Nonlinear Time Trends Research Articles

A Long-Term Analysis of Demographic Processes, Socioeconomic ‘Modernization’ and Forest Expansion in a European Country

This article investigates long-term forest decline and expansion vis-à-vis demographic processes in Italy, evidencing changes in the underlying socioeconomic context considering the ‘modernization theory’. An exploratory data analysis of 58 indicators assessing five basic research dimensions (territory, demography, education, trade and agriculture) and evolving rapidly over the study period (1862–2009), was run to ascertain similarity patterns among indicators and to identify time intervals characterized by homogeneous conditions in different analysis’ domains. Complementing indicators of forest expansion, changes in population structure and dynamics allow an empirical investigation of temporal coherence among demographic and forest transitions in Italy. The time window encompassing the two World Wars, approximately between 1931 and 1951, was identified as a turning point in the forest-socioeconomic system, being characterized by two groups of indicators that follow diverging (linear vs. nonlinear) time trends. A secondary turning point was identified at the beginning of the 1970s. Distinct temporal trends in the studied indicators were also identified using multivariate statistics (before the 1930s, between the 1930s and the 1950s, between the 1950s and the 1970s, from the 1970s onwards) and represent conditions of dynamic equilibrium between socio-ecological contexts, highlighting latent transitions in both population and environment conditions. Our work definitely contributes to an empirical understanding of economic, political and social forces associated with forest transition and demographic transition in advanced economies.

Under-5 Mortality Rates in G7 Countries: Analysis of Fractional Persistence, Structural Breaks and Nonlinear Time Trends.

This paper deals with the analysis of the under-5 mortality rate series in the G7 countries by using fractional integration techniques, including structural breaks and potential nonlinearities in the data. Several features were detected in the results: Firstly, we observed that for the neonatal data, the order of integration is equal to or higher than one in all cases, contrary to what happens for the remaining cases (< 1- < 5years) where mean reversion is found in many cases, especially as we increase the age of death. Thus, shocks affecting the neonatal (< 1month from delivery) mortality rates will have permanent effects requiring special attention to recover the original trends. As expected, all the time trend coefficients were significantly negative and the highest reduction in the mortality rates was obtained in Japan, which might be related with the 17-year increase in life expectancy for the country. Due to the sensitivity of the methodological approaches, the use of robust time series approaches when analyzing child mortality rates is highly recommended.

A Gradual Effects Model for Single-Case Designs

ABSTRACTSingle-case designs are a class of repeated measures experiments used to evaluate the effects of interventions for small or specialized populations, such as individuals with low-incidence disabilities. There has been growing interest in systematic reviews and syntheses of evidence from single-case designs, but there remains a need to further develop appropriate statistical models and effect sizes for data from the designs. We propose a novel model for single-case data that exhibit nonlinear time trends created by an intervention that produces gradual effects, which build up and dissipate over time. The model expresses a structural relationship between a pattern of treatment assignment and an outcome variable, making it appropriate for both treatment reversal and multiple baseline designs. It is formulated as a generalized linear model so that it can be applied to outcomes measured as frequency counts or proportions, both of which are commonly used in single-case research, while providing readily interpretable effect size estimates such as log response ratios or log odds ratios. We demonstrate the gradual effects model by applying it to data from a single-case study and examine the performance of proposed estimation methods in a Monte Carlo simulation of frequency count data.

Accounting for Nonlinearity, Asymmetry, Heterogeneity, and Cross-Sectional Dependence in Energy Modeling: US State-Level Panel Analysis

This paper provides an example of several modeling and econometric advances used in the panel estimation of energy demand elasticities. The paper models the demand of total, industrial, and transport energy consumption and residential and commercial electricity consumption by analyzing US state-based panel data. The paper employs recently developed dynamic panel methods that address heterogeneity, nonstationarity, and cross-sectional dependence. In addition, the paper (i) considers possible nonlinear relationships between energy consumption and income without employing polynomial transformations of integrated income; and (ii) allows for and calculates possible asymmetric relationships between energy consumption and price. Finally, the paper models energy efficiency improvements by a nonlinear time trend. To our knowledge no other paper has combined all of the econometric and modeling advances that are applied here. Most of the results conformed to expectations; however, limited to no evidence of nonlinearities and asymmetries were uncovered.

