Change point models for cognitive tests using semi-parametric maximum likelihood

nlive: an R package to facilitate the application of the sigmoidal and random changepoint mixed models

BACKGROUND

The use of mixed effect models with a specific functional form such as the Sigmoidal Mixed Model and the Piecewise Mixed Model (or Changepoint Mixed Model) with abrupt or smooth random change allows the interpretation of the defined parameters to understand longitudinal trajectories. Currently, there are no interface R packages that can easily fit the Sigmoidal Mixed Model allowing the inclusion of covariates or incorporating recent developments to fit the Piecewise Mixed Model with random change.

RESULTS

To facilitate the modeling of the Sigmoidal Mixed Model, and Piecewise Mixed Model with abrupt or smooth random change, we have created an R package called nlive. All needed pieces such as functions, covariance matrices, and initials generation were programmed. The package was implemented with recent developments such as the polynomial smooth transition of the piecewise mixed model with improved properties over Bacon-Watts, and the stochastic approximation expectation-maximization (SAEM) for efficient estimation. It was designed to help interpretation of the output by providing features such as annotated output, warnings, and graphs. Functionality, including time and convergence, was tested using simulations. We provided a data example to illustrate the package use and output features and interpretation. The package implemented in the R software is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=nlive .

CONCLUSIONS

The nlive package for R fits the Sigmoidal Mixed Model and the Piecewise Mixed: abrupt and smooth. The nlive allows fitting these models with only five mandatory arguments that are intuitive enough to the less sophisticated users.

Climatological and Epidemiological Conditions Are Important Factors Related to the Abundance of bla KPC and Other Antibiotic Resistance Genes (ARGs) in Wastewater Treatment Plants and Their Effluents, in an Endemic Country

Several physicochemical and season factors have been related to the abundance of antibiotic resistance genes (ARGs) in wastewater treatment plants (WWTPs), considered hotspots of bacterial resistance. However, few studies on the subject have been carried out in tropical countries endemic for resistance mechanisms such as bla_KPC. In this study, the occurrence of ARGs, particularly bla_KPC, was determined throughout a WWTP, and the factors related to their abundance were explored. In 2017, wastewater samples were taken from a WWTP in Colombia every 15 days for 6 months, and a total of 44 samples were analyzed by quantitative real-time PCR. sul1, sul2, bla_KPC, and ermB were found to be the most prevalent ARGs. A low average reduction of the absolute abundance ARGs in effluent with respect to influent was observed, as well as a greater absolute abundance of ARGs in the WWTP effluent in the rainy season. Factors such as temperature, pH, oxygen, total organic carbon (TOC), chemical oxygen demand (COD), and precipitation were significantly correlated with the absolute abundance of several of the ARGs evaluated. A generalized linear mixed-effects model analysis showed that dissolved oxygen and precipitation in the sampling day were important factors related to the absolute concentration of bla_KPC over time. In conclusion, the abundance of ARGs in the WWTP could be influenced by endemic conditions and physicochemical and climatological parameters. Therefore, it is necessary to continuously monitor clinical relevant genes in WWTPs from different global regions, even more so in low-income countries where sewage treatment is limited.

Stochastic Functional Estimates in Longitudinal Models with Interval-Censored Anchoring Events

Timelines of longitudinal studies are often anchored by specific events. In the absence of fully observed the anchoring event times, the study timeline becomes undefined, and the traditional longitudinal analysis loses its temporal reference. In this paper, we considered an analytical situation where the anchoring events are interval-censored. We demonstrated that by expressing the regression parameter estimators as stochastic functionals of a plug-in estimate of the unknown anchoring event time distribution, the standard longitudinal models could be extended to accommodate the situation of less well-defined timelines. We showed that for a broad class of longitudinal models, the functional parameter estimates are consistent and asymptotically normally distributed with an convergence rate under mild regularity conditions. Applying the developed theory to linear mixed-effects models, we further proposed a hybrid computational procedure that combines the strengths of the Fisher's scoring method and the expectation-expectation (EM) algorithm, for model parameter estimation. We conducted a simulation study to validate the asymptotic properties and to assess the finite sample performance of the proposed method. A real data analysis was used to illustrate the proposed method. The method fills in a gap in the existing longitudinal analysis methodology for data with less well defined timelines.

