Plea for routinely presenting prediction intervals in meta-analysis

OBJECTIVES

Evaluating the variation in the strength of the effect across studies is a key feature of meta-analyses. This variability is reflected by measures like τ(2) or I(2), but their clinical interpretation is not straightforward. A prediction interval is less complicated: it presents the expected range of true effects in similar studies. We aimed to show the advantages of having the prediction interval routinely reported in meta-analyses.

DESIGN

We show how the prediction interval can help understand the uncertainty about whether an intervention works or not. To evaluate the implications of using this interval to interpret the results, we selected the first meta-analysis per intervention review of the Cochrane Database of Systematic Reviews Issues 2009-2013 with a dichotomous (n=2009) or continuous (n=1254) outcome, and generated 95% prediction intervals for them.

RESULTS

In 72.4% of 479 statistically significant (random-effects p<0.05) meta-analyses in the Cochrane Database 2009-2013 with heterogeneity (I(2)>0), the 95% prediction interval suggested that the intervention effect could be null or even be in the opposite direction. In 20.3% of those 479 meta-analyses, the prediction interval showed that the effect could be completely opposite to the point estimate of the meta-analysis. We demonstrate also how the prediction interval can be used to calculate the probability that a new trial will show a negative effect and to improve the calculations of the power of a new trial.

CONCLUSIONS

The prediction interval reflects the variation in treatment effects over different settings, including what effect is to be expected in future patients, such as the patients that a clinician is interested to treat. Prediction intervals should be routinely reported to allow more informative inferences in meta-analyses.

A brief introduction to mixed effects modelling and multi-model inference in ecology

The use of linear mixed effects models (LMMs) is increasingly common in the analysis of biological data. Whilst LMMs offer a flexible approach to modelling a broad range of data types, ecological data are often complex and require complex model structures, and the fitting and interpretation of such models is not always straightforward. The ability to achieve robust biological inference requires that practitioners know how and when to apply these tools. Here, we provide a general overview of current methods for the application of LMMs to biological data, and highlight the typical pitfalls that can be encountered in the statistical modelling process. We tackle several issues regarding methods of model selection, with particular reference to the use of information theory and multi-model inference in ecology. We offer practical solutions and direct the reader to key references that provide further technical detail for those seeking a deeper understanding. This overview should serve as a widely accessible code of best practice for applying LMMs to complex biological problems and model structures, and in doing so improve the robustness of conclusions drawn from studies investigating ecological and evolutionary questions.

Advances in the meta-analysis of heterogeneous clinical trials I: The inverse variance heterogeneity model

This article examines an improved alternative to the random effects (RE) model for meta-analysis of heterogeneous studies. It is shown that the known issues of underestimation of the statistical error and spuriously overconfident estimates with the RE model can be resolved by the use of an estimator under the fixed effect model assumption with a quasi-likelihood based variance structure - the IVhet model. Extensive simulations confirm that this estimator retains a correct coverage probability and a lower observed variance than the RE model estimator, regardless of heterogeneity. When the proposed IVhet method is applied to the controversial meta-analysis of intravenous magnesium for the prevention of mortality after myocardial infarction, the pooled OR is 1.01 (95% CI 0.71-1.46) which not only favors the larger studies but also indicates more uncertainty around the point estimate. In comparison, under the RE model the pooled OR is 0.71 (95% CI 0.57-0.89) which, given the simulation results, reflects underestimation of the statistical error. Given the compelling evidence generated, we recommend that the IVhet model replace both the FE and RE models. To facilitate this, it has been implemented into free meta-analysis software called MetaXL which can be downloaded from www.epigear.com.

Bayesian model reduction and empirical Bayes for group (DCM) studies

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction.

Bayesian model selection for group studies - revisited

In this paper, we revisit the problem of Bayesian model selection (BMS) at the group level. We originally addressed this issue in Stephan et al. (2009), where models are treated as random effects that could differ between subjects, with an unknown population distribution. Here, we extend this work, by (i) introducing the Bayesian omnibus risk (BOR) as a measure of the statistical risk incurred when performing group BMS, (ii) highlighting the difference between random effects BMS and classical random effects analyses of parameter estimates, and (iii) addressing the problem of between group or condition model comparisons. We address the first issue by quantifying the chance likelihood of apparent differences in model frequencies. This leads to the notion of protected exceedance probabilities. The second issue arises when people want to ask "whether a model parameter is zero or not" at the group level. Here, we provide guidance as to whether to use a classical second-level analysis of parameter estimates, or random effects BMS. The third issue rests on the evidence for a difference in model labels or frequencies across groups or conditions. Overall, we hope that the material presented in this paper finesses the problems of group-level BMS in the analysis of neuroimaging and behavioural data.