The Effect of Minimum Wages on Adolescent Fertility: A Nationwide Analysis.

To investigate the effect of minimum wage laws on adolescent birth rates in the United States. I used a difference-in-differences approach and vital statistics data measured quarterly at the state level from 2003 to 2014. All models included state covariates, state and quarter-year fixed effects, and state-specific quarter-year nonlinear time trends, which provided plausibly causal estimates of the effect of minimum wage on adolescent birth rates. A $1 increase in minimum wage reduces adolescent birth rates by about 2%. The effects are driven by non-Hispanic White and Hispanic adolescents. Nationwide, increasing minimum wages by $1 would likely result in roughly 5000 fewer adolescent births annually.

Analysis of asynchronous longitudinal data with partially linear models

We study partially linear models for asynchronous longitudinal data to incorporate nonlinear time trend effects. Local and global estimating equations are developed for estimating the parametric and nonparametric effects. We show that with a proper choice of the kernel bandwidth parameter, one can obtain consistent and asymptotically normal parameter estimates for the linear effects. Asymptotic properties of the estimated nonlinear effects are established. Extensive simulation studies provide numerical support for the theoretical findings. Data from an HIV study are used to illustrate our methodology.

The effect of cognitive-behavioral therapy as an antidepressive treatment is falling: Reply to Ljòtsson et al. (2017) and Cristea et al. (2017).

This article critically reassesses the nonlinear reanalysis by Ljótsson, Hedman, Mattsson, and Andersson (2017) and reviews Cristea et al.'s (2017) extension of our original meta-analysis (Johnsen & Friborg, 2015) reporting a decline in the effects of cognitive-behavioral therapy (CBT) for treating unipolar depression. Ljótsson et al. fitted a piecewise meta-regression model to the data, indicating a halt in the decline from the year 1995 onward, hence concluding that CBT is not gradually losing its efficacy. We reanalyzed the data for nonlinear time trends and replicated their findings for the 34 studies using the Hamilton Rating Scale for Depression as the outcome but not for the 67 studies using Beck's Depression Inventory as the outcome. The best nonlinear model was quadratic rather than flat (or linear) from 2001 onward, which opposes the conclusion by Ljótsson et al. of stability in effects. Cristea et al. identified additional studies, but their new analyses provided mixed support for a linear decline in CBT effects. They could not dismiss a decline except only in the most stringent analytic condition-namely, when analyzing only 29 randomized controlled trials based on between-groups effect sizes solely. Their study includes several questionable methodological choices, so we expand on the discussion of these disparate meta-analytic findings. Of particular concern is the tendency to downplay the fact that when looking at all of the studies together, there is a clear decline in the effects of CBT, which should concern therapy researchers within the field rather than being explained away. (PsycINFO Database Record

Minimum Cost Linear Trend Free 2n-(n-k) Designs of Resolution IV

This article extends the resolution of time trend free designs for sequential 2n-p experiments from III into IV and minimizes the number of factor level changes between runs (i.e., cost) by constructing a catalog of (2k−2 −1) minimum cost linear trend free resolution IV 2n−(n−k) designs (2k−2 ≤ n ≤ 2k−1−2) from the full 2k factorial experiment using the interactions-main effects assignment technique. Each systematic 2n−(n−k) design in the catalog is economic in minimum number of factor level changes and allows for the estimation of all n main effects unbiased by either the linear time trend (which may be present in the 2n−(n−k) sequentially generated responses) or the non negligible two-factor interactions. This article provides for each 2n−(n−k) design: (1) the defining relation or the alias structure; (2) the k independent generators for sequencing the 2n−(n−k) runs by the generalized foldover scheme; and (3) the minimum cost represented by the total number of factor level changes between the 2n−(n−k) runs. All k main effects of the 2k experiment are excluded from the selection assignment process due to their nonlinear time trend resistance as well as excluding a total of (2k−1 –k +1) interactions violating the resolution IV requirement.

