The analysis of repeated-measures data on schizophrenic reaction times using mixture models

A Bayesian Mixture Modelling of Stop Signal Reaction Time Distributions: The Second Contextual Solution for the Problem of Aftereffects of Inhibition on SSRT Estimations

The distribution of single Stop Signal Reaction Times (SSRT) in the stop signal task (SST) has been modelled with two general methods: a nonparametric method by Hans Colonius (1990) and a Bayesian parametric method by Dora Matzke, Gordon Logan and colleagues (2013). These methods assume an equal impact of the preceding trial type (go/stop) in the SST trials on the SSRT distributional estimation without addressing the relaxed assumption. This study presents the required model by considering a two-state mixture model for the SSRT distribution. It then compares the Bayesian parametric single SSRT and mixture SSRT distributions in the usual stochastic order at the individual and the population level under ex-Gaussian (ExG) distributional format. It shows that compared to a single SSRT distribution, the mixture SSRT distribution is more varied, more positively skewed, more leptokurtic and larger in stochastic order. The size of the results' disparities also depends on the choice of weights in the mixture SSRT distribution. This study confirms that mixture SSRT indices as a constant or distribution are significantly larger than their single SSRT counterparts in the related order. This result offers a vital improvement in the SSRT estimations.

A conversation with Thomas (Tom) R. Belin- 2020 HPSS long-term excellence award winner

At the 2020 International Conference on Health Policy Statistics held in San Diego, Thomas (Tom) R. Belin was awarded the Long-Term Excellence Award from the Health Policy Statistics Section of the American Statistical Association. Dr. Belin was exceptionally and uniquely qualified for this award. Highlights include his innovative statistical applications for health care research and his substantial contributions to the statistics and health policy communities through mentoring and service. In this interview, we asked Tom to share stories about his upbringing, schooling, and career phases to gain insights into his numerous achievements.

A Bayesian Latent Class Model to Predict Kidney Obstruction in the Absence of Gold Standard

Kidney obstruction, if untreated in a timely manner, can lead to irreversible loss of renal function. A widely used technology for evaluations of kidneys with suspected obstruction is diuresis renography. However, it is generally very challenging for radiologists who typically interpret renography data in practice to build high level of competency due to the low volume of renography studies and insufficient training. Another challenge is that there is currently no gold standard for detection of kidney obstruction. Seeking to develop a computer-aided diagnostic (CAD) tool that can assist practicing radiologists to reduce errors in the interpretation of kidney obstruction, a recent study collected data from diuresis renography, interpretations on the renography data from highly experienced nuclear medicine experts as well as clinical data. To achieve the objective, we develop a statistical model that can be used as a CAD tool for assisting radiologists in kidney interpretation. We use a Bayesian latent class modeling approach for predicting kidney obstruction through the integrative analysis of time-series renogram data, expert ratings, and clinical variables. A nonparametric Bayesian latent factor regression approach is adopted for modeling renogram curves in which the coefficients of the basis functions are parameterized via the factor loadings dependent on the latent disease status and the extended latent factors that can also adjust for clinical variables. A hierarchical probit model is used for expert ratings, allowing for training with rating data from multiple experts while predicting with at most one expert, which makes the proposed model operable in practice. An efficient MCMC algorithm is developed to train the model and predict kidney obstruction with associated uncertainty. We demonstrate the superiority of the proposed method over several existing methods through extensive simulations. Analysis of the renal study also lends support to the usefulness of our model as a CAD tool to assist less experienced radiologists in the field.

Estimating mono- and bi-phasic regression parameters using a mixture piecewise linear Bayesian hierarchical model

The dynamics of tumor burden, secreted proteins or other biomarkers over time, is often used to evaluate the effectiveness of therapy and to predict outcomes for patients. Many methods have been proposed to investigate longitudinal trends to better characterize patients and to understand disease progression. However, most approaches assume a homogeneous patient population and a uniform response trajectory over time and across patients. Here, we present a mixture piecewise linear Bayesian hierarchical model, which takes into account both population heterogeneity and nonlinear relationships between biomarkers and time. Simulation results show that our method was able to classify subjects according to their patterns of treatment response with greater than 80% accuracy in the three scenarios tested. We then applied our model to a large randomized controlled phase III clinical trial of multiple myeloma patients. Analysis results suggest that the longitudinal tumor burden trajectories in multiple myeloma patients are heterogeneous and nonlinear, even among patients assigned to the same treatment cohort. In addition, between cohorts, there are distinct differences in terms of the regression parameters and the distributions among categories in the mixture. Those results imply that longitudinal data from clinical trials may harbor unobserved subgroups and nonlinear relationships; accounting for both may be important for analyzing longitudinal data.

