Increasing sensitivity of results by using quantile regression analysis for exploring community resilience

Community resilience offers a conceptual framework for assessing a community's capacity for coping with environmental changes and emergency situations. It is perceived as a core element of sustainable lifestyle, helping to mitigate the community's reaction to crises by facilitating purposeful and collective action on the part of its’ members. The conjoint community resilience assessment measure (CCRAM) provides a standard measure of community resilience including five factors: leadership, collective efficacy, preparedness, place attachment, and social trust. The mean scores of each the factors portray a community resilience profile and the overall CCRAM score is calculated as the average of the scores of the 21 survey items with an equal weight.Two regression models were employed. Logistic regression, a commonly used tool in the field of applied statistics, and quantile regression, which is a non-parametric method that facilitates the detection of the effect of a regressor on various quantiles of the dependent variable.The study aims to demonstrate the innovative use of quantile regression modeling in community resilience analysis.The results demonstrate that the quantile regression was significantly more sensitive to sub-populations than the logistic regression.Having an income below average, which was negatively correlated with perceived community resilience in the logistic model was found to be significant only in the lower (Q10, Q25) resilience quantiles. Age (per year) and previous involvement in emergency situations which were not noted as significant in the logistic regression, were found to be positively associated with perceived community resilience in the lowest quantile. A difference between quantiles of perceived community resilience was noted in regard to size of community. The association between size of community and perceived community resilience which was negative in the logistic regression (residents of larger towns had lower community resilience), was found to be such only up to quantile 75, but it reversed in the highest quantile.It was concluded that the utilization of quantile regression analysis in studies of community resilience can facilitate the creation of tailored response plans, adapted to the needs of sub (such as weaker) populations and help enhance overall community resilience in crises.     

Assessing vegetation recovery from energy development using a dynamic reference approach

Ecologically relevant references are useful for evaluating ecosystem recovery, but references that are temporally static may be less useful when environmental conditions and disturbances are spatially and temporally heterogeneous. This challenge is particularly acute for ecosystems dominated by sagebrush (Artemisia spp.), where communities may require decades to recover from disturbance. We demonstrated application of a dynamic reference approach to studying sagebrush recovery using three decades of sagebrush cover estimates from remote sensing (1985–2018). We modelled recovery on former oil and gas well pads (n = 1200) across southwestern Wyoming, USA, relative to paired references identified by the Disturbance Automated Reference Toolset. We also used quantile regression to account for unmodelled heterogeneity in recovery, and projected recovery from similar disturbance across the landscape. Responses to weather and site‐level factors often differed among quantiles, and sagebrush recovery on former well pads increased more when paired reference sites had greater sagebrush cover. Little (<5%) of the landscape was projected to recover within 100 years for low to mid quantiles, and recovery often occurred at higher elevations with cool and moist annual conditions. Conversely, 48%–78% of the landscape recovered quickly (within 25 years) for high quantiles of sagebrush cover. Our study demonstrates advantages of using dynamic reference sites when studying vegetation recovery, as well as how additional inferences obtained from quantile regression can inform management.     

Quantile regression estimates of animal population trends

Ecologists often estimate population trends of animals in time series of counts using linear regression to estimate parameters in a linear transformation of multiplicative growth models, where logarithms of rates of change in counts in time intervals are used as response variables. We present quantile regression estimates for the median (0.50) and interquartile (0.25, 0.75) relationships as an alternative to mean regression estimates for common density-dependent and density-independent population growth models. We demonstrate that the quantile regression estimates are more robust to outliers and require fewer distributional assumptions than conventional mean regression estimates and can provide information on heterogeneous rates of change ignored by mean regression. We provide quantile regression trend estimates for 2 populations of greater sage-grouse (Centrocercus urophasianus) in Wyoming, USA, and for the Crawford population of Gunnison sage-grouse (Centrocercus minimus) in southwestern Colorado, USA. Our selected Gompertz models of density dependence for both populations of greater sage-grouse had smaller negative estimates of density-dependence terms and less variation in corresponding predicted growth rates (λ) for quantile than mean regression models. In contrast, our selected Gompertz models of density dependence with piecewise linear effects of years for the Crawford population of Gunnison sage-grouse had predicted changes in λ across years from quantile regressions that varied more than those from mean regression because of heterogeneity in estimated λs that were both less and greater than mean estimates. Our results add to literature establishing that quantile regression provides better behaved estimates than mean regression when there are outlying growth rates, including those induced by adjustments for zeros in the time series of counts. The 0.25 and 0.75 quantiles bracketing the median provide robust estimates of population changes (λ) for the central 50% of time series data and provide a 50% prediction interval for a single new prediction without making parametric distributional assumptions or assuming homogeneous λs. Compared to mean estimates, our quantile regression trend estimates for greater sage-grouse indicated less variation in density-dependent λs by minimizing sensitivity to outlying values, and for Gunnison sage-grouse indicated greater variation in density-dependent λs associated with heterogeneity among quantiles.     

