Mixed effects logistic regression models for longitudinal ordinal functional response data with multiple-cause drop-out from the longitudinal study of aging

A Markov random field model with cumulative logistic functions for spatially dependent ordinal data

This paper presents a class of regression models with cumulative logistic functions that are chiefly designed to analyse spatially dependent ordinal data. In contrast to previous works, the proposed model requires neither the sites to be regularly spaced nor the assumption of an underlying continuous variable. It belongs to a more general class of Markov random field models, and can be considered an extension of the ordinal regression model with the proportional odds link function. Our proposed model allows practitioners to interpret the model parameters using odds ratios. Apart from the theoretical developments, this work also highlights the practical aspects of model fitting, including parameterisation, selection of neighbourhood, and calculation of standard errors. Simulation studies with regularly and irregularly spaced sites were conducted. Modelling strategies including pseudo-likelihood methods were found to be useful in both settings. The proposed model and the non-spatial counterpart were applied to the daily air quality index measured in the United Kingdom. The results indicate the presence of spatial effects and the incorporation of spatial effects led to better model performance in terms of various goodness-of-fit measures.

Chiggers (Acariformes: Trombiculoidea) do not increase rates of infection by Batrachochytrium dendrobatidis fungus in the endemic Dwarf Mexican Treefrog Tlalocohyla smithii (Anura: Hylidae)

Amphibian populations are globally declining at an alarming rate, and infectious diseases are among the main causes of their decline. Two micro-parasites, the fungus Batrachochytrium dendrobatidis (Bd) and the virus Ranavirus (RV) have caused mass mortality of amphibians and population declines. Other, less understood epizootics are caused by macro-parasites, such as Trombiculoidea chiggers. Infection with chiggers can affect frog behavior and survival. Furthermore, synergistic effects of co-infection with both macro and micro-parasites may lead to higher morbidity. To better understand these potential synergies, we investigated the presence and co-infection by chiggers, Bd and RV in the endemic frog Tlalocohyla smithii (T. smithii). Co-infection of Bd, RV, and/or chiggers is expected in habitats that are suitable for their co-occurrence; and if infection with one parasite facilitates infection with the others. On the other hand, co-infection could decrease if these parasites were to differ in their micro-environmental requirements (i.e. niche apportionment). A total of 116 frogs of T. smithii were studied during 2014 and 2016 in three streams within the Chamela-Cuixmala Biosphere Reserve in Jalisco, Mexico. Our results show that 31% of the frogs were infected with Trombiculoidea chiggers (Hannemania sp. and Eutrombicula alfreddugesi); Hannemania prevalence increased with air temperature and decreased in sites with high canopies and with water pH values above 8.5 and below 6.7. Bd prevalence was 2.6%, RV prevalence was 0%, and none of the frogs infected with chiggers were co-infected with Bd. Together, this study suggests that chiggers do not facilitate infection with Bd, as these are apportioned in different micro-habitats. Nevertheless, the statistical power to assure this is low. We recommend further epidemiological monitoring of multiple parasites in different geographical locations in order to provide insight on the true hazards, risks and conservation options for amphibian populations.

Global Case-Fatality Rates in Pediatric Severe Sepsis and Septic Shock: A Systematic Review and Meta-analysis

IMPORTANCE

The global patterns and distribution of case-fatality rates (CFRs) in pediatric severe sepsis and septic shock remain poorly described.

OBJECTIVE

We performed a systematic review and meta-analysis of studies of children with severe sepsis and septic shock to elucidate the patterns of CFRs in developing and developed countries over time. We also described factors associated with CFRs.

DATA SOURCES

We searched PubMed, Web of Science, Excerpta Medica database, Cumulative Index of Nursing and Allied Health Literature (CINAHL), and Cochrane Central systematically for randomized clinical trials and prospective observational studies from earliest publication until January 2017, using the keywords "pediatric," "sepsis," "septic shock," and "mortality."

STUDY SELECTION

Studies involving children with severe sepsis and septic shock that reported CFRs were included. Retrospective studies and studies including only neonates were excluded.

DATA EXTRACTION AND SYNTHESIS

We conducted our systematic review and meta-analysis in close accordance to Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. Pooled case-fatality estimates were obtained using random-effects meta-analysis. The associations of study period, study design, sepsis severity, age, and continents in which studies occurred were assessed with meta-regression.