Negative binomial mixed models for analyzing microbiome count data

Background

Recent advances in next-generation sequencing (NGS) technology enable researchers to collect a large volume of metagenomic sequencing data. These data provide valuable resources for investigating interactions between the microbiome and host environmental/clinical factors. In addition to the well-known properties of microbiome count measurements, for example, varied total sequence reads across samples, over-dispersion and zero-inflation, microbiome studies usually collect samples with hierarchical structures, which introduce correlation among the samples and thus further complicate the analysis and interpretation of microbiome count data.

Results

In this article, we propose negative binomial mixed models (NBMMs) for detecting the association between the microbiome and host environmental/clinical factors for correlated microbiome count data. Although having not dealt with zero-inflation, the proposed mixed-effects models account for correlation among the samples by incorporating random effects into the commonly used fixed-effects negative binomial model, and can efficiently handle over-dispersion and varying total reads. We have developed a flexible and efficient IWLS (Iterative Weighted Least Squares) algorithm to fit the proposed NBMMs by taking advantage of the standard procedure for fitting the linear mixed models.

Conclusions

We evaluate and demonstrate the proposed method via extensive simulation studies and the application to mouse gut microbiome data. The results show that the proposed method has desirable properties and outperform the previously used methods in terms of both empirical power and Type I error. The method has been incorporated into the freely available R package BhGLM (http://www.ssg.uab.edu/bhglm/ and http://github.com/abbyyan3/BhGLM), providing a useful tool for analyzing microbiome data.

Dynamic predictions with time-dependent covariates in survival analysis using joint modeling and landmarking

A key question in clinical practice is accurate prediction of patient prognosis. To this end, nowadays, physicians have at their disposal a variety of tests and biomarkers to aid them in optimizing medical care. These tests are often performed on a regular basis in order to closely follow the progression of the disease. In this setting, it is of interest to optimally utilize the recorded information and provide medically relevant summary measures, such as survival probabilities, which will aid in decision making. In this work, we present and compare two statistical techniques that provide dynamically updated estimates of survival probabilities, namely landmark analysis and joint models for longitudinal and time-to-event data. Special attention is given to the functional form linking the longitudinal and event time processes, and to measures of discrimination and calibration in the context of dynamic prediction.

Should age-period-cohort studies return to the methodologies of the 1970s?

Social scientists have recognized the importance of age-period-cohort (APC) models for half a century, but have spent much of this time mired in debates about the feasibility of APC methods. Recently, a new class of APC methods based on modern statistical knowledge has emerged, offering potential solutions. In 2009, Reither, Hauser and Yang used one of these new methods - hierarchical APC (HAPC) modeling - to study how birth cohorts may have contributed to the U.S. obesity epidemic. They found that recent birth cohorts experience higher odds of obesity than their predecessors, but that ubiquitous period-based changes are primarily responsible for the rising prevalence of obesity. Although these findings have been replicated elsewhere, recent commentaries by Bell and Jones call them into question - along with the new class of APC methods. Specifically, Bell and Jones claim that new APC methods do not adequately address model identification and suggest that "solid theory" is often sufficient to remove one of the three temporal dimensions from empirical consideration. They also present a series of simulation models that purportedly show how the HAPC models estimated by Reither et al. (2009) could have produced misleading results. However, these simulation models rest on assumptions that there were no period effects, and associations between period and cohort variables and the outcome were perfectly linear. Those are conditions under which APC models should never be used. Under more tenable assumptions, our own simulations show that HAPC methods perform well, both in recovering the main findings presented by Reither et al. (2009) and the results reported by Bell and Jones. We also respond to critiques about model identification and theoretically-imposed constraints, finding little pragmatic support for such arguments. We conclude by encouraging social scientists to move beyond the debates of the 1970s and toward a deeper appreciation for modern APC methodologies.