A quantile‐slicing approach for sufficient dimension reduction with censored responses

Sufficient dimension reduction (SDR) that effectively reduces the predictor dimension in regression has been popular in high‐dimensional data analysis. Under the presence of censoring, however, most existing SDR methods suffer. In this article, we propose a new algorithm to perform SDR with censored responses based on the quantile‐slicing scheme recently proposed by Kim et al. First, we estimate the conditional quantile function of the true survival time via the censored kernel quantile regression (Shin et al.) and then slice the data based on the estimated censored regression quantiles instead of the responses. Both simulated and real data analysis demonstrate promising performance of the proposed method.     

Smoothed quantile regression analysis of competing risks

Censored quantile regression models, which offer great flexibility in assessing covariate effects on event times, have attracted considerable research interest. In this study, we consider flexible estimation and inference procedures for competing risks quantile regression, which not only provides meaningful interpretations by using cumulative incidence quantiles but also extends the conventional accelerated failure time model by relaxing some of the stringent model assumptions, such as global linearity and unconditional independence. Current method for censored quantile regressions often involves the minimization of the L₁‐type convex function or solving the nonsmoothed estimating equations. This approach could lead to multiple roots in practical settings, particularly with multiple covariates. Moreover, variance estimation involves an unknown error distribution and most methods rely on computationally intensive resampling techniques such as bootstrapping. We consider the induced smoothing procedure for censored quantile regressions to the competing risks setting. The proposed procedure permits the fast and accurate computation of quantile regression parameter estimates and standard variances by using conventional numerical methods such as the Newton–Raphson algorithm. Numerical studies show that the proposed estimators perform well and the resulting inference is reliable in practical settings. The method is finally applied to data from a soft tissue sarcoma study.     

Generalized Exponential Distribution in Flood Frequency Analysis for Polish Rivers

Many distributions have been used in flood frequency analysis (FFA) for fitting the flood extremes data. However, as shown in the paper, the scatter of Polish data plotted on the moment ratio diagram shows that there is still room for a new model. In the paper, we study the usefulness of the generalized exponential (GE) distribution in flood frequency analysis for Polish Rivers. We investigate the fit of GE distribution to the Polish data of the maximum flows in comparison with the inverse Gaussian (IG) distribution, which in our previous studies showed the best fitting among several models commonly used in FFA. Since the use of a discrimination procedure without the knowledge of its performance for the considered probability density functions may lead to erroneous conclusions, we compare the probability of correct selection for the GE and IG distributions along with the analysis of the asymptotic model error in respect to the upper quantile values. As an application, both GE and IG distributions are alternatively assumed for describing the annual peak flows for several gauging stations of Polish Rivers. To find the best fitting model, four discrimination procedures are used. In turn, they are based on the maximized logarithm of the likelihood function (K procedure), on the density function of the scale transformation maximal invariant (QK procedure), on the Kolmogorov-Smirnov statistics (KS procedure) and the fourth procedure based on the differences between the ML estimate of 1% quantile and its value assessed by the method of moments and linear moments, in sequence (R procedure). Due to the uncertainty of choosing the best model, the method of aggregation is applied to estimate of the maximum flow quantiles.     

A censored quantile regression approach for relative survival analysis: Relative survival quantile regression

We propose a censored quantile regression model for the analysis of relative survival data. We create a hybrid data set consisting of the study observations and counterpart randomly sampled pseudopopulation observations imputed from population life tables that adjust for expected mortality. We then fit a censored quantile regression model to the hybrid data incorporating demographic variables (e.g., age, biologic sex, calendar time) corresponding to the population life tables of demographically-similar individuals, a population versus study covariate, and its interactions with the variables of interest. These latter variables can be interpreted as relative survival parameters that depict the differences in failure quantiles between the study participants and their population counterparts.     