Did the health of the Dutch population improve between 2001 and 2008? Investigating age- and gender-specific trends in quality of life.

Although many countries' populations have experienced increasing life expectancy in recent decades, quality of life (QoL) trends in the general population have yet to be investigated. This paper investigates whether QoL changed for the general Dutch population over the period 2001-2008. A beta regression model was employed to address specific features of the QoL distribution (i.e., boundedness, skewness, and heteroskedasticity), as well non-linear age and time trends. Quality-adjusted life expectancy (QALE) was calculated by combining model estimates of mean QoL with mortality rates provided by Statistics Netherlands. Changes in QALE were decomposed into those changes caused by QoL changes and those caused by mortality-rate changes. The results revealed a significant increase in QoL over 2001-2008 for both genders and most ages. For example, QALE for a man/woman aged 20 was found to have increased by 2.3/1.9 healthy years, of which 0.6/0.8 was due to QoL improvements.

Additive mixed models with approximate Dirichlet process mixtures: the EM approach

We consider additive mixed models for longitudinal data with a nonlinear time trend. As random effects distribution an approximate Dirichlet process mixture is proposed that is based on the truncated version of the stick breaking presentation of the Dirichlet process and provides a Gaussian mixture with a data driven choice of the number of mixture components. The main advantage of the specification is its ability to identify clusters of subjects with a similar random effects structure. For the estimation of the trend curve the mixed model representation of penalized splines is used. An Expectation-Maximization algorithm is given that solves the estimation problem and that exhibits advantages over Markov chain Monte Carlo approaches, which are typically used when modeling with Dirichlet processes. The method is evaluated in a simulation study and applied to theophylline data and to body mass index profiles of children.

The Effects of Minimum Wages over the Business Cycle

This study examines whether the low-skilled employment effects of minimum wage increases differ over the state business cycle. Controlling for spatial heterogeneity via state-specific productivity shocks to the low-skilled sector and state-specific non-linear time trends, the results suggest that minimum wage increases between 1989 and 2012 reduce low-skilled employment more during recessions than expansions. Estimated employment elasticities with respect to the minimum wage range from 0 to −0.2 during state economic expansions, but reach as high as −0.3 during troughs in the business cycle.

MP58-19 PATIENT-REPORTED HEALTH RELATED QUALITY-OF-LIFE (HRQOL) OUTCOMES OF PATIENTS ON ACTIVE SURVEILLANCE: RESULTS OF A PROSPECTIVE, LONGITUDINAL, SINGLE-CENTER STUDY

INTRODUCTION AND OBJECTIVES: Treatment options for clinically localized PCa may negatively impact a patient’s HRQOL to varying degree. Active surveillance (AS) offers patients the potential for preservation of HRQOL without compromising curability. However, there is a lack of prospective, patient-reported data on the HRQOL outcomes of patients managed by AS relative to radical prostatectomy (RP) and brachytherapy (BT). From a prospective, longitudinal HRQOL protocol using validated instruments for patient-reported functional outcomes, we analyzed voiding, bowel, sexual function, urinary incontinence, and physical/emotional functioning among patients managed by AS, RP, and BT at our institution. METHODS: Between 2007-2013, 591 patients PCa were enrolled in a prospective, longitudinal HRQOL protocol. HRQOL domains were assessed at various time points by a 48-item validated HRQOL instrument (Giesler et al. Qual Life Res 2000). Overall, 67 patients were managed by AS, 116 by BT, and 407 with RP (174 open and 223 robotic). A mixed effect model with random intercepts was fitted to the longitudinal data. The time was treated as categorical instead of continuous to reflect possible non-linear time trend. RESULTS: Statistically significant differences for BT compared to AS and RP were noted for voiding (irritative and obstructive symptoms) and bowel function, where patients reported worsening symptoms as soon as 6 months with partial recovery 12 months (P value < 0.001 for all). Erectile function and incontinence were most affected by RP when compared to AS and BT, with recovery also noted 12 months (P value < 0.001 for all). Each domain is illustrated in Figure 1. CONCLUSIONS: HRQOL among patients on AS is stable over 1-2 years for all domains. Urinary and bowel function for AS is significantly better than BT. Sexual function and incontinence for AS is significantly better than RP. This information is anticipated to be useful for patients and physicians when deciding upon the merits of AS over radical therapy for the treatment of localized PCa.