Exploring the effects of roadway characteristics on the frequency and severity of head-on crashes: case studies from Malaysian federal roads

Head-on crashes are among the most severe collision types and of great concern to road safety authorities. Therefore, it justifies more efforts to reduce both the frequency and severity of this collision type. To this end, it is necessary to first identify factors associating with the crash occurrence. This can be done by developing crash prediction models that relate crash outcomes to a set of contributing factors. This study intends to identify the factors affecting both the frequency and severity of head-on crashes that occurred on 448 segments of five federal roads in Malaysia. Data on road characteristics and crash history were collected on the study segments during a 4-year period between 2007 and 2010. The frequency of head-on crashes were fitted by developing and comparing seven count-data models including Poisson, standard negative binomial (NB), random-effect negative binomial, hurdle Poisson, hurdle negative binomial, zero-inflated Poisson, and zero-inflated negative binomial models. To model crash severity, a random-effect generalized ordered probit model (REGOPM) was used given a head-on crash had occurred. With respect to the crash frequency, the random-effect negative binomial (RENB) model was found to outperform the other models according to goodness of fit measures. Based on the results of the model, the variables horizontal curvature, terrain type, heavy-vehicle traffic, and access points were found to be positively related to the frequency of head-on crashes, while posted speed limit and shoulder width decreased the crash frequency. With regard to the crash severity, the results of REGOPM showed that horizontal curvature, paved shoulder width, terrain type, and side friction were associated with more severe crashes, whereas land use, access points, and presence of median reduced the probability of severe crashes. Based on the results of this study, some potential countermeasures were proposed to minimize the risk of head-on crashes.

Using hierarchical Bayesian binary probit models to analyze crash injury severity on high speed facilities with real-time traffic data

Severe crashes are causing serious social and economic loss, and because of this, reducing crash injury severity has become one of the key objectives of the high speed facilities' (freeway and expressway) management. Traditional crash injury severity analysis utilized data mainly from crash reports concerning the crash occurrence information, drivers' characteristics and roadway geometric related variables. In this study, real-time traffic and weather data were introduced to analyze the crash injury severity. The space mean speeds captured by the Automatic Vehicle Identification (AVI) system on the two roadways were used as explanatory variables in this study; and data from a mountainous freeway (I-70 in Colorado) and an urban expressway (State Road 408 in Orlando) have been used to identify the analysis result's consistence. Binary probit (BP) models were estimated to classify the non-severe (property damage only) crashes and severe (injury and fatality) crashes. Firstly, Bayesian BP models' results were compared to the results from Maximum Likelihood Estimation BP models and it was concluded that Bayesian inference was superior with more significant variables. Then different levels of hierarchical Bayesian BP models were developed with random effects accounting for the unobserved heterogeneity at segment level and crash individual level, respectively. Modeling results from both studied locations demonstrate that large variations of speed prior to the crash occurrence would increase the likelihood of severe crash occurrence. Moreover, with considering unobserved heterogeneity in the Bayesian BP models, the model goodness-of-fit has improved substantially. Finally, possible future applications of the model results and the hierarchical Bayesian probit models were discussed.

Meta-analysis of binary outcomes via generalized linear mixed models: a simulation study

Background

Systematic reviews and meta-analyses of binary outcomes are widespread in all areas of application. The odds ratio, in particular, is by far the most popular effect measure. However, the standard meta-analysis of odds ratios using a random-effects model has a number of potential problems. An attractive alternative approach for the meta-analysis of binary outcomes uses a class of generalized linear mixed models (GLMMs). GLMMs are believed to overcome the problems of the standard random-effects model because they use a correct binomial-normal likelihood. However, this belief is based on theoretical considerations, and no sufficient simulations have assessed the performance of GLMMs in meta-analysis. This gap may be due to the computational complexity of these models and the resulting considerable time requirements.

Methods

The present study is the first to provide extensive simulations on the performance of four GLMM methods (models with fixed and random study effects and two conditional methods) for meta-analysis of odds ratios in comparison to the standard random effects model.

Results

In our simulations, the hypergeometric-normal model provided less biased estimation of the heterogeneity variance than the standard random-effects meta-analysis using the restricted maximum likelihood (REML) estimation when the data were sparse, but the REML method performed similarly for the point estimation of the odds ratio, and better for the interval estimation.

