Semiparametric Mixed Model Research Articles

A semiparametric joint model for terminal trend of quality of life and survival in palliative care research.

Palliative medicine is an interdisciplinary specialty focusing on improving quality of life (QOL) for patients with serious illness and their families. Palliative care programs are available or under development at over 80% of large US hospitals (300+ beds). Palliative care clinical trials present unique analytic challenges relative to evaluating the palliative care treatment efficacy which is to improve patients' diminishing QOL as disease progresses towards end of life (EOL). A unique feature of palliative care clinical trials is that patients will experience decreasing QOL during the trial despite potentially beneficial treatment. Often longitudinal QOL and survival data are highly correlated which, in the face of censoring, makes it challenging to properly analyze and interpret terminal QOL trend. To address these issues, we propose a novel semiparametric statistical approach to jointly model the terminal trend of QOL and survival data. There are two sub-models in our approach: a semiparametric mixed effects model for longitudinal QOL and a Cox model for survival. We use regression splines method to estimate the nonparametric curves and AIC to select knots. We assess the model performance through simulation to establish a novel modeling approach that could be used in future palliative care research trials. Application of our approach in a recently completed palliative care clinical trial is also presented.

Bayesian semiparametric reproductive dispersion mixed models for non-normal longitudinal data: estimation and case influence analysis

ABSTRACTSemiparametric reproductive dispersion mixed model (SPRDMM) is a natural extension of the reproductive dispersion model and the semiparametric mixed model. In this paper, we relax the normality assumption of random effects in SPRDMM and use a truncated and centred Dirichlet process prior to specify random effects, and present the Bayesian P-spline to approximate the smoothing unknown function. A hybrid algorithm combining the block Gibbs sampler and the Metropolis–Hastings algorithm is implemented to sample observations from the posterior distribution. Also, we develop Bayesian case deletion influence measure for SPRDMM based on the φ-divergence and present those computationally feasible formulas. Several simulation studies and a real example are presented to illustrate the proposed methodologies.

Inferences in semi-parametric dynamic mixed models for longitudinal count data

This paper considers a semi-parametric mixed model for longitudinal counts under the assumption that for conditional on a common random effect over time the repeated count responses of an individual follow a Poisson AR(1) (auto-regressive order 1) non-stationary correlation structure. A step-by-step estimation approach is developed which provides consistent estimators for the non-parametric function, regression parameters, variance of the random effects, and auto-correlation structure of the model. Proofs for the consistency properties of the estimators along with their convergence rates are derived. A simulation study is conducted to examine first the estimation effects on parameters when the non-parametric function is ignored, and then an overall estimation study is carried out in the presence of the non-parametric function by including its estimation as well.

Time-varying latent model for longitudinal data with informative observation and terminal event times

Longitudinal data often occur in follow-up studies, and in many situations, there may exist informative observation times and a dependent terminal event such as death that stops the follow-up. We propose a semiparametric mixed effect model with time-varying latent effects in the analysis of longitudinal data with informative observation times and a dependent terminal event. Estimating equation approaches are developed for parameter estimation, and asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is provided.

Semiparametric Identification and Fisher Information

This paper relates identification with statistical information in semiparametric models, extending to the semiparametric case some of the results previously given in Fisher (1966) and Rothenberg (1971). The paper first establishes a sufficient and necessary condition for semiparametric identification of (finite-dimensional) parameters or linear functionals in a class of models that are affine in a nonparametric parameter. It characterizes identified parameters (identified parameters with zero Fisher information) in this setting. This characterization is used to show that semiparametric irregular identification is a common feature of many economic models of practical interest. Sufficient conditions for regular and irregular identification are given for nonlinear models. The paper also establishes a link between semiparametric identification and completeness of the conditional distribution of observed variables given unobservables, and uses this link to prove that the non-random parameters of the semiparametric mixed Logit model are irregularly identified.