MP58-20 HEALTH-RELATED QUALITY OF LIFE IN MEN UNDERGOING ACTIVE SURVEILLANCE VS. RADICAL PROSTATECTOMY FOR LOW RISK PROSTATE CANCER: A PROSPECTIVE MULTI-INSTITUTIONAL STUDY

INTRODUCTION AND OBJECTIVES: Treatment options for clinically localized PCa may negatively impact a patient’s HRQOL to varying degree. Active surveillance (AS) offers patients the potential for preservation of HRQOL without compromising curability. However, there is a lack of prospective, patient-reported data on the HRQOL outcomes of patients managed by AS relative to radical prostatectomy (RP) and brachytherapy (BT). From a prospective, longitudinal HRQOL protocol using validated instruments for patient-reported functional outcomes, we analyzed voiding, bowel, sexual function, urinary incontinence, and physical/emotional functioning among patients managed by AS, RP, and BT at our institution. METHODS: Between 2007-2013, 591 patients PCa were enrolled in a prospective, longitudinal HRQOL protocol. HRQOL domains were assessed at various time points by a 48-item validated HRQOL instrument (Giesler et al. Qual Life Res 2000). Overall, 67 patients were managed by AS, 116 by BT, and 407 with RP (174 open and 223 robotic). A mixed effect model with random intercepts was fitted to the longitudinal data. The time was treated as categorical instead of continuous to reflect possible non-linear time trend. RESULTS: Statistically significant differences for BT compared to AS and RP were noted for voiding (irritative and obstructive symptoms) and bowel function, where patients reported worsening symptoms as soon as 6 months with partial recovery 12 months (P value < 0.001 for all). Erectile function and incontinence were most affected by RP when compared to AS and BT, with recovery also noted 12 months (P value < 0.001 for all). Each domain is illustrated in Figure 1. CONCLUSIONS: HRQOL among patients on AS is stable over 1-2 years for all domains. Urinary and bowel function for AS is significantly better than BT. Sexual function and incontinence for AS is significantly better than RP. This information is anticipated to be useful for patients and physicians when deciding upon the merits of AS over radical therapy for the treatment of localized PCa.

Reference chart of inspiratory muscle strength: a new tool to monitor the effect of pre-operative training

ObjectivesTo develop a reference chart to monitor inspiratory muscle strength during pre-operative inspiratory muscle training for patients at high risk of developing postoperative pulmonary complications awaiting coronary artery bypass graft (CABG) surgery. DesignSecondary data analysis using patients from the intervention arm of a randomised clinical trial. SettingUniversity medical centre. ParticipantsPatients at high risk of developing postoperative pulmonary complications awaiting CABG surgery. InterventionsPatients performed inspiratory muscle training seven times per week for at least 2 weeks before surgery. Main outcome measuresMaximal inspiratory muscle strength. ResultsA new reference chart was produced using a non-linear time trend model with a normal error structure. ConclusionsThe chart is a novel tool for monitoring the progress of inspiratory muscle training for physiotherapy practice. Wider use of this chart is recommended.