Conclusions

It is difficult to recommend the use of GLMMs in the practice of meta-analysis. The problem of finding uniformly good methods of the meta-analysis for binary outcomes is still open.

Electronic supplementary material

The online version of this article (10.1186/s12874-018-0531-9) contains supplementary material, which is available to authorized users.

Maximum likelihood estimation for semiparametric regression models with multivariate interval-censored data

Interval-censored multivariate failure time data arise when there are multiple types of failure or there is clustering of study subjects and each failure time is known only to lie in a certain interval. We investigate the effects of possibly time-dependent covariates on multivariate failure times by considering a broad class of semiparametric transformation models with random effects, and we study nonparametric maximum likelihood estimation under general interval-censoring schemes. We show that the proposed estimators for the finite-dimensional parameters are consistent and asymptotically normal, with a limiting covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood. In addition, we develop an EM algorithm that converges stably for arbitrary datasets. Finally, we assess the performance of the proposed methods in extensive simulation studies and illustrate their application using data derived from the Atherosclerosis Risk in Communities Study.

Understanding and misunderstanding group mean centering: a commentary on Kelley et al.'s dangerous practice

Kelley et al. argue that group-mean-centering covariates in multilevel models is dangerous, since-they claim-it generates results that are biased and misleading. We argue instead that what is dangerous is Kelley et al.'s unjustified assault on a simple statistical procedure that is enormously helpful, if not vital, in analyses of multilevel data. Kelley et al.'s arguments appear to be based on a faulty algebraic operation, and on a simplistic argument that parameter estimates from models with mean-centered covariates must be wrong merely because they are different than those from models with uncentered covariates. They also fail to explain why researchers should dispense with mean-centering when it is central to the estimation of fixed effects models-a common alternative approach to the analysis of clustered data, albeit one increasingly incorporated within a random effects framework. Group-mean-centering is, in short, no more dangerous than any other statistical procedure, and should remain a normal part of multilevel data analyses where it can be judiciously employed to good effect.

Personalized screening intervals for biomarkers using joint models for longitudinal and survival data

Screening and surveillance are routinely used in medicine for early detection of disease and close monitoring of progression. Motivated by a study of patients who received a human tissue valve in the aortic position, in this work we are interested in personalizing screening intervals for longitudinal biomarker measurements. Our aim in this paper is 2-fold: First, to appropriately select the model to use at the time point the patient was still event-free, and second, based on this model to select the optimal time point to plan the next measurement. To achieve these two goals, we combine information theory measures with optimal design concepts for the posterior predictive distribution of the survival process given the longitudinal history of the subject.

Clarifying hierarchical age-period-cohort models: A rejoinder to Bell and Jones

Previously, Reither et al. (2015) demonstrated that hierarchical age-period-cohort (HAPC) models perform well when basic assumptions are satisfied. To contest this finding, Bell and Jones (2015) invent a data generating process (DGP) that borrows age, period and cohort effects from different equations in Reither et al. (2015). When HAPC models applied to data simulated from this DGP fail to recover the patterning of APC effects, B&J reiterate their view that these models provide "misleading evidence dressed up as science." Despite such strong words, B&J show no curiosity about their own simulated data--and therefore once again misapply HAPC models to data that violate important assumptions. In this response, we illustrate how a careful analyst could have used simple descriptive plots and model selection statistics to verify that (a) period effects are not present in these data, and (b) age and cohort effects are conflated. By accounting for the characteristics of B&J's artificial data structure, we successfully recover the "true" DGP through an appropriately specified model. We conclude that B&Js main contribution to science is to remind analysts that APC models will fail in the presence of exact algebraic effects (i.e., effects with no random/stochastic components), and when collinear temporal dimensions are included without taking special care in the modeling process. The expanded list of coauthors on this commentary represents an emerging consensus among APC scholars that B&J's essential strategy--testing HAPC models with data simulated from contrived DGPs that violate important assumptions--is not a productive way to advance the discussion about innovative APC methods in epidemiology and the social sciences.