Estimating extreme daily pollen loads for Szeged, Hungary using previous-day meteorological variables

The aim of this paper is to analyse how meteorological elements relate to extreme Ambrosia pollen load on the one hand and to extreme total pollen load excluding Ambrosia pollen on the other for Szeged, Southern Hungary. The data set comes from a 9-year period (1999–2007) and includes previous-day means of five meteorological variables and actual-day values of the two pollen variables. Factor analysis with special transformation was performed on the meteorological and pollen load data in order to find out the strength and direction of the association of the meteorological and pollen variables. Then, using selected low and high quantiles corresponding to probability distributions of Ambrosia pollen and the remaining pollen loads, the quantile and beyond-quantile averages of pollen loads were compared and evaluated. Finally, a nearest neighbour (NN) technique was applied to discriminate between extreme and non-extreme pollen events using meteorological elements as explaining variables. The observed below or above quantile events are compared with events obtained from NN decisions. The number of events exceeding the quantile of 90% and not exceeding that of 10% is strongly underestimated. However, the procedure works well for quantiles of 20 and 80%, and even better for those of 30 and 70%. Using a nearest neighbour technique, explaining variables in decreasing order of their influence on Ambrosia pollen load are temperature, global solar flux, relative humidity, air pressure and wind speed, while on the load of the remaining pollen are temperature, relative humidity, global solar flux, air pressure and wind speed.     

Association of allergic rhinitis or asthma with pollen and chemical pollutants in Szeged,Hungary, 1999–2007

The effect of biological (pollen) and chemical air pollutants on respiratory hospital admissions for the Szeged region in Southern Hungary is analysed. A 9-year (1999–2007) database includes—besides daily number of respiratory hospital admissions—daily mean concentrations of CO, PM₁₀, NO, NO₂, O₃ and SO₂. Two pollen variables (Ambrosia and total pollen excluding Ambrosia) are also included. The analysis was performed for patients with chronic respiratory complaints (allergic rhinitis or asthma bronchiale) for two age categories (adults and the elderly) of males and females. Factor analysis was performed to clarify the relative importance of the pollutant variables affecting respiratory complaints. Using selected low and high quantiles corresponding to probability distributions of respiratory hospital admissions, averages of two data sets of each air pollutant variable were evaluated. Elements of these data sets were chosen according to whether actual daily patient numbers were below or above their quantile value. A nonparametric regression technique was applied to discriminate between extreme and non-extreme numbers of respiratory admissions using pollen and chemical pollutants as explanatory variables. The strongest correlations between extreme patient numbers and pollutants can be observed during the pollen season of Ambrosia, while the pollen-free period exhibits the weakest relationships. The elderly group with asthma bronchiale is characterised by lower correlations between extreme patient numbers and pollutants compared to adults and allergic rhinitis, respectively. The ratio of the number of correct decisions on the exceedance of a quantile resulted in similar conclusions as those obtained by using multiple correlations.     

Tensor response quantile regression with neuroimaging data

Collecting neuroimaging data in the form of tensors (i.e. multidimensional arrays) has become more common in mental health studies, driven by an increasing interest in studying the associations between neuroimaging phenotypes and clinical disease manifestation. Motivated by a neuroimaging study of post-traumatic stress disorder (PTSD) from the Grady Trauma Project, we study a tensor response quantile regression framework, which enables novel analyses that confer a detailed view of the potentially heterogeneous association between a neuroimaging phenotype and relevant clinical predictors. We adopt a sensible low-rank structure to represent the association of interest, and propose a simple two-step estimation procedure which is easy to implement with existing software. We provide rigorous theoretical justifications for the intuitive two-step procedure. Simulation studies demonstrate good performance of the proposed method with realistic sample sizes in neuroimaging studies. We conduct the proposed tensor response quantile regression analysis of the motivating PTSD study to investigate the association between fMRI resting-state functional connectivity and PTSD symptom severity. Our results uncover non-homogeneous effects of PTSD symptoms on brain functional connectivity, which cannot be captured by existing tensor response methods.     

Obesity in China: The Differential Impacts of Covariates Along the BMI Distribution

Growing prosperity and changing diets have contributed to a surge in obesity prevalence in China. Previous research has investigated the relationships between BMI and several socioeconomic, diet‐related, and health‐related variables in China. This study proposes that such relationships are likely to differ along the conditional BMI distribution, and seeks to investigate such quantile‐dependent variation in effects. Special attention is paid to how variables affect the upper tail of the conditional BMI distribution where overweight and obesity concerns are more acute. Quantile regressions (QRs) and ordinary least squares (OLS) regressions are estimated. The sample consists of 3,407 adult individuals aged 20–45 who participated in the China Health and Nutrition Survey (CHNS), 2006. Substantial cross quantile variation is observed in the relationships between several key variables and BMI. The QR shows that the relationship between energy intake and BMI is largely insignificant in the lower and middle quantiles, whereas the upper quantiles show a positive and significant effect substantially larger than predicted by the least squares regression and by previous studies. This implies that a food‐based strategy aimed at limiting energy intake can be an effective way to fight obesity in China. The negative association between smoking and BMI, on the other hand, is found largely to hold only in the lower and middle quantiles, with the upper tail relatively unaffected by smoking status. Thus, smoking cessation policies may not exacerbate obesity.     

