State selection in Markov models for panel data with application to psoriatic arthritis

Markov multistate models in continuous‐time are commonly used to understand the progression over time of disease or the effect of treatments and covariates on patient outcomes. The states in multistate models are related to categorisations of the disease status, but there is often uncertainty about the number of categories to use and how to define them. Many categorisations, and therefore multistate models with different states, may be possible. Different multistate models can show differences in the effects of covariates or in the time to events, such as death, hospitalisation, or disease progression. Furthermore, different categorisations contain different quantities of information, so that the corresponding likelihoods are on different scales, and standard, likelihood‐based model comparison is not applicable. We adapt a recently developed modification of Akaike's criterion, and a cross‐validatory criterion, to compare the predictive ability of multistate models on the information which they share. All the models we consider are fitted to data consisting of observations of the process at arbitrary times, often called ‘panel’ data. We develop an implementation of these criteria through Hidden Markov models and apply them to the comparison of multistate models for the Health Assessment Questionnaire score in psoriatic arthritis. This procedure is straightforward to implement in the R package ‘msm’. Copyright © 2015 John Wiley & Sons, Ltd.     

Regression analysis of mixed panel count data with dependent terminal events

Event history studies are commonly conducted in many fields, and a great deal of literature has been established for the analysis of the two types of data commonly arising from these studies: recurrent event data and panel count data. The former arises if all study subjects are followed continuously, while the latter means that each study subject is observed only at discrete time points. In reality, a third type of data, a mixture of the two types of the data earlier, may occur and furthermore, as with the first two types of the data, there may exist a dependent terminal event, which may preclude the occurrences of recurrent events of interest. This paper discusses regression analysis of mixed recurrent event and panel count data in the presence of a terminal event and an estimating equation‐based approach is proposed for estimation of regression parameters of interest. In addition, the asymptotic properties of the proposed estimator are established, and a simulation study conducted to assess the finite‐sample performance of the proposed method suggests that it works well in practical situations. Finally, the methodology is applied to a childhood cancer study that motivated this study. Copyright © 2017 John Wiley & Sons, Ltd.     

Semiparametric transformation models for panel count data with correlated observation and follow‐up times

The statistical analysis of panel count data has recently attracted a great deal of attention, and a number of approaches have been developed. However, most of these approaches are for situations where the observation and follow‐up processes are independent of the underlying recurrent event process unconditional or conditional on covariates. In this paper, we discuss a more general situation where both the observation and the follow‐up processes may be related with the recurrent event process of interest. For regression analysis, we present a class of semiparametric transformation models and develop some estimating equations for estimation of regression parameters. Numerical studies under different settings conducted for assessing the proposed methodology suggest that it works well for practical situations, and the approach is applied to a skin cancer study that motivated the study. Copyright © 2013 John Wiley & Sons, Ltd.     

Health and wealth of elderly couples: causality tests using dynamic panel data models

A positive relationship between socio-economic status (SES) and health, the "health-wealth gradient", is repeatedly found in many industrialized countries. This study analyzes competing explanations for this gradient: causal effects from health to wealth (health causation) and causal effects from wealth to health (wealth or social causation). Using six biennial waves of couples aged 51-61 in 1992 from the US Health and Retirement Study, we test for causality in panel data models incorporating unobserved heterogeneity and a lag structure supported by specification tests. In contrast to tests relying on models with only first order lags or without unobserved heterogeneity, these tests provide no evidence of causal wealth health effects. On the other hand, we find strong evidence of causal effects from both spouses' health on household wealth. We also find an effect of the husband's health on the wife's mental health, but no other effects from one spouse's health to health of the other spouse.     

Using test-retest reliability data to improve estimates of relative risk: an application of latent class analysis

The paper discusses the problem of interval estimation for the relative risk when some test-retest data are available on random subsamples drawn from case-control studies. It is shown that, although the upper portion of the interval may be very wide indeed, the lower bound of the interval estimate may be improved considerably by the collection of even modest amounts of repeat measurements.     