A Monte Carlo Study of Design Procedures for the Semi-parametric Mixed Logit Model

AbstractWe determine efficient designs for choice-based conjoint analysis for the semi-parametric mixed logit model which captures latent consumer heterogeneity in a very flexible way. Different methods constructing one or multiple designs are tested. Additionally we apply Halton draws and determine a minimum potential design for prior draws to reduce computation times caused by accounting for latent heterogeneity of consumers. As main efficiency criteria for the construction of designs we consider measures related to D-error and entropy. As additional benchmarks we generate designs both randomly and by an approach which starts from orthogonal designs developed for linear models. We compare these alternative design procedures by simulating choices for different constellations on the basis of the semi-parametric mixed logit model. Using these simulated choices we estimate parameters of the semi-parametric mixed logit model in the next step. ANOVA with root mean squared error between estimated and true coefficient values as dependent variable shows that performance of design procedures depends on dissimilarity and segment size. Following a mean-standard deviation approach we determine which procedure should be used under different constellations or lack of prior information. Overall, either constructing ten designs based on

Dynamics of Disease Progression and Gastrostomy Tube Placement in Children and Adolescents with Cystic Fibrosis: Application of Joint Models for Longitudinal and Time-to-Event Data.

Previous small-sample studies have examined the effect of gastrostomy (g-) tube placement on weight, height, and lung function in adolescent patients with cystic fibrosis (CF), but there are no RCTs to date reporting efficacy. The goal of this study was to implement a dynamic prediction model to 1) understand the role of rapid lung function decline in g-tube placement in real-world clinical settings; 2) provide a prognostic tool with the potential to aid clinicians in optimizing the timing of g-tube placement, in relation to rate of lung function decline and current nutrition status. A dynamic prediction model was developed, utilizing data on patients 6-21 years of age from the Cystic Fibrosis Foundation Patient Registry (1997-2013). A joint model was implemented, which coupled a semiparametric mixed model to characterize rapid lung function decline with a time-to-event model to identify risk factors for g-tube initiation. The 4,034 individuals (21.3%) who underwent g-tube placement during adolescence or young adulthood had poorer nutrition and lung function at baseline and initially had increased rates of pancreatic enzyme use, infection and gastroesophageal reflux disease, compared to those who did not receive g-tubes; these associations changed over follow up. Rapid lung function decline was associated with increased risk of g-tube supplementation. By jointly modeling longitudinal patterns of lung function decline with g-tube delivery, it is possible to construct prognostic aids to evaluate treatment delivery in relation to the onset of rapid lung function decline and other important clinical markers. These algorithms have the potential to enable more effective monitoring of disease progression and promote more timely treatment delivery.

A generalized semiparametric mixed model for analysis of multivariate health care utilization data.

Health care utilization is an outcome of interest in health services research. Two frequently studied forms of utilization are counts of emergency department (ED) visits and hospital admissions. These counts collectively convey a sense of disease exacerbation and cost escalation. Different types of event counts from the same patient form a vector of correlated outcomes. Traditional analysis typically model such outcomes one at a time, ignoring the natural correlations between different events, and thus failing to provide a full picture of patient care utilization. In this research, we propose a multivariate semiparametric modeling framework for the analysis of multiple health care events following the exponential family of distributions in a longitudinal setting. Bivariate nonparametric functions are incorporated to assess the concurrent nonlinear influences of independent variables as well as their interaction effects on the outcomes. The smooth functions are estimated using the thin plate regression splines. A maximum penalized likelihood method is used for parameter estimation. The performance of the proposed method was evaluated through simulation studies. To illustrate the method, we analyzed data from a clinical trial in which ED visits and hospital admissions were considered as bivariate outcomes.

Inference in semi-parametric spline mixed models for longitudinal data

In this paper, the authors investigate a robust semi-parametric mixed effects model for analyzing longitudinal data with an unspecified mean response function. The robust method, developed in the framework of the maximum likelihood, is used to bound the influence of potential outliers when estimating the model parameters. The authors also present a robust test procedure for assessing the significance of a variance component in the mixed model. An application is provided using a clinical dataset from a retinopathy of prematurity study in which longitudinal measurements were obtained from premature infants treated with supplemental oxygen. The empirical properties of the proposed estimators are also studied in simulations.