The effects of health expenditure on infant mortality in sub-Saharan Africa: evidence from panel data analysis

INTRODUCTION

Although health expenditure in sub-Saharan African countries is the lowest compared with other regions in the world, most African countries have improved their budget allocations to health care over the past 15 years. The majority of health care sources in sub-Saharan Africa are private and largely involve out-of-pocket expenditure, which may prevent healthcare access. Access to healthcare is a known predictor of infant mortality. Therefore the objective of this study is to determine the impact of health care expenditure on infant mortality in sub-Saharan Africa.

METHODS

The study used panel data from World Bank Development Indictors (WDI) from 2000 to 2015 covering 46 countries in sub-Saharan Africa. The random effects model was selected over the fixed effects model based on the Hausman test to assess the effect of health care expenditure on infant and neonatal mortality.

RESULTS

Both public and external health care spending showed a significant negative association with infant and neonatal mortality. However, private health expenditure was not significantly associated with either infant or neonatal mortality. In this study, private expenditure includes funds from households, corporations and non-profit organizations. Public expenditure include domestic revenue as internal transfers and grants, transfers, subsidies to voluntary health insurance beneficiaries, non-profit institutions serving households or enterprise financing schemes as well as compulsory prepayment and social health insurance contributions. External health expenditure is composed of direct foreign transfers and foreign transfers distributed by government encompassing all financial inflows into the national health system from outside the country.

CONCLUSION

Health care expenditure remains a crucial component of reducing infant and neonatal mortality in sub-Saharan African countries. In the region, where health infrastructure is largely underdeveloped, increasing health expenditure will contribute to progress towards reducing infant and neonatal mortality during the Sustainable Development Goals (SDGs) era. Therefore, governments in the region need to increase amounts allocated to health care service delivery in order to reduce infant mortality.

Birth weight and perfluorooctane sulfonic acid: a random-effects meta-regression analysis

Supplemental Digital Content is available in the text.

Perfluorooctane sulfonic acid (PFOS) is a ubiquitous environmental contaminant. Most people in developed countries have detectable serum concentrations. Lower birth weight has been associated with serum PFOS in studies world-wide, many of which have been published only recently.

Effectiveness of cable barriers, guardrails, and concrete barrier walls in reducing the risk of injury

Roadway departure crashes tend to be severe, especially when the roadside exposes the occupants of errant vehicles to excessive injury hazards. As a cost-effective method when the clear zone width is insufficient, road barriers are often installed to prevent errant vehicles from colliding with dangerous obstacles or traversing steep slopes. This paper focuses on the safety performance of road barriers in Indiana in reducing the risk of injury. The objective of the study presented here is to compare the risk of injury among different hazardous events faced by an occupant in a single-vehicle crash. The studied hazardous events include rolling over, striking three types of barriers (guardrails, concrete barrier walls, and cable barriers) with different barrier offsets to the edge of the travelled way, and striking various roadside objects. A total of 2124 single-vehicle crashes (3257 occupants) that occurred between 2008 and 2012 on 517 pair-matched homogeneous barrier and non-barrier segments were analyzed. A binary logistic regression model with mixed effects was estimated for vehicle occupants. The segment pairing process and the use of random effects were able to handle the commonality within the same segment pair as well as the heterogeneity across segment pairs. The modeling results revealed that hitting a barrier is associated with lower risk of injury than a high-hazard event (hitting a pole, rollover, etc.). The odds of injury are reduced by 39% for median concrete barrier walls offset 15-18ft from the travelled way, reduced by 65% for a guardrail face offset 5-55ft, reduced by 85% for near-side median cable barriers (offset between 10ft and 29ft), and reduced by 78% with far-side median cable barriers (offset at least 30ft). Comparing different types of barriers is useful where some types of barriers can be used alternatively. This study found that the odds of injury are 43% lower when striking a guardrail instead of a median concrete barrier offset 15-18ft and 65% lower when striking a median concrete barrier offset 7-14ft. The odds of injury when striking a near-side median cable barrier is 57% lower than the odds for a guardrail face. This reduction for a far side median cable barrier is 37%. Thus, a guardrail should be preferred over a concrete wall and a cable barrier should be preferred over a guardrail where the road and traffic conditions allow. In the light of the results, installing median cable barriers on both sides of the median to reduce their lateral offset is beneficial for safety. The study also found that the unexplained heterogeneity across vehicles is much larger than it was across matched segment pairs.