Sequential analysis of latent variables using mixed-effect latent variable models: Impact of non-informative and informative missing data

Sequential methods allowing for early stopping of clinical trials are widely used in various therapeutic areas. These methods allow for the analysis of different types of endpoints (quantitative, qualitative, time to event) and often provide, in average, substantial reductions in sample size as compared with single-stage designs while maintaining pre-specified type I and II errors. Sequential methods are also used when analysing particular endpoints that cannot be directly measured, such as depression, quality of life, or cognitive functioning, which are often measured through questionnaires. These types of endpoints are usually referred to as latent variables and should be analysed with latent variable models. In addition, in most clinical trials studying such latent variables, incomplete data are not uncommon and the missing data process might also be non-ignorable. We investigated the impact of informative or non-informative missing data on the statistical properties of the double triangular test (DTT), combined with the mixed-effects Rasch model (MRM) for dichotomous responses or the traditional method based on observed patient's scores (S) to the questionnaire. The achieved type I errors for the DTT were usually close to the target value of 0.05 for both methods, but increased slightly for the MRM when informative missing data were present. The DTT was very close to the nominal power of 0.95 when the MRM was used, but substantially underpowered with the S method (reduction of about 23 per cent), irrespective of whether informative missing data were present or not. Moreover, the DTT using the MRM allowed for reaching a conclusion (under H(0) or H(1)) with fewer patients than the S method, the average sample number for the latter increasing importantly when the proportion of missing data increased. Incorporating MRM in sequential analysis of latent variables might provide a more powerful method than the traditional S method, even in the presence of non-informative or informative missing data.     

A joint latent class analysis for adjusting survival bias with application to a trauma transfusion study

There is no clear classification rule to rapidly identify trauma patients who are severely hemorrhaging and may need substantial blood transfusions. Massive transfusion (MT), defined as the transfusion of at least 10 units of red blood cells within 24 h of hospital admission, has served as a conventional surrogate that has been used to develop early predictive algorithms and establish criteria for ordering an MT protocol from the blood bank. However, the conventional MT rule is a poor proxy, because it is likely to misclassify many severely hemorrhaging trauma patients as they could die before receiving the 10th red blood cells transfusion. In this article, we propose to use a latent class model to obtain a more accurate and complete metric in the presence of early death. Our new approach incorporates baseline patient information from the time of hospital admission, by combining respective models for survival time and usage of blood products transfused within the framework of latent class analysis. To account for statistical challenges, caused by induced dependent censoring inherent in 24‐h sums of transfusions, we propose to estimate an improved standard via a pseudo‐likelihood function using an expectation‐maximization algorithm with the inverse weighting principle. We evaluated the performance of our new standard in simulation studies and compared with the conventional MT definition using actual patient data from the Prospective Observational Multicenter Major Trauma Transfusion study. Copyright © 2015 John Wiley & Sons, Ltd.     

Mixture models for cancer survival analysis: application to population-based data with covariates

The interest in estimating the probability of cure has been increasing in cancer survival analysis as the curability of many cancer diseases is becoming a reality. Mixture survival models provide a way of modelling time to death when cure is possible, simultaneously estimating death hazard of fatal cases and the proportion of cured case. In this paper we propose an application of a parametric mixture model to relative survival rates of colon cancer patients from the Finnish population-based cancer registry, and including major survival determinants as explicative covariates. Disentangling survival into two different components greatly facilitates the analysis and the interpretation of the role of prognostic factors on survival patterns. For example, age plays a different role in determining, from one side, the probability of cure, and, from the other side, the life expectancy of fatal cases. The results support the hypothesis that observed survival trends are really due to a real prognostic gain for more recently diagnosed patients.     

Flexible models for the analysis of growth data with an application to height prediction

We show how recent developments in the theory of multilevel statistical modelling can be applied to the analysis of growth data and in particular to the prediction of adult height. This approach is both statistically efficient and very flexible.     