MAIN OUTCOMES AND MEASURES

Meta-analyses to provide pooled estimates of CFR of pediatric severe sepsis and septic shock over time.

RESULTS

Ninety-four studies that included 7561 patients were included. Pooled CFRs were higher in developing countries (31.7% [95% CI, 27.3%-36.4%]) than in developed countries (19.3% [95% CI, 16.4%-22.7%]; P < .001). Meta-analysis of CFRs also showed significant heterogeneity across studies. Continents that include mainly developing countries reported higher CFRs (adjusted odds ratios: Africa, 7.89 [95% CI, 6.02-10.32]; P < .001; Asia, 3.81 [95% CI, 3.60-4.03]; P < .001; South America, 2.91 [95% CI, 2.71-3.12]; P < .001) than North America. Septic shock was associated with higher CFRs than severe sepsis (adjusted odds ratios, 1.47 [95% CI, 1.41-1.54]). Younger age was also a risk factor (adjusted odds ratio, 0.95 [95% CI, 0.94-0.96] per year of increase in age). Earlier study eras were associated with higher CFRs (adjusted odds ratios for 1991-2000, 1.24 [95% CI, 1.13-1.37]; P < .001) compared with 2011 to 2016. Time-trend analysis showed higher CFRs over time in developing countries than developed countries.

CONCLUSIONS AND RELEVANCE

Despite the declining trend of pediatric severe sepsis and septic shock CFRs, the disparity between developing and developed countries persists. Further characterizations of vulnerable populations and collaborations between developed and developing countries are warranted to reduce the burden of pediatric sepsis globally.

Survival models and health sequences

Survival studies often generate not only a survival time for each patient but also a sequence of health measurements at annual or semi-annual check-ups while the patient remains alive. Such a sequence of random length accompanied by a survival time is called a survival process. Robust health is ordinarily associated with longer survival, so the two parts of a survival process cannot be assumed independent. This paper is concerned with a general technique-reverse alignment-for constructing statistical models for survival processes, here termed revival models. A revival model is a regression model in the sense that it incorporates covariate and treatment effects into both the distribution of survival times and the joint distribution of health outcomes. The revival model also determines a conditional survival distribution given the observed history, which describes how the subsequent survival distribution is determined by the observed progression of health outcomes.

A Fast EM Algorithm for Fitting Joint Models of a Binary Response and Multiple Longitudinal Covariates Subject to Detection Limits

Joint modeling techniques have become a popular strategy for studying the association between a response and one or more longitudinal covariates. Motivated by the GenIMS study, where it is of interest to model the event of survival using censored longitudinal biomarkers, a joint model is proposed for describing the relationship between a binary outcome and multiple longitudinal covariates subject to detection limits. A fast, approximate EM algorithm is developed that reduces the dimension of integration in the E-step of the algorithm to one, regardless of the number of random effects in the joint model. Numerical studies demonstrate that the proposed approximate EM algorithm leads to satisfactory parameter and variance estimates in situations with and without censoring on the longitudinal covariates. The approximate EM algorithm is applied to analyze the GenIMS data set.

A random pattern mixture model for ordinal outcomes with informative dropouts

We extend a random pattern mixture joint model for longitudinal ordinal outcomes and informative dropouts. The patients are generalized to 'pattern' groups based on known covariates that are potentially surrogated for the severity of the underlying condition. The random pattern effects are defined as the latent effects linking the dropout process and the ordinal longitudinal outcome. Conditional on the random pattern effects, the longitudinal outcome and the dropout times are assumed independent. Estimates are obtained via the Expectation-maximization algorithm. We applied the model to the end-stage renal disease data. Anemia was found to be significantly affected by the baseline iron treatment when the dropout information was adjusted via the study model; as opposed to an independent or shared parameter model. Simulations were performed to evaluate the performance of the random pattern mixture model under various assumptions.