Predictors of High Profit and High Deficit Outliers under SwissDRG of a Tertiary Care Center

Principles

Case weights of Diagnosis Related Groups (DRGs) are determined by the average cost of cases from a previous billing period. However, a significant amount of cases are largely over- or underfunded. We therefore decided to analyze earning outliers of our hospital as to search for predictors enabling a better grouping under SwissDRG.

Methods

28,893 inpatient cases without additional private insurance discharged from our hospital in 2012 were included in our analysis. Outliers were defined by the interquartile range method. Predictors for deficit and profit outliers were determined with logistic regressions. Predictors were shortlisted with the LASSO regularized logistic regression method and compared to results of Random forest analysis. 10 of these parameters were selected for quantile regression analysis as to quantify their impact on earnings.

Results

Psychiatric diagnosis and admission as an emergency case were significant predictors for higher deficit with negative regression coefficients for all analyzed quantiles (p<0.001). Admission from an external health care provider was a significant predictor for a higher deficit in all but the 90% quantile (p<0.001 for Q10, Q20, Q50, Q80 and p = 0.0017 for Q90). Burns predicted higher earnings for cases which were favorably remunerated (p<0.001 for the 90% quantile). Osteoporosis predicted a higher deficit in the most underfunded cases, but did not predict differences in earnings for balanced or profitable cases (Q10 and Q20: p<0.00, Q50: p = 0.10, Q80: p = 0.88 and Q90: p = 0.52). ICU stay, mechanical and patient clinical complexity level score (PCCL) predicted higher losses at the 10% quantile but also higher profits at the 90% quantile (p<0.001).

Conclusion

We suggest considering psychiatric diagnosis, admission as an emergencay case and admission from an external health care provider as DRG split criteria as they predict large, consistent and significant losses.     

应用混合模型和分位数回归分析东黄海小黄鱼肥满度空间异质性

基于2008-2010年黄海南部近海(SYS)、东海北部外海(NECS)和东海中部近海(MECS)小黄鱼体长和体质量数据,采用均值回归和分位数回归模型,解析了小黄鱼幼鱼和成鱼群体体长-体质量关系的空间变异.结果表明: 协方差模型和线性混合模型的残差标准误基本一致,线性模型残差标准误最高.从线性混合模型对特定区域和总体区域平均体质量计算的相对比值来看,SYS和NECS幼鱼群体的平均体质量高于总体平均值,但MECS低于总体平均值;成鱼群体则为NECS平均体质量高于总体平均值,MECS和SYS低于总体平均值.分位回归估计的肥满度和异速生长指数结果显示,幼鱼群体在不同分位的估计参数呈显著变化,SYS异速生长指数均值为2.85,在0.1~0.95分位的估计值变化范围为2.63~2.96.MECS和NECS参数估计值和置信区间在各分位数呈异质性变化,低分位时,NECS估计值在3个调查区域中最低,MECS最高;高分位时,MECS和NECS均高于SYS.对低分位0.25、中分位0.5和高分位0.75分位数的异速体长体质量关系的方差分析结果显示,低分位和高分位数之间体长 体质量关系极为显著(0.25∶0.75,F=6.38,df=1737,P<0.01),低分位数和中分位数之间为显著(0.25∶0.5,F=2.35,df=1737,P=0.039),中分位数和高分位数之间接近显著(0.5∶0.75,F=2.21,df=1737,P=0.051).成鱼群体SYS异速生长指数均值为3.01,在0.1~0.95分位的估计值变化范围为2.77~3.10.低分位和高分位数之间体长 体质量关系差异达到显著水平(0.25∶0.75,F=3.31,df=2793,P=0.01),低分位和中分位之间差异不显著(0.25∶0.5,F=0.98,df=2793,P=0.43),而高分位和中分位之间则差异极显著(0.5∶0.75,F=3.56,df=2793,P<0.01).     