Functional linear models for zero‐inflated count data with application to modeling hospitalizations in patients on dialysis

We propose functional linear models for zero‐inflated count data with a focus on the functional hurdle and functional zero‐inflated Poisson (ZIP) models. Although the hurdle model assumes the counts come from a mixture of a degenerate distribution at zero and a zero‐truncated Poisson distribution, the ZIP model considers a mixture of a degenerate distribution at zero and a standard Poisson distribution. We extend the generalized functional linear model framework with a functional predictor and multiple cross‐sectional predictors to model counts generated by a mixture distribution. We propose an estimation procedure for functional hurdle and ZIP models, called penalized reconstruction, geared towards error‐prone and sparsely observed longitudinal functional predictors. The approach relies on dimension reduction and pooling of information across subjects involving basis expansions and penalized maximum likelihood techniques. The developed functional hurdle model is applied to modeling hospitalizations within the first 2 years from initiation of dialysis, with a high percentage of zeros, in the Comprehensive Dialysis Study participants. Hospitalization counts are modeled as a function of sparse longitudinal measurements of serum albumin concentrations, patient demographics, and comorbidities. Simulation studies are used to study finite sample properties of the proposed method and include comparisons with an adaptation of standard principal components regression. Copyright © 2014 John Wiley & Sons, Ltd.     

伴有协变量的潜在类别模型在出生缺陷预防知识分析中的应用

目的 探讨伴有协变量的潜在类别模型在两分类资料聚类分析中的应用。方法 利用伴有协变量的潜在类别模型对南京市鼓楼区建围产期保健小卡的3 739例孕妇的出生缺陷预防知识调查问卷进行聚类分析。结果 将孕妇的出生缺陷预防知识知晓率分成高、中、低3个类别,分别有2 093人(55.98%)、1 431人(38.27%)与215人(5.75%)。15个条目的因子载荷介于0.0857到0.5131之间,不同教育程度、不同职业及不同家庭人均月收入的知晓率在3个类所占比重的差异较大。结论 潜在类别模型可用于出生缺陷预防知识知晓率的聚类分析,考虑教育程度、职业及家庭人均月收入为协变量是有必要的。     

Bayesian penalized spline models for the analysis of spatio‐temporal count data

In recent years, the availability of infectious disease counts in time and space has increased, and consequently, there has been renewed interest in model formulation for such data. In this paper, we describe a model that was motivated by the need to analyze hand, foot, and mouth disease surveillance data in China. The data are aggregated by geographical areas and by week, with the aims of the analysis being to gain insight into the space–time dynamics and to make short‐term predictions, which will aid in the implementation of public health campaigns in those areas with a large predicted disease burden. The model we develop decomposes disease‐risk into marginal spatial and temporal components and a space–time interaction piece. The latter is the crucial element, and we use a tensor product spline model with a Markov random field prior on the coefficients of the basis functions. The model can be formulated as a Gaussian Markov random field and so fast computation can be carried out using the integrated nested Laplace approximation approach. A simulation study shows that the model can pick up complex space–time structure and our analysis of hand, foot, and mouth disease data in the central north region of China provides new insights into the dynamics of the disease. Copyright © 2015 John Wiley & Sons, Ltd.     

A demonstration of modeling count data with an application to physical activity

Objectives

To introduce a new, patient-oriented predictive index as a measure of gain in certainty.

Study design

Algebraic equations.

Results

A new measure is suggested based on error rates in a patient population. The new Predictive Summary Index (PSI) reflects the true total gain in certainty obtained by performing a diagnostic test based on knowledge of disease prevalence, i.e., the overall additional certainty. We show that the overall gain in certainty can be expressed in the form of the following expression: PSI = PPV+NPV-1. PSI is a more comprehensive measure than the post-test probability or the Youden Index (J). The reciprocal of J is interpreted as the number of persons with a given disease who need to be examined in order to detect correctly one person with the disease. The reciprocal of PSI is suggested as the number of persons who need to be examined in order to correctly predict a diagnosis of the disease.

Conclusion

PSI provides more information than J and the predictive values, making it more appropriate in a clinical setting.     