Panel forecasts of country-level Covid-19 infections

We use a dynamic panel data model to generate density forecasts for daily active Covid-19 infections for a panel of countries/regions. Our specification that assumes the growth rate of active infections can be represented by autoregressive fluctuations around a downward sloping deterministic trend function with a break. Our fully Bayesian approach allows us to flexibly estimate the cross-sectional distribution of slopes and then implicitly use this distribution as prior to construct Bayes forecasts for the individual time series. We find some evidence that information from locations with an early outbreak can sharpen forecast accuracy for late locations. There is generally a lot of uncertainty about the evolution of active infection, due to parameter and shock uncertainty, in particular before and around the peak of the infection path. Over a one-week horizon, the empirical coverage frequency of our interval forecasts is close to the nominal credible level. Weekly forecasts from our model are published at https://laurayuliu.com/covid19-panel-forecast/.

Regional variation in health care utilization in Sweden - the importance of demand-side factors

BACKGROUND

Differences in health care utilization across geographical areas are well documented within several countries. If the variation across areas cannot be explained by differences in medical need, it can be a sign of inefficiency or misallocation of public health care resources.

METHODS

In this observational, longitudinal panel study we use regional level data covering the 21 Swedish regions (county councils) over 13 years and a random effects model to assess to what degree regional variation in outpatient physician visits is explained by observed demand factors such as health, demography and socio-economic factors.

RESULTS

The results show that regional mortality, as a proxy for population health, and demography do not explain regional variation in visits to primary care physicians, but explain about 50% of regional variation in visits to outpatient specialists. Adjusting for socio-economic and basic supply-side factors explains 33% of the regional variation in primary physician visits, but adds nothing to explaining the variation in specialist visits.

CONCLUSION

50-67% of regional variation remains unexplained by a large number of observable regional characteristics, indicating that omitted and possibly unobserved factors contribute substantially to the regional variation. We conclude that variations in health care utilization across regions is not very well explained by underlying medical need and demand, measured by mortality, demographic and socio-economic factors.

Sample size calculation in multi-centre clinical trials

Background

Multi-centre randomized controlled clinical trials play an important role in modern evidence-based medicine. Advantages of collecting data from more than one site are numerous, including accelerated recruitment and increased generalisability of results. Mixed models can be applied to account for potential clustering in the data, in particular when many small centres contribute patients to the study. Previously proposed methods on sample size calculation for mixed models only considered balanced treatment allocations which is an unlikely outcome in practice if block randomisation with reasonable choices of block length is used.

Methods

We propose a sample size determination procedure for multi-centre trials comparing two treatment groups for a continuous outcome, modelling centre differences using random effects and allowing for arbitrary sample sizes. It is assumed that block randomisation with fixed block length is used at each study site for subject allocation. Simulations are used to assess operation characteristics such as power of the sample size approach. The proposed method is illustrated by an example in disease management systems.

Results

A sample size formula as well as a lower and upper boundary for the required overall sample size are given. We demonstrate the superiority of the new sample size formula over the conventional approach of ignoring the multi-centre structure and show the influence of parameters such as block length or centre heterogeneity. The application of the procedure on the example data shows that large blocks require larger sample sizes, if centre heterogeneity is present.

Conclusion

Unbalanced treatment allocation can result in substantial power loss when centre heterogeneity is present but not considered at the planning stage. When only few patients by centre will be recruited, one has to weigh the risk of imbalance between treatment groups due to large blocks and the risk of unblinding due to small blocks. The proposed approach should be considered when planning multi-centre trials.

Electronic supplementary material

The online version of this article (10.1186/s12874-018-0602-y) contains supplementary material, which is available to authorized users.

Multiple moderator meta-analysis using the R-package Meta-CART

In meta-analysis, heterogeneity often exists between studies. Knowledge about study features (i.e., moderators) that can explain the heterogeneity in effect sizes can be useful for researchers to assess the effectiveness of existing interventions and design new potentially effective interventions. When there are multiple moderators, they may amplify or attenuate each other's effect on treatment effectiveness. However, in most meta-analysis studies, interaction effects are neglected due to the lack of appropriate methods. The method meta-CART was recently proposed to identify interactions between multiple moderators. The analysis result is a tree model in which the studies are partitioned into more homogeneous subgroups by combinations of moderators. This paper describes the R-package metacart, which provides user-friendly functions to conduct meta-CART analyses in R. This package can fit both fixed- and random-effects meta-CART, and can handle dichotomous, categorical, ordinal and continuous moderators. In addition, a new look ahead procedure is presented. The application of the package is illustrated step-by-step using diverse examples.