Wildfire Selectivity for Land Cover Type: Does Size Matter?

Previous research has shown that fires burn certain land cover types disproportionally to their abundance. We used quantile regression to study land cover proneness to fire as a function of fire size, under the hypothesis that they are inversely related, for all land cover types. Using five years of fire perimeters, we estimated conditional quantile functions for lower (avoidance) and upper (preference) quantiles of fire selectivity for five land cover types - annual crops, evergreen oak woodlands, eucalypt forests, pine forests and shrublands. The slope of significant regression quantiles describes the rate of change in fire selectivity (avoidance or preference) as a function of fire size. We used Monte-Carlo methods to randomly permutate fires in order to obtain a distribution of fire selectivity due to chance. This distribution was used to test the null hypotheses that 1) mean fire selectivity does not differ from that obtained by randomly relocating observed fire perimeters; 2) that land cover proneness to fire does not vary with fire size. Our results show that land cover proneness to fire is higher for shrublands and pine forests than for annual crops and evergreen oak woodlands. As fire size increases, selectivity decreases for all land cover types tested. Moreover, the rate of change in selectivity with fire size is higher for preference than for avoidance. Comparison between observed and randomized data led us to reject both null hypotheses tested ( = 0.05) and to conclude it is very unlikely the observed values of fire selectivity and change in selectivity with fire size are due to chance.     

Development of a Summarized Health Index (SHI) for Use in Predicting Survival in Sea Turtles

Veterinary care plays an influential role in sea turtle rehabilitation, especially in endangered species. Physiological characteristics, hematological and plasma biochemistry profiles, are useful references for clinical management in animals, especially when animals are during the convalescence period. In this study, these factors associated with sea turtle surviving were analyzed. The blood samples were collected when sea turtles remained alive, and then animals were followed up for surviving status. The results indicated that significantly negative correlation was found between buoyancy disorders (BD) and sea turtle surviving (p < 0.05). Furthermore, non-surviving sea turtles had significantly higher levels of aspartate aminotranspherase (AST), creatinine kinase (CK), creatinine and uric acid (UA) than surviving sea turtles (all p < 0.05). After further analysis by multiple logistic regression model, only factors of BD, creatinine and UA were included in the equation for calculating summarized health index (SHI) for each individual. Through evaluation by receiver operating characteristic (ROC) curve, the result indicated that the area under curve was 0.920 ± 0.037, and a cut-off SHI value of 2.5244 showed 80.0% sensitivity and 86.7% specificity in predicting survival. Therefore, the developed SHI could be a useful index to evaluate health status of sea turtles and to improve veterinary care at rehabilitation facilities.     

Gene Expression Profile for Predicting Survival in Advanced-Stage Serous Ovarian Cancer Across Two Independent Datasets

Background

Advanced-stage ovarian cancer patients are generally treated with platinum/taxane-based chemotherapy after primary debulking surgery. However, there is a wide range of outcomes for individual patients. Therefore, the clinicopathological factors alone are insufficient for predicting prognosis. Our aim is to identify a progression-free survival (PFS)-related molecular profile for predicting survival of patients with advanced-stage serous ovarian cancer.

Methodology/Principal Findings

Advanced-stage serous ovarian cancer tissues from 110 Japanese patients who underwent primary surgery and platinum/taxane-based chemotherapy were profiled using oligonucleotide microarrays. We selected 88 PFS-related genes by a univariate Cox model (p<0.01) and generated the prognostic index based on 88 PFS-related genes after adjustment of regression coefficients of the respective genes by ridge regression Cox model using 10-fold cross-validation. The prognostic index was independently associated with PFS time compared to other clinical factors in multivariate analysis [hazard ratio (HR), 3.72; 95% confidence interval (CI), 2.66–5.43; p<0.0001]. In an external dataset, multivariate analysis revealed that this prognostic index was significantly correlated with PFS time (HR, 1.54; 95% CI, 1.20–1.98; p = 0.0008). Furthermore, the correlation between the prognostic index and overall survival time was confirmed in the two independent external datasets (log rank test, p = 0.0010 and 0.0008).

Conclusions/Significance

The prognostic ability of our index based on the 88-gene expression profile in ridge regression Cox hazard model was shown to be independent of other clinical factors in predicting cancer prognosis across two distinct datasets. Further study will be necessary to improve predictive accuracy of the prognostic index toward clinical application for evaluation of the risk of recurrence in patients with advanced-stage serous ovarian cancer.     