Zero-inflated models for regression analysis of count data: a study of growth and development

Poisson regression is widely used in medical studies, and can be extended to negative binomial regression to allow for heterogeneity. When there is an excess number of zero counts, a useful approach is to used a mixture model with a proportion P of subjects not at risk, and a proportion of 1--P at-risk subjects who take on outcome values following a Poisson or negative binomial distribution. Covariate effects can be incorporated into both components of the models. In child assessment, fine motor development is often measured by test items that involve a process of imitation and a process of fine motor exercise. One such developmental milestone is 'building a tower of cubes'. This study analyses the impact of foetal growth and postnatal somatic growth on this milestone, operationalized as the number of cubes and measured around the age of 22 months. It is shown that the two aspects of early growth may have different implications for imitation and fine motor dexterity. The usual approach of recording and analysing the milestone as a binary outcome, such as whether the child can build a tower of three cubes, may leave out important information.     

Developmental typology of trajectories to nighttime bladder control: epidemiologic application of longitudinal latent class analysis

The authors aimed to characterize developmental trajectories to nighttime continence by applying two latent class models-longitudinal latent class analysis (LLCA) and latent class growth analysis (LCGA)-to data on nighttime bed-wetting from a population-based birth cohort, the Medical Research Council 1946 National Survey of Health and Development cohort. Data on a binary outcome (wetting in the past month vs. not wetting) were available for children at six ages (4, 6, 8, 9, 11, and 15 years) assessed in 1950, 1952, 1954, 1955, 1957, and 1961. For 3,272 children with complete data (62.5% of the cohort), results of sequential model comparisons (T classes vs. T + 1 classes) and chi-square goodness-of-fit tests were evaluated using parametric bootstrapping. At least four trajectory classes (LLCA and LCGA) were identified. Associations between class membership and the prevalence of related measures were examined using a confirmatory latent class analysis approach. Inclusion of 1,483 children with partially incomplete data (n = 4,755; 90.9% of the cohort) enabled the authors to refine trajectories further: normal development (prevalence = 84.0%); delayed acquisition of bladder control ("transient" (8.7%) and "persistent" (1.8%)), capturing primary enuresis; chronic bed-wetting (2.6%), or experiencing night wetting until age 15 years; and a final trajectory (relapse = 2.9%) capturing secondary or onset enuresis. This empirically based, typologic approach to analysis of extensive longitudinal data in a general population sample provides an alternative perspective to that offered by traditional diagnostic criteria.     

Analysis of overdispersed count data: application to the Human Papillomavirus Infection in Men (HIM) Study

The Poisson model can be applied to the count of events occurring within a specific time period. The main feature of the Poisson model is the assumption that the mean and variance of the count data are equal. However, this equal mean-variance relationship rarely occurs in observational data. In most cases, the observed variance is larger than the assumed variance, which is called overdispersion. Further, when the observed data involve excessive zero counts, the problem of overdispersion results in underestimating the variance of the estimated parameter, and thus produces a misleading conclusion. We illustrated the use of four models for overdispersed count data that may be attributed to excessive zeros. These are Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial models. The example data in this article deal with the number of incidents involving human papillomavirus infection. The four models resulted in differing statistical inferences. The Poisson model, which is widely used in epidemiology research, underestimated the standard errors and overstated the significance of some covariates.     

A nonlinear latent class model for joint analysis of multivariate longitudinal data and a binary outcome

We consider a joint model for exploring association between several correlated longitudinal markers and a clinical event. A nonlinear growth mixture model exhibits the different latent classes of evolution of the latent quantity underlying the correlated longitudinal markers and a logistic regression models the probability of occurence of the clinical event according to the latent classes. By introducing a flexible nonlinear transformation including parameters to be estimated between each marker and the latent process, the model also deals with non-Gaussian continuous markers. Through an application on cognitive ageing, the two advantages of the model are underlined: (1) the latent profiles of evolution associated with the clinical event are described including covariate effects in the longitudinal model but also in the probability of class membership and in the probability of occurence of the event, and (2) a diagnostic and a prognostic tools are derived from the model for early detection of the clinical event using any available information about the longitudinal markers.