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In longitudinal studies, we observe measurements of the same variables at different time points to track the changes in their pattern over time. In such studies, scheduling of the data collection waves (i.e. time of participants' visits) is often pre-determined to accommodate ease of project management and compliance. Hence, it is common to schedule those visits at equally spaced time intervals. However, recent publications based on simulated experiments indicate that the power of studies and the precision of model parameter estimators is related to the participants' visiting schemes. In this paper, we consider the longitudinal studies that investigate the changing pattern of a disease outcome, (e.g. the accelerated cognitive decline of senior adults). Such studies are often analyzed by the broken-stick model, consisting of two segments of linear models connected at an unknown change-point. We formulate this design problem into a high-dimensional optimization problem and derive its analytical solution. Based on this solution, we propose an optimal design of the visiting scheme that maximizes the power (i.e. reduce the variance of estimators) to identify the onset of accelerated decline. Using both simulation studies and evidence from real data, we demonstrate our optimal design outperforms the standard equally-spaced design. Applying our novel design to plan the longitudinal studies, researchers can improve the power of detecting pattern change without collecting extra data., Comment: 5 figures

Multistate models can be used to describe transitions over time across states. In the presence of interval-censored times for transitions, the likelihood is constructed using transition probabilities. Models are specified using proportional hazards model for the transitions. Time-dependency is usually defined by parametric models, which can be too restrictive. Nonparametric hazards specification with splines allow for flexible modelling of time-dependency without making strong model assumptions. Penalised maximum likelihood is used to estimate the models. Selecting the optimal amount of smoothing is challenging as the problem involves multiple penalties. We propose an automatic and efficient method to estimate multistate models with splines in the presence of interval-censoring. The method is illustrated with a data analysis and a simulation study., Comment: 20 pages, 4 figures, 2 tables

Continuous-time multi-state survival models can be used to describe health-related processes over time. In the presence of interval-censored times for transitions between the living states, the likelihood is constructed using transition probabilities. Models can be specified using parametric or semi-parametric shapes for the hazards. Semi-parametric hazards can be fitted using $P$-splines and penalised maximum likelihood estimation. This paper presents a method to estimate flexible multi-state models which allows for parametric and semi-parametric hazard specifications. The estimation is based on a scoring algorithm. The method is illustrated with data from the English Longitudinal Study of Ageing.

Background. Health economic evaluations of interventions against infectious diseases are commonly based on the predictions of ordinary differential equation (ODE) systems or Markov models (MMs). Standard MMs are static, whereas ODE systems are usually dynamic and account for herd immunity which is crucial to prevent overestimation of infection prevalence. Complex ODE systems including probabilistic model parameters are computationally intensive. Thus, mainly ODE-based models including deterministic parameters are presented in the literature. These do not account for parameter uncertainty. As a consequence, probabilistic sensitivity analysis (PSA), a crucial component of health economic evaluations, cannot be conducted straightforwardly. Methods. We present a dynamic MM under a Bayesian framework. We extend a static MM by incorporating the force of infection into the state allocation algorithm. The corresponding output is based on dynamic changes in prevalence and thus accounts for herd immunity. In contrast to deterministic ODE-based models, PSA can be conducted straightforwardly. We introduce a case study of a fictional sexually transmitted infection and compare our dynamic Bayesian MM to a deterministic and a Bayesian ODE system. The models are calibrated to time series data. Results. By means of the case study, we show that our methodology produces outcome which is comparable to the "gold standard" of the Bayesian ODE system. Conclusions. In contrast to ODE systems in the literature, the setting of the dynamic MM is probabilistic at manageable computational effort (including calibration). The run time of the Bayesian ODE system is 44 times longer.

In 2004 the Dutch Department of Social Affairs conducted a survey to assess the extent of noncompliance with social security regulations. The survey was conducted among 870 recipients of social security benefits and included a series of sensitive questions about regulatory noncompliance. Due to the sensitive nature of the questions the randomized response design was used. Although randomized response protects the privacy of the respondent, it is unlikely that all respondents followed the design. In this paper we introduce a model that allows for respondents displaying self-protective response behavior by consistently giving the nonincriminating response, irrespective of the outcome of the randomizing device. The dependent variable denoting the total number of incriminating responses is assumed to be generated by the application of randomized response to a latent Poisson variable denoting the true number of rule violations. Since self-protective responses result in an excess of observed zeros in relation to the Poisson randomized response distribution, these are modeled as observed zero-inflation. The model includes predictors of the Poisson parameters, as well as predictors of the probability of self-protective response behavior., Comment: Published in at http://dx.doi.org/10.1214/07-AOAS135 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)