A viewpoint on change point modeling for cognitive aging research: Moving from description to intervention and practice

Chronological age is a commonly-used time metric, but there may be more relevant time measures in older adulthood. This paper reviews change point modeling, a type of analysis increasingly common in cognitive aging research but with limited application in applied research. Here, we propose a new application of such models for cognitive training studies. Change point models have the potential to assess intervention outcomes such as compression of morbidity or reduced decline after an event (e.g., reduced cognitive decline after a dementia diagnosis) as well as changes in outcome trajectories across different intervention dosages (e.g., initial vs. booster training). Through change point modeling, we can better understand how interventions impact cognitive aging trajectories.

Bayesian change-point modelling of the effects of 3-points-for-a-win rule in football

We examine the effects of the 3-points-for-a-win (3pfaw) rule in the football world. Data that form the basis of our analyses come from seven leagues around the world (Albania, Brazil, England, Germany, Poland, Romania, and Scotland) and consist of mean goals and proportions of decided matches over a period of about six years before- and about seven years after the introduction of the rule in the respective leagues. Bayesian change-point analyses and Shiryaev-Roberts tests show that the rule had no effects on the mean goals but, indeed, had increasing effects on the proportions of decided matches in most of the leagues studied. This, in turn, implies that while the rule has given teams the incentive to aim at winning matches, such aim was not achieved by scoring excess goals. Instead, it was achieved by scoring enough goals in order to win and, at the same time, defending enough in order not to lose. Our results are in accordance with recent findings on comparing the values of attack and defense - that, in top-level football, not conceding a goal is more valuable than scoring a single goal.

A curvilinear bivariate random changepoint model to assess temporal order of markers

In biomedical research, various longitudinal markers measuring different quantities are often collected over time. For example, repeated measures of psychometric scores are very informative about the degradation process toward dementia. These trajectories are generally nonlinear with an acceleration of the decline a few years before the diagnosis and a large heterogeneity between psychometric tests depending on the underlying cognitive function to be evaluated and the metrological properties of the test. Comparing the times of acceleration of the decline before diagnosis between cognitive tests is useful to better understand the natural history of the disease. Our objective is to propose a bivariate random changepoint model that allows for the comparison of the mean time of change between two markers. A frequentist approach is proposed that gives validated statistical tests to assess the temporal order of the changepoints. Using a spline transformation function, the model is designed to handle non-Gaussian data, that are common for cognitive scores which frequently exhibit a strong ceiling effect. The procedure is assessed through a simulation study and applied to a French cohort of elderly to identify the order of the decline of several cognitive scores. The whole methodology has been implemented in a R package freely available.

A Three-Factor Structure of Cognitive Functioning Among Unimpaired Carriers and Non-Carriers of Autosomal-Dominant Alzheimer's Disease

BACKGROUND

There is a need to find cognitive markers that can help identify individuals at risk for Alzheimer's disease (AD), and that can be used to reliably measure cognitive decline.

OBJECTIVE

We tested whether a theoretically driven three-factor structure would characterize cognitive functioning in individuals who are genetically-determined to develop AD due to a mutation in Presenilin-1 (PSEN1) gene. We also examined whether these factors could distinguish cognitively unimpaired PSEN1 mutation carriers from age-matched non-carrier family members.

METHODS

1,395 cognitively unimpaired members of a Colombian kindred with the PSEN1 E280A mutation were included in the study. A confirmatory factor analysis examined the fit of the three-factor model comprising episodic memory (MMSE memory recall, CERAD-COL Word list recall, and Constructional praxis recall), executive function (Phonemic fluency and WCST perseverative errors), and psychomotor processing speed (TMT-A and WAIS-III Digit Symbol).

RESULTS

The three-factor model provided an excellent fit for all participants (p = 0.24; RMSEA = 0.01). Further, the episodic memory (p = 0.0004, d = 0.25) and executive functioning (p = 0.001, d = 0.18) factors distinguished cognitively unimpaired carriers from non-carriers. The episodic memory factor provided the earliest indication of preclinical cognitive decline at 35 years of age, nine years before individuals' estimated age of clinical onset.

CONCLUSIONS

The three theoretically derived cognitive factors provide a reliable measure of cognition and may be useful for the early detection of AD, as well as for measuring disease progression. However, longitudinal studies are needed to confirm that these factors can be used to track the progression of cognitive decline in preclinical AD.