Trends in Food and Beverage Sources among US Children and Adolescents: 1989-2010

Despite the historical rise and recent plateau of child overweight and obesity, levels remain exceedingly high. To understand these trends and identify targets for intervention it is important to examine concomitant trends in children's diets. The objective of our analysis was to describe 21-year trends in total energy intake and the major food and beverage sources of energy among 2- to 18-year-olds in the United States. Six nationally representative surveys were examined in 2012, the Continuing Survey of Food Intakes by Individuals (1989-1991 and 1994-1996, 1998) and the National Health and Nutrition Examination Survey (2003-2004, 2005-2006, 2007-2008, and 2009-2010). Total energy intake among US children and adolescents rose considerably from 1989 to 2004, and subsequently declined through 2010. Seven sources were consistently major contributors across all time points: sugar-sweetened beverages, pizza, full-fat milk, grain-based desserts, breads, pasta dishes, and savory snacks. Intakes of full-fat milk, meats and processed meat products, ready-to-eat cereals, burgers, fried potatoes, fruit juice, and vegetables decreased from 1989-2010 whereas intakes of nonfat milk, poultry, sweet snacks and candies, and tortilla- and corn-based dishes increased linearly over the 21-year period. Significant nonlinear time trends were observed with recent decreases in intakes of sugar-sweetened beverages, pizza, pasta dishes, breads and rolls, and savory snacks and recent increases in intake of fruit. Energy intakes of US children began to decline in 2003-2004 and continued to decline through 2009-2010. However, among preschool children (aged 2 to 5 years) and children from low-income families, total energy intakes in 2009-2010 still remained significantly higher than in 1989-1991.

Socioeconomic disparities in maternity care among Indian adolescents, 1990-2006.

BackgroundIndia, with a population of more than 1.21 billion, has the highest maternal mortality in the world (estimated to be 56000 in 2010); and adolescent (aged 15–19) mortality shares 9% of total maternal deaths. Addressing the maternity care needs of adolescents may have considerable ramifications for achieving the Millennium Development Goal (MDG)–5. This paper assesses the socioeconomic differentials in accessing full antenatal care and professional attendance at delivery by adolescent mothers (aged 15–19) in India during 1990–2006.Methods and FindingsData from three rounds of the National Family Health Survey of India conducted during 1992–93, 1998–99, and 2005–06 were analyzed. The Cochran-Armitage and Chi-squared test for linear and non-linear time trends were applied, respectively, to understand the trend in the proportion of adolescent mothers utilizing select maternity care services during 1990–2006. Using pooled multivariate logistic regression models, the probability of select maternal healthcare utilization among women by key socioeconomic characteristics was appraised. After adjusting for potential socio-demographic and economic characteristics, the likelihood of adolescents accessing full antenatal care increased by only 4% from 1990 to 2006. However, the probability of adolescent women availing themselves of professional attendance at delivery increased by 79% during the same period. The study also highlights the desolate disparities in maternity care services among adolescents across the most and the least favoured groups.ConclusionMaternal care interventions in India need focused programs for rural, uneducated, poor adolescent women so that they can avail themselves of measures to delay child bearing, and for better antenatal consultation and delivery care in case of pregnancy. This study strongly advocates the promotion of a comprehensive ‘adolescent scheme’ along the lines of ‘Continuum of Maternal, Newborn and Child health Care’ to address the unmet need of reproductive and maternal healthcare services among adolescent women in India.

Global, regional, and national trends in haemoglobin concentration and prevalence of total and severe anaemia in children and pregnant and non-pregnant women for 1995-2011: a systematic analysis of population-representative data.