Testing treatment effect in schizophrenia clinical trials with heavy patient dropout using latent class growth mixture models

By examining the outcome trajectories of the dropout patients with different reasons in the schizophrenia trials, we note that although patients are recruited from the same protocol that have compatible baseline characteristics, they may respond differently even to the same treatment. Some patients show consistent improvement while others only have temporary relief. This creates different patient subpopulations characterized by their response and dropout patterns. At the same time, those who continue to improve seem to be more likely to complete the study while those who only experience temporary relief have a higher chance to drop out. Such phenomenon appears to be quite general in schizophrenia clinical trials. This simultaneous inhomogeneity both in patient response as well as dropout patterns creates a scenario of missing not at random and therefore results in biases when we use the statistical methods based on the missing at random assumption to test treatment efficacy. In this paper, we propose to use the latent class growth mixture model, which is a special case of the latent mixture model, to conduct the statistical analyses in such situation. This model allows us to take the inhomogeneity among subpopulations into consideration to make more accurate inferences on the treatment effect at any visit time. Comparing with the conventional statistical methods such as mixed-effects model for repeated measures, we demonstrate through simulations that the proposed latent mixture model approach gives better control on the Type I error rate in testing treatment effect. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

Examining the Association between Patient-Reported Symptoms of Attention and Memory Dysfunction with Objective Cognitive Performance: A Latent Regression Rasch Model Approach

OBJECTIVE

Patient-reported cognition generally exhibits poor concordance with objectively assessed cognitive performance. In this article, we introduce latent regression Rasch modeling and provide a step-by-step tutorial for applying Rasch methods as an alternative to traditional correlation to better clarify the relationship of self-report and objective cognitive performance. An example analysis using these methods is also included.

METHOD

Introduction to latent regression Rasch modeling is provided together with a tutorial on implementing it using the JAGS programming language for the Bayesian posterior parameter estimates. In an example analysis, data from a longitudinal neurocognitive outcomes study of 132 breast cancer patients and 45 non-cancer matched controls that included self-report and objective performance measures pre- and post-treatment were analyzed using both conventional and latent regression Rasch model approaches.

RESULTS

Consistent with previous research, conventional analysis and correlations between neurocognitive decline and self-reported problems were generally near zero. In contrast, application of latent regression Rasch modeling found statistically reliable associations between objective attention and processing speed measures with self-reported Attention and Memory scores.

CONCLUSIONS

Latent regression Rasch modeling, together with correlation of specific self-reported cognitive domains with neurocognitive measures, helps to clarify the relationship of self-report with objective performance. While the majority of patients attribute their cognitive difficulties to memory decline, the Rash modeling suggests the importance of processing speed and initial learning. To encourage the use of this method, a step-by-step guide and programming language for implementation is provided. Implications of this method in cognitive outcomes research are discussed.

INTERMITTENT DEGRADATION AND SCHIZOTYPY

Intermittent degradation refers to transient detrimental disruptions in task performance. This phenomenon has been repeatedly observed in the performance data of patients with schizophrenia. Whether intermittent degradation is a feature of the liability for schizophrenia (i.e., schizotypy) is an open question. Further, the specificity of intermittent degradation to schizotypy has yet to be investigated. To address these questions, 92 undergraduate participants completed a battery of self-report questionnaires assessing schizotypy and psychological state variables (e.g., anxiety, depression), and their reaction times were recorded as they did so. Intermittent degradation was defined as the number of times a subject’s reaction time for questionnaire items met or exceeded three standard deviations from his or her mean reaction time after controlling for each item’s information processing load. Intermittent degradation scores were correlated with questionnaire scores. Our results indicate that intermittent degradation is associated with total scores on measures of positive and disorganized schizotypy, but unrelated to total scores on measures of negative schizotypy and psychological state variables. Intermittent degradation is interpreted as potentially derivative of schizotypy and a candidate endophenotypic marker worthy of continued research.