A hypothesis testing procedure for random changepoint mixed models

In biomedical research, random changepoint mixed models are used to take into account an individual breakpoint in a biomarker trajectory. This may be observed in the cognitive decline measured by psychometric tests in the prediagnosis phase of Alzheimer's disease. The existence, intensity and duration of this accelerated decline can depend on individual characteristics. The main objective of our work is to propose inferential methods to assess the existence of this phase of accelerated decline, ie, the existence of a random changepoint. To do so, we use a mixed model with two linear phases and test the nullity of the parameter measuring the difference of slopes between the two phases. Because we face the issue of nuisance parameters being unidentifiable under the null hypothesis, the supremum of the classic score test statistic on these parameters is used. The asymptotic distribution of the supremum under the null is approached with a perturbation method based on the multiplier bootstrap. The performance of our testing procedure is assessed via simulations and the test is applied to the French cohort PAQUID of elderly subjects to study the shape of the prediagnosis decline according to educational level. The test is significant for both educational levels and the estimated trajectories confirmed that educational level is a good marker for cognitive reserve.

When does cognitive decline begin? A systematic review of change point studies on accelerated decline in cognitive and neurological outcomes preceding mild cognitive impairment, dementia, and death

Older adults who ultimately develop dementia experience accelerated cognitive decline long before diagnosis. A similar acceleration in cognitive decline occurs in the years before death as well. To evaluate preclinical and terminal cognitive decline, past researchers have incorporated change points in their analyses of longitudinal data, identifying point estimates of how many years prior to diagnosis or death that decline begins to accelerate. The current systematic review aimed to summarize the published literature on preclinical and terminal change points in relation to mild cognitive impairment (MCI), dementia, and death, identifying the order in which cognitive and neurological outcomes decline and factors that modify the onset and rate of decline. A systematic search protocol yielded 35 studies, describing 16 longitudinal cohorts, modeling change points for cognitive and neurological outcomes preceding MCI, dementia, or death. Change points for cognitive abilities ranged from 3-7 years prior to MCI diagnosis, 1-11 years prior to dementia diagnosis, and 3-15 years before death. No sequence of decline was observed preceding MCI or death, but the following sequence was tentatively accepted for Alzheimer's disease: verbal memory, visuospatial ability, executive functions and fluency, and last, verbal IQ. Some of the modifiers of the onset and rate of decline examined by previous researchers included gender, education, genetics, neuropathology, and personality. Change point analyses evidence accelerated decline preceding MCI, dementia, and death, but moderators of the onset and rate of decline remain ambiguous due to between-study modeling differences, and coordinated analyses may improve comparability across future studies. (PsycINFO Database Record

Distribution-free estimation of local growth rates around interval censored anchoring events

Biological processes are usually defined on timelines that are anchored by specific events. For example, cancer growth is typically measured by the change in tumor size from the time of oncogenesis. In the absence of such anchoring events, longitudinal assessments of the outcome lose their temporal reference. In this paper, we considered the estimation of local change rates in the outcomes when the anchoring events are interval-censored. Viewing the subject-specific anchoring event times as random variables from an unspecified distribution, we proposed a distribution-free estimation method for the local growth rates around the unobserved anchoring events. We expressed the rate parameters as stochastic functionals of the anchoring time distribution and showed that under mild regularity conditions, consistent and asymptotically normal estimates of the rate parameters could be achieved, with a n convergence rate. We conducted a carefully designed simulation study to evaluate the finite sample performance of the method. To motivate and illustrate the use of the proposed method, we estimated the skeletal growth rates of male and female adolescents, before and after the unobserved pubertal growth spurt (PGS) times.

Presymptomatic atrophy in autosomal dominant Alzheimer's disease: A serial magnetic resonance imaging study

INTRODUCTION

Identifying at what point atrophy rates first change in Alzheimer's disease is important for informing design of presymptomatic trials.

METHODS

Serial T1-weighted magnetic resonance imaging scans of 94 participants (28 noncarriers, 66 carriers) from the Dominantly Inherited Alzheimer Network were used to measure brain, ventricular, and hippocampal atrophy rates. For each structure, nonlinear mixed-effects models estimated the change-points when atrophy rates deviate from normal and the rates of change before and after this point.

RESULTS

Atrophy increased after the change-point, which occurred 1-1.5 years (assuming a single step change in atrophy rate) or 3-8 years (assuming gradual acceleration of atrophy) before expected symptom onset. At expected symptom onset, estimated atrophy rates were at least 3.6 times than those before the change-point.

DISCUSSION

Atrophy rates are pathologically increased up to seven years before "expected onset". During this period, atrophy rates may be useful for inclusion and tracking of disease progression.

Cognitive Decline in a Colombian Kindred With Autosomal Dominant Alzheimer Disease: A Retrospective Cohort Study

IMPORTANCE

Data from an autosomal dominant Alzheimer disease (ADAD) kindred were used to track the longitudinal trajectory of cognitive decline associated with preclinical ADAD and explore factors that may modify the rate of cognitive decline.