A Bayesian Shrinkage Model for Incomplete Longitudinal Binary Data with Application to the Breast Cancer Prevention Trial

We consider inference in randomized longitudinal studies with missing data that is generated by skipped clinic visits and loss to follow-up. In this setting, it is well known that full data estimands are not identified unless unverified assumptions are imposed. We assume a non-future dependence model for the drop-out mechanism and partial ignorability for the intermittent missingness. We posit an exponential tilt model that links non-identifiable distributions and distributions identified under partial ignorability. This exponential tilt model is indexed by non-identified parameters, which are assumed to have an informative prior distribution, elicited from subject-matter experts. Under this model, full data estimands are shown to be expressed as functionals of the distribution of the observed data. To avoid the curse of dimensionality, we model the distribution of the observed data using a Bayesian shrinkage model. In a simulation study, we compare our approach to a fully parametric and a fully saturated model for the distribution of the observed data. Our methodology is motivated by, and applied to, data from the Breast Cancer Prevention Trial.

A semiparametric joint model for longitudinal and survival data with application to hemodialysis study

In many longitudinal clinical studies, the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject's susceptibility to progression of the disease. It is of scientific and clinical interest to relate such quantities to a later time-to-event clinical endpoint such as patient survival. This is usually done with a shared parameter model. In such models, the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject-level severity or susceptibility (also called frailty in statistical terms). In this article, we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed-effect model, and the conditional distribution of the survival data is given by a Cox proportional hazard model. We allow unknown regression coefficients and time-dependent covariates in both models. The proposed estimators are maximizers of an exact correction to the joint log likelihood with the frailties eliminated as nuisance parameters, an idea that originated from correction of covariate measurement error in measurement error models. The corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators. Unlike most published methods for joint modeling, the proposed estimation procedure does not rely on distributional assumptions of the frailties. The proposed method was studied in simulations and applied to a data set from the Hemodialysis Study.

Effects of ignoring baseline on modeling transitions from intact cognition to dementia

This paper evaluates the effect of ignoring baseline when modeling transitions from intact cognition to dementia with mild cognitive impairment (MCI) and global impairment (GI) as intervening cognitive states. Transitions among states are modeled by a discrete-time Markov chain having three transient (intact cognition, MCI, and GI) and two competing absorbing states (death and dementia). Transition probabilities depend on two covariates, age and the presence/absence of an apolipoprotein E-epsilon4 allele, through a multinomial logistic model with shared random effects. Results are illustrated with an application to the Nun Study, a cohort of 678 participants 75+ years of age at baseline and followed longitudinally with up to ten cognitive assessments per nun.

Shared random effects analysis of multi-state Markov models: application to a longitudinal study of transitions to dementia

Multi-state models are appealing tools for analysing data about the progression of a disease over time. In this paper, we consider a multi-state Markov chain with two competing absorbing states: dementia and death and three transient non-demented states: cognitively normal, amnestic mild cognitive impairment (amnestic MCI), and non-amnestic mild cognitive impairment (non-amnestic MCI). The likelihood function for the data is derived and estimates for the effects of the covariates on transitions are determined when the process can be viewed as a polytomous logistic regression model with shared random effects. The presence of a shared random effect not only complicates the formulation of the likelihood but also its evaluation and maximization. Three approaches for maximizing the likelihood are compared using a simulation study; the first method is based on the Gauss-quadrature technique, the second method is based on importance sampling ideas, and the third method is based on an expansion by Taylor series. The best approach is illustrated using a longitudinal study on a cohort of cognitively normal subjects, followed annually for conversion to mild cognitive impairment (MCI) and/or dementia, conducted at the Sanders Brown Center on Aging at the University of Kentucky.

A mixed-effects model for cognitive decline with non-monotone non-response from a two-phase longitudinal study of dementia

Most longitudinal studies of elderly are characterized by substantial drop-out due to death and many other factors beyond the control of the investigators. In a two-phase longitudinal study of dementia, subjects with cognitive impairment skip the first phase survey in the next follow-up, leading to intermittent missing variables measured in that phase. In the context of analysing pre-dementia cognitive decline in an elderly population, both of the two causes of non-response can potentially be informative in the sense that the missingness is dependent on the unobserved outcome. To take these factors into account, mixed-effects models are constructed to allow the outcome and the multiple causes of missing values to share the same 'random parameter' or random effect. The crucial assumption of our model is that the random effects of the model for the outcome and that of the model for the missing-data indicators are linked in a deterministic manner. It can be thought of as an approximation of a more general and realistic situation, in which the two models have distinct, yet dependent, random effects. We conduct a simulation study to investigate possible deviations of the estimates under such a scenario. A second simulation illustrates the magnitude of the bias in estimating the difference of decline rate between two groups when the random effects are linked in different manners for the two groups.