Developing Exposure/Response Models for Anticancer Drug Treatment: Special Considerations

Anticancer agents often have a narrow therapeutic index (TI), requiring precise dosing to ensure sufficient exposure for clinical activity while minimizing toxicity. These agents frequently have complex pharmacology, and combination therapy may cause schedule-specific effects and interactions. We review anticancer drug development, showing how integration of modeling and simulation throughout development can inform anticancer dose selection, potentially improving the late-phase success rate. This article has a companion article in Clinical Pharmacology & Therapeutics with practical examples.

A hierarchical finite mixture model that accommodates zero-inflated counts, non-independence, and heterogeneity

A number of mixture modeling approaches assume both normality and independent observations. However, these two assumptions are at odds with the reality of many data sets, which are often characterized by an abundance of zero-valued or highly skewed observations as well as observations from biologically related (i.e., non-independent) subjects. We present here a finite mixture model with a zero-inflated Poisson regression component that may be applied to both types of data. This flexible approach allows the use of covariates to model both the Poisson mean and rate of zero inflation and can incorporate random effects to accommodate non-independent observations. We demonstrate the utility of this approach by applying these models to a candidate endophenotype for schizophrenia, but the same methods are applicable to other types of data characterized by zero inflation and non-independence.

Intra-individual variability in high-functioning patients with schizophrenia

Intra-individual variability of reaction times (IIV) can be employed as a measure of the stability of information processing, which has been proposed to be fundamentally disturbed in schizophrenia. However, the theoretical and clinical significance of IIV is not clear, in part because it has previously been investigated in subject groups with generalized cognitive impairment. Therefore, the purpose of the study was to assess IIV in high-functioning patients with schizophrenia and relatively preserved cognitive performance. 28 high-functioning patients with schizophrenia and 28 controls performed a Go/Nogo task and a Continuous Performance Test. In contrast to average measures of task performance, IIV differentiated consistently and with large effect size between groups. Modelling with an Ex-Gaussian distribution revealed that patients have a higher proportion of slow responses reflected by an increased tau parameter. The tau parameter was correlated with work capability in the sample with schizophrenia. In conclusion, IIV is an easily obtained measure, which is highly sensitive to fundamental cognitive deficits not directly visible in a high-functioning patient group. The response pattern with more exceedingly slow reactions could reflect a core deficit in the stability of information processing. The relationship with work capability suggests investigation of IIV as a clinical measure.

A Bayesian hierarchical mixture model for platelet derived growth factor receptor phosphorylation to improve estimation of progression-free survival in prostate cancer

Advances in understanding the biological underpinnings of many cancers have led increasingly to the use of molecularly targeted anti-cancer therapies. Because the platelet-derived growth factor receptor (PDGFR) has been implicated in the progression of prostate cancer bone metastases, it is of great interest to examine possible relationships between PDGFR inhibition and therapeutic outcomes. Here, we analyze the association between change in activated PDGFR (p-PDGFR) and progression free survival (PFS) time based on large within-patient samples of cell-specific p-PDGFR values taken before and after treatment from each of 88 prostate cancer patients. To utilize these paired samples as covariate data in a regression model for PFS time, and because the p-PDGFR distributions are bimodal, we first employ a Bayesian hierarchical mixture model to obtain a deconvolution of the pre-treatment and post-treatment within-patient p-PDGFR distributions. We evaluate fits of the mixture model and a non-mixture model that ignores the bimodality by using a supnorm metric to compare the empirical distribution of each p-PDGFR data set with the corresponding fitted distribution under each model. Our results show that first using the mixture model to account for the bimodality of the within-patient p-PDGFR distributions, and then using the posterior within-patient component mean changes in p-PDGFR so obtained as covariates in the regression model for PFS time provides an improved estimation.