SummaryBackgroundLow haemoglobin concentrations and anaemia are important risk factors for the health and development of women and children. We estimated trends in the distributions of haemoglobin concentration and in the prevalence of anaemia and severe anaemia in young children and pregnant and non-pregnant women between 1995 and 2011.MethodsWe obtained data about haemoglobin and anaemia for children aged 6–59 months and women of childbearing age (15–49 years) from 257 population-representative data sources from 107 countries worldwide. We used health, nutrition, and household surveys; summary statistics from WHO's Vitamin and Mineral Nutrition Information System; and summary statistics reported by other national and international agencies. We used a Bayesian hierarchical mixture model to estimate haemoglobin distributions and systematically addressed missing data, non-linear time trends, and representativeness of data sources. We quantified the uncertainty of our estimates.FindingsGlobal mean haemoglobin improved slightly between 1995 and 2011, from 125 g/L (95% credibility interval 123–126) to 126 g/L (124–128) in non-pregnant women, from 112 g/L (111–113) to 114 g/L (112–116) in pregnant women, and from 109 g/L (107–111) to 111 g/L (110–113) in children. Anaemia prevalence decreased from 33% (29–37) to 29% (24–35) in non-pregnant women, from 43% (39–47) to 38% (34–43) in pregnant women, and from 47% (43–51) to 43% (38–47) in children. These prevalences translated to 496 million (409–595 million) non-pregnant women, 32 million (28–36 million) pregnant women, and 273 million (242–304 million) children with anaemia in 2011. In 2011, concentrations of mean haemoglobin were lowest and anaemia prevalence was highest in south Asia and central and west Africa.InterpretationChildren's and women's haemoglobin statuses improved in some regions where concentrations had been low in the 1990s, leading to a modest global increase in mean haemoglobin and a reduction in anaemia prevalence. Further improvements are needed in some regions, particularly south Asia and central and west Africa, to improve the health of women and children and achieve global targets for reducing anaemia.FundingBill & Melinda Gates Foundation, Grand Challenges Canada, and the UK Medical Research Council.

Modelling house prices using multilevel structured additive regression

This paper analyzes house price data belonging to three hierarchical levels of spatial units. House selling prices with associated individual attributes (the elementary level-1) are grouped within municipalities (level-2), which form districts (level-3), which are themselves nested in counties (level-4). Additionally to individual attributes, explanatory covariates with possibly nonlinear effects are available on two of these spatial resolutions. We apply a multilevel version of structured additive regression (STAR) models to regress house prices on individual attributes and locational neighbourhood characteristics in a four-level hierarchical model. In multilevel STAR models the regression coefficients of a particular nonlinear term may themselves obey a regression model with structured additive predictor. The framework thus allows to incorporate nonlinear covariate effects and time trends, smooth spatial effects and complex interactions at every level of the hierarchy of the multilevel model. Moreover, we are able to decompose the spatial heterogeneity effect and investigate its magnitude at different spatial resolutions allowing for improved predictive quality even in the case of unobserved spatial units. Statistical inference is fully Bayesian and based on highly efficient Markov chain Monte Carlo simulation techniques that take advantage of the hierarchical structure in the data.

Multilevel structured additive regression

Models with structured additive predictor provide a very broad and rich framework for complex regression modeling. They can deal simultaneously with nonlinear covariate effects and time trends, unit- or cluster-specific heterogeneity, spatial heterogeneity and complex interactions between covariates of different type. In this paper, we propose a hierarchical or multilevel version of regression models with structured additive predictor where the regression coefficients of a particular nonlinear term may obey another regression model with structured additive predictor. In that sense, the model is composed of a hierarchy of complex structured additive regression models. The proposed model may be regarded as an extended version of a multilevel model with nonlinear covariate terms in every level of the hierarchy. The model framework is also the basis for generalized random slope modeling based on multiplicative random effects. Inference is fully Bayesian and based on Markov chain Monte Carlo simulation techniques. We provide an in depth description of several highly efficient sampling schemes that allow to estimate complex models with several hierarchy levels and a large number of observations within a couple of minutes (often even seconds). We demonstrate the practicability of the approach in a complex application on childhood undernutrition with large sample size and three hierarchy levels.

Semiparametric trending panel data models with cross-sectional dependence

A semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross-sectional dependence in both the regressors and the residuals. A pooled semiparametric profile likelihood dummy variable approach based on the first-stage local linear fitting is developed to estimate both the parameter vector and the nonlinear time trend function. As both the time series length T and the cross-sectional size N tend to infinity, the resulting estimator of the parameter vector is asymptotically normal with a root-(NT) convergence rate. Meanwhile, the asymptotic distribution for the nonparametric estimator of the trend function is also established with a root-(NTh) convergence rate. Two simulated examples are provided to illustrate the finite sample performance of the proposed method. In addition, the proposed model and estimation method are applied to a CPI data set as well as an input–output data set.