Mixed effect regression analysis for a cluster-based two-stage outcome-auxiliary-dependent sampling design with a continuous outcome.

Two-stage design is a well-known cost-effective way for conducting biomedical studies when the exposure variable is expensive or difficult to measure. Recent research development further allowed one or both stages of the two-stage design to be outcome dependent on a continuous outcome variable. This outcome-dependent sampling feature enables further efficiency gain in parameter estimation and overall cost reduction of the study (e.g. Wang, X. and Zhou, H., 2010. Design and inference for cancer biomarker study with an outcome and auxiliary-dependent subsampling. Biometrics 66, 502-511; Zhou, H., Song, R., Wu, Y. and Qin, J., 2011. Statistical inference for a two-stage outcome-dependent sampling design with a continuous outcome. Biometrics 67, 194-202). In this paper, we develop a semiparametric mixed effect regression model for data from a two-stage design where the second-stage data are sampled with an outcome-auxiliary-dependent sample (OADS) scheme. Our method allows the cluster- or center-effects of the study subjects to be accounted for. We propose an estimated likelihood function to estimate the regression parameters. Simulation study indicates that greater study efficiency gains can be achieved under the proposed two-stage OADS design with center-effects when compared with other alternative sampling schemes. We illustrate the proposed method by analyzing a dataset from the Collaborative Perinatal Project.

A Semiparametric Mixed Model Approach to Phase I Profile Monitoring

Profile monitoring is an approach in quality control best used where the process data follow a profile (or curve). The majority of previous studies in profile monitoring focused on the parametric (P) modeling of either linear or nonlinear profiles, with both fixed and random effects, under the assumption of correct model specification. More recently, in the absence of an obvious P model, nonparametric (NP) methods have been employed in the profile monitoring context. For situations where a P model is adequate over part of the data but inadequate of other parts, we propose a semiparametric procedure that combines both P and NP profile fits. We refer to our semiparametric procedure as mixed model robust profile monitoring (MMRPM). These three methods (P, NP and MMRPM) can account for the autocorrelation within profiles and treat the collection of profiles as a random sample from a common population. For each approach, we propose a version of Hotelling's T2 statistic for use in Phase I analysis to determine unusual profiles based on the estimated random effects and obtain the corresponding control limits. Simulation results show that our MMRPM method performs well in making decisions regarding outlying profiles when compared to methods based on a misspecified P model or based on NP regression. In addition, however, the MMRPM method is robust to model misspecification because it also performs well when compared to a correctly specified P model. The proposed chart is able to detect changes in Phase I data and has easily calculated control limits. We apply all three methods to the automobile engine data of Amiri et al.5 and find that the NP and the MMRPM methods indicate signals that did not occur in a P approach. Copyright © 2012 John Wiley & Sons, Ltd.

Testing the Effectiveness of Community-Based Dengue Vector Control Interventions Using Semiparametric Mixed Models

To evaluate the results obtained though intersectoral coordination and community empowerment in one study carried out during 6 years in Playa Municipality, Cuba. A longitudinal assessment comparing one intervention and one control area was conducted. The intervention encompasses two main stages separated by two dengue outbreaks. The first stage, focused on strengthening intersectoral coordination, was initiated in January 2000. In August 2003, a complementary strategy, focused on community empowerment and was initiated in half of the intervention area. In the control area, routine dengue control activities continued without additional input. We used entomologic surveillance data from January 1999 to December 2005 to assess the effectiveness. We computed the Breteau index (BI) per health area and the 95% confidence interval for the difference between the BIs at each time point. A semiparametric mixed model to capture the evolution in time of Aedes aegypti larval densities was fitted. The BI in the control area showed the lowest value before starting the intervention. This was reversed 1 year after launching intersectoral activities for dengue control in the intervention area. In spite of spraying actions in all areas, the differences in BI between intervention and control areas remain significant until December 2002. Although for the next 2 years no differences were observed, they become significant again in December 2004, which corresponds with the implementation of the complementary community-based vector control strategy in the intervention area. The model fitted identified monotonous trends over time and reversal trends at particular moments. The confidence bands indicate sections with significant differences between areas. Our data increase the evidence that the intersectoral coordination and community empowerment strategy for A. aegypti control is effective.