Intra-individual reaction time variability in schizophrenia, depression and borderline personality disorder

Intra-individual reaction time variability (IIV) in neuropsychological task performance reflects short term fluctuations in performance. Increased IIV has been reported in patients with schizophrenia and could be related to a deficient neural timing mechanism, but the role of IIV in adult patients with other psychiatric disorders has not been established. Therefore, we compared IIV measures obtained in a Go/Nogo task from patients with schizophrenia, major depression and borderline personality disorder. IIV was increased for patients with schizophrenia. When correcting for differences in mean reaction time, depressive and borderline patients also showed increased IIV. Importantly, all groups showed a strong association between IIV and accuracy of task performance. This suggests that increased IIV might be a sensitive marker for the efficiency of top-down attentional control in all diagnostic groups. Aside from these similarities, the complete results including measures of IIV, mean reaction time and accuracy show differential patterns for patients with schizophrenia compared to those with borderline personality disorder or depression. These results are discussed with respect to common versus disorder-specific neural mechanisms underlying increased IIV.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Are population pharmacokinetic and/or pharmacodynamic models adequately evaluated? A survey of the literature from 2002 to 2004

Model evaluation is an important issue in population analyses. We aimed to perform a systematic review of all population pharmacokinetic and/or pharmacodynamic analyses published between 2002 and 2004 to survey the current methods used to evaluate models and to assess whether those models were adequately evaluated. We selected 324 articles in MEDLINE using defined key words and built a data abstraction form composed of a checklist of items to extract the relevant information from these articles with respect to model evaluation. In the data abstraction form, evaluation methods were divided into three subsections: basic internal methods (goodness-of-fit [GOF] plots, uncertainty in parameter estimates and model sensitivity), advanced internal methods (data splitting, resampling techniques and Monte Carlo simulations) and external model evaluation. Basic internal evaluation was the most frequently described method in the reports: 65% of the models involved GOF evaluation. Standard errors or confidence intervals were reported for 50% of fixed effects but only for 22% of random effects. Advanced internal methods were used in approximately 25% of models: data splitting was more often used than bootstrap and cross-validation; simulations were used in 6% of models to evaluate models by a visual predictive check or by a posterior predictive check. External evaluation was performed in only 7% of models. Using the subjective synthesis of model evaluation for each article, we judged the models to be adequately evaluated in 28% of pharmacokinetic models and 26% of pharmacodynamic models. Basic internal evaluation was preferred to more advanced methods, probably because the former is performed easily with most software. We also noticed that when the aim of modelling was predictive, advanced internal methods or more stringent methods were more often used.

Evaluating pharmacokinetic/pharmacodynamic models using the posterior predictive check

The posterior predictive check (PPC) is a model evaluation tool. It assigns a value (pPPC) to the probability that the value of a given statistic computed from data arising under an analysis model is as or more extreme than the value computed from the real data themselves. If this probability is too small, the analysis model is regarded as invalid for the given statistic. Properties of the PPC for pharmacokinetic (PK) and pharmacodynamic (PD) model evaluation are examined herein for a particularly simple simulation setting: extensive sampling of a single individual's data arising from simple PK/PD and error models. To test the performance characteristics of the PPC, repeatedly, "real" data are simulated and for a variety of statistics, the PPC is applied to an analysis model, which may (null hypothesis) or may not (alternative hypothesis) be identical to the simulation model. Five models are used here: (PK1) mono-exponential with proportional error, (PK2) biexponential with proportional error, (PK2 epsilon) biexponential with additive error, (PD1) Emax model with additive error under the logit transform, and (PD2) sigmoid Emax model with additive error under the logit transform. Six simulation/analysis settings are studied. The first three, (PK1/PK1), (PK2/PK2), and (PD1/PD1) evaluate whether the PPC has appropriate type-I error level, whereas the second three (PK2/PK1), (PK2 epsilon/PK2), and (PD2/PD1) evaluate whether the PPC has adequate power. For a set of 100 data sets simulated/analyzed under each model pair according to a stipulated extensive sampling design, the pPPC is computed for a number of statistics in three different ways (each way uses a different approximation to the posterior distribution on the model parameters). We find that in general; (i) The PPC is conservative under the null in the sense that for many statistics, prob(pPPC < or = alpha) < alpha for small alpha. With respect to such statistics, this means that useful models will rarely be regarded incorrectly as invalid. A high correlation of a statistic with the parameter estimates obtained from the same data used to compute the statistic (a measure of statistical "sufficiency") tends to identify the most conservative statistics. (ii) Power is not very great, at least for the alternative models we tested, and it is especially poor with "statistics" that are in part a function of parameters as well as data. Although there is a tendency for nonsufficient statistics (as we have measured this) to have greater power, this is by no means an infallible diagnostic. (iii) No clear advantage for one or another method of approximating the posterior distribution on model parameters is found.

