological films, we provide a finite-difference model to approximate its solutions. The variables of interest are measured in absolute scales, whence the need of preserving the positivity of the solutions is a mathematical constraint that must be observed. In this work, we provide a numerical discretization of our mathematical model which is capable of preserving the non-negative character of approximations under suitable conditions on the model and computational parameters. As opposed to the nonlinear model which motivates this report, our numerical technique is a linear method which, under suitable circumstances, may be represented by an M-matrix. The fact that our method is a positivity-preserving scheme is established using the inverse-positive properties of these matrices. Computer simulations corroborate the validity of the theoretical findings.

Demographic strategies of plant invaders in temporally varying environments

AbstractPlant populations may have evolved different demographic strategies to cope with temporal environmental variation. According to the demographic buffering hypothesis, vital rates that are most critical to population persistence are buffered against environmental variation and vary little over time, whereas the demographic lability hypothesis suggests that populations may track and benefit from environmental variation. While the hypotheses of demographic strategies have been widely tested in plant and animal species, they have not been explicitly examined for invasive plants, or in relation to different modelling methods (deterministic vs. stochastic). Here, we tested the demographic buffering and lability hypotheses for 23 populations of eight invasive plant species in relation to life form (woody vs. herbaceous species) and population growth rate using deterministic and stochastic modelling methods, and absolute and relative scales. We found that conclusions of demographic strategies depended on scale, with an absolute scale resulting in stronger negative correlations between the variability and importance of vital rates (i.e., buffering) than a relative scale. Conclusions of demographic strategies were also affected by life form that interacted with method. The populations of woody invaders exhibited buffering regardless of the method used, while for the populations of herbaceous species, deterministic calculations suggested buffering and stochastic calculations suggested lability. Overall, our findings emphasise the role of life form and methodological issues that need to be considered when exploring demographic strategies in fluctuating environments.

Linear Growth Faltering Should Be Assessed in Absolute and Relative Terms

Dear Editor:The concept of standard deviations was first proposed by KarlPearson 120 y ago (1) to account for the fact that an absolutemeasure (e.g., in centimeters or kilograms) may have differentinterpretations depending on how much variability there iswithin a population. Had Pearson still been among us, he wouldnot be surprised by the findings of Leroy et al. (2)—namely,that conflicting results are produced when growth faltering isassessed in absolute (centimeters) or relative (z scores) scales.Leroy et al. reanalyzed data from 51 national surveys in low-and middle-income countries included in our 2010 publication onthe timing of growth faltering (3). Consistent with our findings,they concluded that there was substantial faltering during the first2 y of life. Thereafter, mean height-for-age, expressed as z scoresor SDs of the WHO Child Growth Standards (HAZ), remainedstable at a z score of approximately 21.8upto5yofage.Inthesame age range, however, they found that the mean absoluteheight-for-age deficit (HAD) increasedby ;2cm(Figure1intheirarticle). Their extensive reanalyses were not quite necessary.Simple arithmetic applying our 2010 results to the WHO ChildGrowth Standards will reveal that the mean deficit of a 21.8zscoreat24mocorrespondsto 25.5cm,whereasthesame zscorevalue corresponds to 28.2 cm at 60 mo (averaging boys and girls),adifferenceof2.7cm.In general, their article is well balanced. Their main conclusionsdonotdetractfromthoseinouroriginalpublications(3,4),namelythatthefirst1000dconstitute aunique windowof opportunityfornutritionalinterventions.However,wemusttakeexceptiontotheirsweepingconclusionthat“HAD, ratherthanHAZ,shouldbeusedtodescribeandcomparechangesinheight.”Takingtheirargumentto its extreme, a 2-cm deficit for 24-mo-old boys ( 20.65 z score)would be equivalent to a 2-cm deficit in 19-y-old men (2 0.27z score) (5), and such a population would have remained stableovertimeintermsofheightdeficit.Onemightjustaswellarguethatthere was definite catch-up in relative (SD) terms, and that being2cmshortofthemedianasanadultispreferabletobeing2cmshortat the age of 2 y.There are many instances in biology and in public health inwhich absolute and relative scales provide apparently contra-dictory results. For example, if stunting prevalence in group Adecreases from 40% to 20% and prevalence in group Bdecreases from 10% to 5%, the absolute gap is reduced from30 to 15 percentage points, but the relative measure (prevalenceratio)remains4-fold.Choosing1measureovertheotherimpliesa value judgment (6), and there is no single correct answer.We argue that expressing growth faltering in absolute termsprovides an alternative, complementary approach to the relativemeasures used in our earlier publications. Each approach hasa different interpretation, and both are worth presenting (7).It is not only a matter of when growth falters. It is alsoa matter of which tissues and organs grow more rapidly duringdifferent age ranges, such as the well-documented rapid braingrowth in the first 2 y (8). Emphasis on the first 1000 d is basednot only on the magnitude of faltering but also on its long-termimpact on adult human capital, as well as on the fact thatpromoting rapid weight gain after this critical window has beenstrongly associated with the risk of noncommunicable diseasesin adulthood (9,10). Although rapid linear growth after the ageof 2 y does not appear to lead to increased noncommunicabledisease risk (11), at the present state of knowledge one cannotbe sure that promotion of linear growth will not also lead toexcessive weight gain. Therefore, although from an academicstandpoint both absolute and relative faltering are noteworthy,from a programmatic standpoint focusing on the correction ofabsolute deficits after 2 y of age may be detrimental.Cesar G Victora*Postgraduate Program in EpidemiologyFederal University of PelotasPelotas RS, BrazilMercedes de OnisDepartment of NutritionWHOGeneva, SwitzerlandRoger ShrimptonDepartment of Global Community Health andBehavioral SciencesSchool of Public Health and Tropical MedicineTulane UniversityNew Orleans, LA

Entrenched geographical and socioeconomic disparities in child mortality: trends in absolute and relative inequalities in Cambodia.

BackgroundCambodia has made considerable improvements in mortality rates for children under the age of five and neonates. These improvements may, however, mask considerable disparities between subnational populations. In this paper, we examine the extent of the country's child mortality inequalities.MethodsMortality rates for children under-five and neonates were directly estimated using the 2000, 2005 and 2010 waves of the Cambodian Demographic Health Survey. Disparities were measured on both absolute and relative scales using rate differences and ratios, and where applicable, slope and relative indices of inequality by levels of rural/urban location, regions and household wealth.FindingsSince 2000, considerable reductions in under-five and to a lesser extent in neonatal mortality rates have been observed. This mortality decline has, however, been accompanied by an increase in relative inequality in both rates of child mortality for geography-related stratifying markers. For absolute inequality amongst regions, most trends are increasing, particularly for neonatal mortality, but are not statistically significant. The only exception to this general pattern is the statistically significant positive trend in absolute inequality for under-five mortality in the Coastal region. For wealth, some evidence for increases in both relative and absolute inequality for neonates is observed.ConclusionDespite considerable gains in reducing under-five and neonatal mortality at a national level, entrenched and increased geographical and wealth-based inequality in mortality, at least on a relative scale, remain. As expected, national progress seems to be associated with the period of political and macroeconomic stability that started in the early 2000s. However, issues of quality of care and potential non-inclusive economic growth might explain remaining disparities, particularly across wealth and geography markers. A focus on further addressing key supply and demand side barriers to accessing maternal and child health care and on the social determinants of health will be essential in narrowing inequalities.