Semiparametric modeling of autonomous nonlinear dynamical systems with application to plant growth

We propose a semiparametric model for autonomous nonlinear dynamical systems and devise an estimation procedure for model fitting. This model incorporates subject-specific effects and can be viewed as a nonlinear semiparametric mixed effects model. We also propose a computationally efficient model selection procedure. We show by simulation studies that the proposed estimation as well as model selection procedures can efficiently handle sparse and noisy measurements. Finally, we apply the proposed method to a plant growth data used to study growth displacement rates within meristems of maize roots under two different experimental conditions.

The use of semiparametric mixed models to analyze PamChip® peptide array data: an application to an oncology experiment

Phosphorylation by protein kinases is a central theme in biological systems. Aberrant protein kinase activity has been implicated in a variety of human diseases (e.g. cancer). Therefore, modulation of kinase activity represents an attractive therapeutic approach for the treatment of human illnesses. Thus, identification of signature peptides is crucial for protein kinase targeting and can be achieved by using PamChip(®) microarray technology. We propose a flexible semiparametric mixed model for analyzing PamChip(®) data. This approach enables the estimation of the phosphorylation rate (Velocity) as a function of time together with pointwise confidence intervals. Using a publicly available dataset, we show that our model is capable of adequately fitting the kinase activity profiles and provides velocity estimates over time. Moreover, it allows to test for differences in the velocity of kinase inhibition between responding and non-responding cell lines. This can be done at individual time point as well as for the entire velocity profile. pushpike@med.kuleuven.be Supplementary data are available at Bioinformatics online.

Malnutrition among children under the age of five in the Democratic Republic of Congo (DRC): does geographic location matter?

BackgroundAlthough there are inequalities in child health and survival in the Democratic Republic of Congo (DRC), the influence of distal determinants such as geographic location on children's nutritional status is still unclear. We investigate the impact of geographic location on child nutritional status by mapping the residual net effect of malnutrition while accounting for important risk factors.MethodsWe examine spatial variation in under-five malnutrition with flexible geo-additive semi-parametric mixed model while simultaneously controlling for spatial dependence and possibly nonlinear effects of covariates within a simultaneous, coherent regression framework based on Markov Chain Monte Carlo techniques. Individual data records were constructed for children. Each record represents a child and consists of nutritional status information and a list of covariates. For the 8,992 children born within the last five years before the survey, 3,663 children have information on anthropometric measures.Our novel empirical approach is able to flexibly determine to what extent the substantial spatial pattern of malnutrition is driven by detectable factors such as socioeconomic factors and can be attributable to unmeasured factors such as conflicts, political, environmental and cultural factors.ResultsAlthough childhood malnutrition was more pronounced in all provinces of the DRC, after accounting for the location's effects, geographic differences were significant: malnutrition was significantly higher in rural areas compared to urban centres and this difference persisted after multiple adjustments. The findings suggest that models of nutritional intervention must be carefully specified with regard to residential location.ConclusionChildhood malnutrition is spatially structured and rates remain very high in the provinces that rely on the mining industry and comparable to the level seen in Eastern provinces under conflicts. Even in provinces such as Bas-Congo that produce foods, childhood malnutrition is higher probably because of the economic decision to sell more than the population consumes. Improving maternal and child nutritional status is a prerequisite for achieving MDG 4, to reduce child mortality rate in the DRC.