A simple imputation method for longitudinal studies with non-ignorable non-responses

Missing data are a common problem in longitudinal studies in the health sciences. Motivated by data from the Muscatine Coronary Risk Factor (MCRF) study, a longitudinal study of obesity, we propose a simple imputation method for handling non-ignorable non-responses (i.e., when non-response is related to the specific values that should have been obtained) in longitudinal studies with either discrete or continuous outcomes. In the proposed approach, two regression models are specified; one for the marginal mean of the response, the other for the conditional mean of the response given non-response patterns. Statistical inference for the model parameters is based on the generalized estimating equations (GEE) approach. An appealing feature of the proposed method is that it can be readily implemented using existing, widely-available statistical software. The method is illustrated using longitudinal data on obesity from the MCRF study.

Prevention of missing data in clinical research studies

Missing data is a problem that is ubiquitous to all clinical studies and a source of multiple problems from an analytic point of view (reduced statistical power, increased the type I error, bias) Statistical approaches have been developed to analyze data collected from trials with missing data. Understanding and implementing the appropriate statistical technique is essential but should be differentiated from preventive approaches that are designed to reduce rates of missing data In this article, we draw attention to these preventive efforts. Seven steps to minimizing the amount of missing data are defined as documentation, training, monitoring reports, patient contact, data entry and management, pilot studies, and communication. Although the implementation of these approaches is time consuming and costly, the overall quality of the study is increased. Despite efforts devoted to areas, no study is without missing data. Once the study is completed, it is essential to assess the pattern of missing data and apply the appropriate statistical analysis.

A multistate Markov chain model for longitudinal, categorical quality-of-life data subject to non-ignorable missingness

Quality-of-life (QOL) is an important outcome in clinical research, particularly in cancer clinical trials. Typically, data are collected longitudinally from patients during treatment and subsequent follow-up. Missing data are a common problem, and missingness may arise in a non-ignorable fashion. In particular, the probability that a patient misses an assessment may depend on the patient's QOL at the time of the scheduled assessment. We propose a Markov chain model for the analysis of categorical outcomes derived from QOL measures. Our model assumes that transitions between QOL states depend on covariates through generalized logit models or proportional odds models. To account for non-ignorable missingness, we incorporate logistic regression models for the conditional probabilities of observing measurements, given their actual values. The model can accommodate time-dependent covariates. Estimation is by maximum likelihood, summing over all possible values of the missing measurements. We describe options for selecting parsimonious models, and we study the finite-sample properties of the estimators by simulation. We apply the techniques to data from a breast cancer clinical trial in which QOL assessments were made longitudinally, and in which missing data frequently arose.

Mixed effects logistic regression models for multiple longitudinal binary functional limitation responses with informative drop-out and confounding by baseline outcomes

In the context of analyzing multiple functional limitation responses collected longitudinally from the Longitudinal Study of Aging (LSOA), we investigate the heterogeneity of these outcomes with respect to their associations with previous functional status and other risk factors in the presence of informative drop-out and confounding by baseline outcomes. We accommodate the longitudinal nature of the multiple outcomes with a unique extension of the nested random effects logistic model with an autoregressive structure to include drop-out and baseline outcome components with shared random effects. Estimation of fixed effects and variance components is by maximum likelihood with numerical integration. This shared parameter selection model assumes that drop-out is conditionally independent of the multiple functional limitation outcomes given the underlying random effect representing an individual's trajectory of functional status across time. Whereas it is not possible to fully assess the adequacy of this assumption, we assess the robustness of this approach by varying the assumptions underlying the proposed model such as the random effects structure, the drop-out component, and omission of baseline functional outcomes as dependent variables in the model. Heterogeneity among the associations between each functional limitation outcome and a set of risk factors for functional limitation, such as previous functional limitation and physical activity, exists for the LSOA data of interest. Less heterogeneity is observed among the estimates of time-level random effects variance components that are allowed to vary across functional outcomes and time. We also note that. under an autoregressive structure, bias results from omitting the baseline outcome component linked to the follow-up outcome component by subject-level random effects.