A new look at reaction time in schizophrenia

Schizophrenia patients demonstrate impaired manual reaction time (RT), but not saccadic RT, when given traditional tasks. To determine whether the manual RT time impairment could be eliminated by providing imperative stimuli to the finger (thus providing stimulus-response compatibility), we tested 28 chronic schizophrenic patients on finger-lift RT to visual (VIS), tactile plus visual (TAC+VIS), and auditory plus tactile plus visual (AUD+TAC+VIS) stimuli. The patients (a) were significantly slower than controls (n=28) in all three tasks, (b) showed bimodality, with 43% of patients having means and variances nearly identical to control values, and (c) had RTs significantly closer to control values in the TAC+VIS and AUD+TAC+VIS tasks than in the VIS task. The inability to normalize finger-lift RT in schizophrenia represents a genuine slowing of this response system regardless of stimulus-response compatibility. We consider other possible explanations for the differences between manual and saccadic RT, including the notion that excess processing capacity for saccadic RT may be masking possible deficits in that system.

A latent class mixed model for analysing biomarker trajectories with irregularly scheduled observations

This paper considers a latent class model to uncover subpopulation structure for both biomarker trajectories and the probability of disease outcome in highly unbalanced longitudinal data. A specific pattern of trajectories can be viewed as a latent class in a finite mixture where membership in latent classes is modelled with a polychotomous logistic regression. The biomarker trajectories within a latent class are described by a linear mixed model with possibly time-dependent covariates and the probabilities of disease outcome are estimated via a class specific model. Thus the method characterizes biomarker trajectory patterns to unveil the relationship between trajectories and outcomes of disease. The coefficients for the model are estimated via a generalized EM (GEM) algorithm, a natural tool to use when latent classes and random coefficients are present. Standard errors of the coefficients are calculated using a parametric bootstrap. The model fitting procedure is illustrated with data from the Nutritional Prevention of Cancer trials; we use prostate specific antigen (PSA) as the biomarker for prostate cancer and the goal is to examine trajectories of PSA serial readings in individual subjects in connection with incidence of prostate cancer.

Intermittent degradation in performance in schizophrenia

In a series of repeated trials, schizophrenic patients often fluctuate in performance. Our data suggest that it may be useful, not just to report an increased variance relative to nonschizophrenics, but to model these fluctuations concretely as transitions between a relatively normal and an abnormal cognitive state - an intermittent degradation in performance that may be related to transient abnormalities in CNS functioning. We define 'dialipsis' as a temporary substitution of a less efficient process of task performance. This phenomenon is mentioned in the literature, but the descriptions of dialipsis are heuristic rather than based on a statistical model. We present a mixture model in which the ordinary and degraded states are described by distinct ANOVA structures, each with its own task, subject and interaction effects, with transitions between them occurring at random times. We discuss ways of detecting dialipsis and comparing the mixture model statistically with alternative models.

Markov chain Monte Carlo methods in biostatistics

Appropriate models in biostatistics are often quite complicated. Such models are typically most easily fit using Bayesian methods, which can often be implemented using simulation techniques. Markov chain Monte Carlo (MCMC) methods are an important set of tools for such simulations. We give an overview and references of this rapidly emerging technology along with a relatively simple example. MCMC techniques can be viewed as extensions of iterative maximization techniques, but with random jumps rather than maximizations at each step. Special care is needed when implementing iterative maximization procedures rather than closed-form methods, and even more care is needed with iterative simulation procedures: it is substantially more difficult to monitor convergence to a distribution than to a point. The most reliable implementations of MCMC build upon results from simpler models fit using combinations of maximization algorithms and noniterative simulations, so that the user has a rough idea of the location and scale of the posterior distribution of the quantities of interest under the more complicated model. These concerns with implementation, however, should not deter the biostatistician from using MCMC methods, but rather help to ensure wise use of these powerful techniques.