OBJECTIVES

To evaluate the onset and rate of cognitive decline during preclinical ADAD and the effect of socioeconomic, vascular, and genetic factors on the cognitive decline.

DESIGN, SETTING, AND PARTICIPANTS

We performed a retrospective cohort study from January 1, 1995, through June 31, 2012, of individuals from Antioquia, Colombia, who tested positive for the ADAD-associated PSEN1 E280A mutation. Data analysis was performed from August 20, 2014, through November 30, 2015. A mixed-effects model was used to estimate annual rates of change in cognitive test scores and to mark the onset of cognitive decline.

MAIN OUTCOMES AND MEASURES

Memory, language, praxis, and total scores from the Consortium to Establish a Registry for Alzheimer Disease test battery. Chronologic age was used as a time scale in the models. We explore the effects of sex; educational level; socioeconomic status; residence area; occupation type; marital status; history of hypertension, diabetes mellitus, and dyslipidemia; tobacco and alcohol use; and APOE ε4 on the rates of cognitive decline.

RESULTS

A total of 493 carriers met the inclusion criteria and were analyzed. A total of 256 carriers had 2 or more assessments. At the time of the initial assessment, participants had a mean (SD) age of 33.4 (11.7) years and a mean (SD) educational level of 7.2 (4.2) years. They were predominantly female (270 [54.8%]), married (293 [59.4%]), and of low socioeconomic status (322 [65.3%]). Word list recall scores provided the earliest indicator of preclinical cognitive decline at 32 years of age, 12 and 17 years before the kindred's respective median ages at mild cognitive impairment and dementia onset. After the change point, carriers had a statistically significant cognitive decline with a loss of 0.24 (95% CI, -0.26 to -0.22) points per year for the word list recall test and 2.13 (95% CI, -2.29 to -1.96) points per year for total scores. Carriers with high educational levels had an increase of approximately 36% in the rate of cognitive decline after the change point when compared with those with low educational levels (-2.89 vs -2.13 points per year, respectively). Onset of cognitive decline was delayed by 3 years in individuals with higher educational levels compared with those with lower educational levels. Those with higher educational level, middle/high socioeconomic status, history of diabetes and hypertension, and tobacco and alcohol use had a steeper cognitive decline after onset.

CONCLUSIONS AND RELEVANCE

Preclinical cognitive decline was evident in PSEN1 E280A mutation carriers 12 years before the onset of clinical impairment. Educational level may be a protective factor against the onset of cognitive impairment.

Sample size and classification error for Bayesian change-point models with unlabelled sub-groups and incomplete follow-up

Many medical (and ecological) processes involve the change of shape, whereby one trajectory changes into another trajectory at a specific time point. There has been little investigation into the study design needed to investigate these models. We consider the class of fixed effect change-point models with an underlying shape comprised two joined linear segments, also known as broken-stick models. We extend this model to include two sub-groups with different trajectories at the change-point, a change and no change class, and also include a missingness model to account for individuals with incomplete follow-up. Through a simulation study, we consider the relationship of sample size to the estimates of the underlying shape, the existence of a change-point, and the classification-error of sub-group labels. We use a Bayesian framework to account for the missing labels, and the analysis of each simulation is performed using standard Markov chain Monte Carlo techniques. Our simulation study is inspired by cognitive decline as measured by the Mini-Mental State Examination, where our extended model is appropriate due to the commonly observed mixture of individuals within studies who do or do not exhibit accelerated decline. We find that even for studies of modest size (n = 500, with 50 individuals observed past the change-point) in the fixed effect setting, a change-point can be detected and reliably estimated across a range of observation-errors.

Longitudinal mixed-effects models for latent cognitive function

A mixed-effects regression model with a bent-cable change-point predictor is formulated to describe potential decline of cognitive function over time in the older population. For the individual trajectories, cognitive function is considered to be a latent variable measured through an item response theory model given longitudinal test data. Individual-specific parameters are defined for both cognitive function and the rate of change over time, using the change-point predictor for non-linear trends. Bayesian inference is used, where the Deviance Information Criterion and the L-criterion are investigated for model comparison. Special attention is given to the identifiability of the item response parameters. Item response theory makes it possible to use dichotomous and polytomous test items, and to take into account missing data and survey-design change during follow-up. This will be illustrated in an application where data stem from the Cambridge City over-75s Cohort Study.