Nonparametric quantile inference with competing risks data

A conceptually simple quantile inference procedure is proposedfor cause-specific failure probabilities with competing risksdata. The quantiles are defined using the cumulative incidencefunction, which is intuitively meaningful in the competing–risksset–up. We establish the uniform consistency and weakconvergence of a nonparametric estimator of this quantile function.These results form the theoretical basis for extensions of standardone–sample and two–sample quantile inference forindependently censored data. This includes the constructionof confidence intervals and bands for the quantile function,and two–sample tests. Simulation studies and a real dataexample illustrate the practical utility of the methodology.     

Bent Line Quantile Regression with Application to an Allometric Study of Land Mammals' Speed and Mass

Summary Quantile regression, which models the conditional quantiles of the response variable given covariates, usually assumes a linear model. However, this kind of linearity is often unrealistic in real life. One situation where linear quantile regression is not appropriate is when the response variable is piecewise linear but still continuous in covariates. To analyze such data, we propose a bent line quantile regression model. We derive its parameter estimates, prove that they are asymptotically valid given the existence of a change‐point, and discuss several methods for testing the existence of a change‐point in bent line quantile regression together with a power comparison by simulation. An example of land mammal maximal running speeds is given to illustrate an application of bent line quantile regression in which this model is theoretically justified and its parameters are of direct biological interests.     

Breastfeeding and Childhood Obesity: Shift of the Entire BMI Distribution or Only the Upper Parts?

A protective effect of breastfeeding on overweight (binary) has been reported by meta-analyses using logistic regression, whereas studies using linear regression and BMI (continuous) detected no significant association. To assess the relationship of these differences with different outcome classification, we compared results for linear, logistic, and quantile regression models in a cross-sectional data set of considerable size. Height, weight, and questionnaire data on 9,368 preschool children were collected during school-entry examinations in 1999 and 2002 in Bavaria, Southern Germany. We calculated multivariable linear, logistic, and quantile regression models with outcomes BMI, overweight, obesity, and BMI quantiles (as appropriate). Models considered the covariates breastfeeding (breastfed vs. never breastfed), gender, age, smoking in pregnancy, TV watching, maternal BMI, parental education, and early infant weight gain. No significant association was found in the linear regression model. In the logistic model, a significant association was observed for obesity (odds ratio: 0.72 (95% confidence interval (CI) 0.55, 0.94)). In quantile regression no significant point estimates were observed for the percentiles of 0.4-0.8. However, breastfeeding reduced the BMI of children having values on the 90th and 97th percentiles by -0.23 (95% CI -0.39, -0.07) and -0.26 (95% CI -0.45, -0.07) kg/m(2), respectively, on average. In contrast, breastfeeding was significantly associated with a low shift toward higher BMI values for BMI quantiles of 0.03 and from 0.1 to 0.3. The detection of associations between breastfeeding and childhood body composition might be related to the coding of the response variable (continuous or binary) and the statistical method used (linear, logistic, or quantile regression). Quantile regression should additionally be applied in such studies.     

Understanding Child Stunting in India: A Comprehensive Analysis of Socio-Economic,Nutritional and Environmental Determinants Using Additive Quantile Regression

Background

Most attempts to address undernutrition, responsible for one third of global child deaths, have fallen behind expectations. This suggests that the assumptions underlying current modelling and intervention practices should be revisited.

Objective

We undertook a comprehensive analysis of the determinants of child stunting in India, and explored whether the established focus on linear effects of single risks is appropriate.

Design

Using cross-sectional data for children aged 0–24 months from the Indian National Family Health Survey for 2005/2006, we populated an evidence-based diagram of immediate, intermediate and underlying determinants of stunting. We modelled linear, non-linear, spatial and age-varying effects of these determinants using additive quantile regression for four quantiles of the Z-score of standardized height-for-age and logistic regression for stunting and severe stunting.

Results

At least one variable within each of eleven groups of determinants was significantly associated with height-for-age in the 35% Z-score quantile regression. The non-modifiable risk factors child age and sex, and the protective factors household wealth, maternal education and BMI showed the largest effects. Being a twin or multiple birth was associated with dramatically decreased height-for-age. Maternal age, maternal BMI, birth order and number of antenatal visits influenced child stunting in non-linear ways. Findings across the four quantile and two logistic regression models were largely comparable.

Conclusions

Our analysis confirms the multifactorial nature of child stunting. It emphasizes the need to pursue a systems-based approach and to consider non-linear effects, and suggests that differential effects across the height-for-age distribution do not play a major role.