A single-level random-effects cross-lagged panel model for longitudinal mediation analysis

Cross-lagged panel models (CLPMs) are widely used to test mediation with longitudinal panel data. One major limitation of the CLPMs is that the model effects are assumed to be fixed across individuals. This assumption is likely to be violated (i.e., the model effects are random across individuals) in practice. When this happens, the CLPMs can potentially yield biased parameter estimates and misleading statistical inferences. This article proposes a model named a random-effects cross-lagged panel model (RE-CLPM) to account for random effects in CLPMs. Simulation studies show that the RE-CLPM outperforms the CLPM in recovering the mean indirect and direct effects in a longitudinal mediation analysis when random effects exist in the population. The performance of the RE-CLPM is robust to a certain degree, even when the random effects are not normally distributed. In addition, the RE-CLPM does not produce harmful results when the model effects are in fact fixed in the population. Implications of the simulation studies and potential directions for future research are discussed.

Modelling and estimation of nonlinear quantile regression with clustered data

In regression applications, the presence of nonlinearity and correlation among observations offer computational challenges not only in traditional settings such as least squares regression, but also (and especially) when the objective function is nonsmooth as in the case of quantile regression. Methods are developed for the modelling and estimation of nonlinear conditional quantile functions when data are clustered within two-level nested designs. The proposed estimation algorithm is a blend of a smoothing algorithm for quantile regression and a second order Laplacian approximation for nonlinear mixed models. This optimization approach has the appealing advantage of reducing the original nonsmooth problem to an approximated L 2 problem. While the estimation algorithm is iterative, the objective function to be optimized has a simple analytic form. The proposed methods are assessed through a simulation study and two applications, one in pharmacokinetics and one related to growth curve modelling in agriculture.

Economic development and road traffic injuries and fatalities in Thailand: an application of spatial panel data analysis, 2012-2016

Background

Road traffic injuries (RTIs) have been one of the most critical public health problems in Thailand for decades. The objective of this study was to examine to what extent provincial economy was associated with RTIs, road traffic deaths and case fatality rate in Thailand.

Methods

A secondary data analysis on time-series data was applied. The unit of analysis was a panel of 77 provinces during 2012–2016. Data were obtained from relevant public authorities, including the Ministry of Public Health. Descriptive statistics and econometric models, using negative binomial (NB) regression, negative binomial regression with random-effects (RE) model, and spatial Durbin model (SDM) were employed. The main predictor variable was gross domestic product (GDP) per capita and the outcome variables were incidence proportion of RTIs, traffic deaths and case fatality rate. The analysis was adjusted for key covariates.

Results

The incidence proportion of RTIs rose from 449.0 to 524.9 cases per 100,000 population from 2012 till 2016, whereas the incidence of traffic fatalities fluctuated between 29.7 and 33.2 deaths per 100,000 population. Case fatality rate steadily stood at 0.06–0.07 deaths per victim. RTIs and traffic deaths appeared to be positively correlated with provincial economy in the NB regression and the RE model. In the SDM, a log-Baht increase in GDP per capita (equivalent to a growth of GDP per capita by about 2.7 times) enlarged the incidence proportion of injuries and deaths by about a quarter (23.8–30.7%) with statistical significance. No statistical significance was found in case fatality rate by the SDM. The SDM also presented the best model fitness relative to other models.

Conclusion

The incidence proportion of traffic injuries and deaths appeared to rise alongside provincial prosperity. This means that RTIs-preventive measures should be more intensified in economically well-off areas. Furthermore, entrepreneurs and business sectors that gain economic benefit in a particular province should share responsibility in RTIs prevention in the area where their businesses are running. Further studies that explore others determinants of road safety, such as patterns of vehicles used, attitudes and knowledge of motorists, investment in safety measures, and compliance with traffic laws, are recommended.