On Estimating the Relationship between Longitudinal Measurements and Time‐to‐Event Data Using a Simple Two‐Stage Procedure

Ye, Lin, and Taylor (2008, Biometrics 64, 1238-1246) proposed a joint model for longitudinal measurements and time-to-event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two-stage regression calibration approach that is simpler to implement than a joint modeling approach. In the first stage of their approach, the mixed model is fit without regard to the time-to-event data. In the second stage, the posterior expectation of an individual's random effects from the mixed-model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause a bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach that can be applied for both discrete and continuous time-to-event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008). In agreement with the methodology proposed by Ye et al. (2008), an advantage of our proposed approach over joint modeling is that it can be implemented with standard statistical software and does not require complex estimation techniques.

Longitudinal Data Analysis with Event Time as a Covariate

We consider the estimation of a nonparametric smooth function of some event time in a semiparametric mixed effects model from repeatedly measured data when the event time is subject to right censoring. The within-subject correlation is captured by both cross-sectional and time-dependent random effects, where the latter is modeled by a nonhomogeneous Ornstein–Uhlenbeck stochastic process. When the censoring probability depends on other variables in the model, which often happens in practice, the event time data are not missing completely at random. Hence, the complete case analysis by eliminating all the censored observations may yield biased estimates of the regression parameters including the smooth function of the event time, and is less efficient. To remedy, we derive the likelihood function for the observed data by modeling the event time distribution given other covariates. We propose a two-stage pseudo-likelihood approach for the estimation of model parameters by first plugging an estimator of the conditional event time distribution into the likelihood and then maximizing the resulting pseudo-likelihood function. Empirical evaluation shows that the proposed method yields negligible biases while significantly reduces the estimation variability. This research is motivated by the project of hormone profile estimation around age at the final menstrual period for the cohort of women in the Michigan Bone Health and Metabolism Study.

Bayesian analysis of semiparametric reproductive dispersion mixed-effects models

Semiparametric reproductive dispersion mixed-effects model (SPRDMM) is an extension of the reproductive dispersion model and the semiparametric mixed model, and it includes many commonly encountered models as its special cases. A Bayesian procedure is developed for analyzing SPRDMMs on the basis of P-spline estimates of nonparametric components. A hybrid algorithm combining the Gibbs sampler and the Metropolis-Hastings algorithm is used to simultaneously obtain the Bayesian estimates of unknown parameters, smoothing function and random effects, as well as their standard error estimates. The Bayes factor for model comparison is employed to select better approximation of the smoothing function via path sampling. Several simulation studies and a real example are used to illustrate the proposed methodologies.

On Estimating the Relationship between Longitudinal Measurements and Time-to-Event Data Using a Simple Two-Stage Procedure

Summary Ye, Lin, and Taylor (2008, Biometrics 64, 1238–1246) proposed a joint model for longitudinal measurements and time-to-event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two-stage regression calibration approach that is simpler to implement than a joint modeling approach. In the first stage of their approach, the mixed model is fit without regard to the time-to-event data. In the second stage, the posterior expectation of an individual's random effects from the mixed-model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause a bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach that can be applied for both discrete and continuous time-to-event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008). In agreement with the methodology proposed by Ye et al. (2008), an advantage of our proposed approach over joint modeling is that it can be implemented with standard statistical software and does not require complex estimation techniques.

Semiparametric Modeling of Longitudinal Measurements and Time‐to‐Event Data–A Two‐Stage Regression Calibration Approach

In this article we investigate regression calibration methods to jointly model longitudinal and survival data using a semiparametric longitudinal model and a proportional hazards model. In the longitudinal model, a biomarker is assumed to follow a semiparametric mixed model where covariate effects are modeled parametrically and subject-specific time profiles are modeled nonparametrially using a population smoothing spline and subject-specific random stochastic processes. The Cox model is assumed for survival data by including both the current measure and the rate of change of the underlying longitudinal trajectories as covariates, as motivated by a prostate cancer study application. We develop a two-stage semiparametric regression calibration (RC) method. Two variations of the RC method are considered, risk set regression calibration and a computationally simpler ordinary regression calibration. Simulation results show that the two-stage RC approach performs well in practice and effectively corrects the bias from the naive method. We apply the proposed methods to the analysis of a dataset for evaluating the effects of the longitudinal biomarker PSA on the recurrence of prostate cancer.