Statistical Analysis with Missing Data

Functional connectivity networks, derived from resting-state fMRI data, have been found as effective biomarkers for identifying mild cognitive impairment (MCI) from healthy elderly. However, the traditional functional connectivity network is essentially a low-order network with the assumption that the brain activity is static over the entire scanning period, ignoring temporal variations among the correlations derived from brain region pairs. To overcome this limitation, we proposed a new type of sparse functional connectivity network to precisely describe the relationship of temporal correlations among brain regions. Specifically, instead of using the simple pairwise Pearson’s correlation coefficient as connectivity, we first estimate the temporal low-order functional connectivity for each region pair based on an ULS Group constrained-UOLS regression algorithm, where a combination of ultra-least squares (ULS) criterion with a Group constrained topology structure detection algorithm is applied to detect the topology of functional connectivity networks, aided by an Ultra-Orthogonal Least Squares (UOLS) algorithm to estimate connectivity strength. Compared to the classical least squares criterion which only measures the discrepancy between the observed signals and the model prediction function, the ULS criterion takes into consideration the discrepancy between the weak derivatives of the observed signals and the model prediction function and thus avoids the overfitting problem. By using a similar approach, we then estimate the high-order functional connectivity from the low-order connectivity to characterize signal flows among the brain regions. We finally fuse the low-order and the high-order networks using two decision trees for MCI classification. Experimental results demonstrate the effectiveness of the proposed method on MCI classification.

Fusion of ULS Group Constrained High- and Low-Order Sparse Functional Connectivity Networks for MCI Classification

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Analysis of ordinal data in clinical and experimental studies.

A Bayesian approach was developed, tested, and applied to model ordinal response data in monotone non-decreasing processes with measurement errors. An inhomogeneous hidden Markov model with continuous state-space was considered to incorporate measurement errors in the categorical response at the same time that the non-decreasing patterns were kept. The computational difficulties were avoided by including latent variables that allowed implementing an efficient Markov chain Monte Carlo method. A simulation-based analysis was carried out to validate the approach, whereas the proposed approach was applied to analyze aortic aneurysm progression data.

https://www.mdpi.com/2227-7390/8/4/622/pdf

A Hidden Markov Model to Address Measurement Errors in Ordinal Response Scale and Non-Decreasing Process

Dementia, including Alzheimer's Disease (AD), is a growing problem worldwide. Prevention or early detection of the disease or a prodromal cognitive decline is necessary. By means of our long-term follow-up "Vogel Study", we aim to predict the pathological cognitive decline of a German cohort (mean age was 73.9 ± 1.55 years at first visit) with three measurement time points within 6 years per participant. Especially in samples of the elderly and subjects with chronic or comorbid diseases, dropouts are one of the biggest problems of long-term studies. In contrast to the large number of research articles conducted on the course of dementia, little research has been done on the completion of treatment. To ensure unbiased and reliable predictors of cognitive decline from study completers, our objective was to determine predictors of dropout. We conducted multivariate analyses of (co-)variance (MANCOVAs) and multinomial logistic regression analyses to compare and predict the subject's dropout behavior at the second visit 3 years after baseline (full participation, partial participation, no participation/dropout) with neuropsychiatric, cognitive, blood, and lifestyle variables. Lower performance in declarative memory, attention, and visual-spatial processing predicted dropout rather than full participation. Lower performance in visual-spatial processing predicted partial participation as opposed to full participation. Furthermore, lower performance in Mini-Mental Status Examination (MMSE) predicted whether subjects dropped out or participated partially instead of full participation. Baseline cognitive parameters are associated with dropouts at follow-up with a loss of impaired participants. We expect a bias into a healthier sample over time.

Factors associated with dropout in the longitudinal Vogel Study of cognitive decline

Analysis of ordinal longitudinal data under nonignorable missingness and misreporting: An application to Alzheimer’s disease study

The primary objective in this article is to look into the analysis of clustered ordinal model where complete information on one or more covariates cease to occur. In addition, we also focus on the analysis of miscategorized data that occur in many situations as outcomes are often classified into a category that does not truly reflect its actual state. A general model structure is assumed to accommodate the information that is obtained via surrogate variables. The theoretical motivation actually developed while encountering an orthodontic data to investigate the effects of age, sex and food habit on the extent of plaque deposit. The model we propose is quite flexible and is capable of tackling those additional noises like miscategorization and missingness, which occur in the data most frequently. A new two-step approach has been proposed to estimate the parameters of model framed. A rigorous simulation study has also been carried out to justify the validity of the model taken up for analysis. Copyright © 2015 John Wiley & Sons, Ltd.

Clustered data analysis under miscategorized ordinal outcomes and missing covariates

In many occasions, particularly in biomedical studies, data are unavailable for some responses and covariates. This leads to biased inference in the analysis when a substantial proportion of responses or a covariate or both are missing. Except a few situations, methods for missing data have earlier been considered either for missing response or for missing covariates, but comparatively little attention has been directed to account for both missing responses and missing covariates, which is partly attributable to complexity in modeling and computation. This seems to be important as the precise impact of substantial missing data depends on the association between two missing data processes as well. The real difficulty arises when the responses are ordinal by nature. We develop a joint model to take into account simultaneously the association between the ordinal response variable and covariates and also that between the missing data indicators. Such a complex model has been analyzed here by using the Markov chain Monte Carlo approach and also by the Monte Carlo relative likelihood approach. Their performance on estimating the model parameters in finite samples have been looked into. We illustrate the application of these two methods using data from an orthodontic study. Analysis of such data provides some interesting information on human habit.

On analyzing ordinal data when responses and covariates are both missing at random.

In clinical trials, patient's disease severity is usually assessed on a Likert-type scale. Patients, however, may miss one or more follow-up visits (non-monotone missing). The statistical analysis of non-Gaussian longitudinal data with non-monotone missingness is difficult to handle, particularly when both response and time-dependent covariates are subject to such missingness. Even when the number of patients with intermittent missing data is small, ignoring those patients from analysis seems to be unsatisfactory. The focus of the current investigation is to study the progression of Alzheimer's disease by incorporating a non-ignorable missing data mechanism for both response and covariates in a longitudinal setup. Combining the cumulative logit longitudinal model for Alzheimer's disease progression with the bivariate binary model for the missing pattern, we develop a joint likelihood. The parameters are then estimated using the Monte Carlo Newton Raphson Expectation Maximization (MCNREM) method. This approach is quite easy to handle and the convergence of the estimates is attained in a reasonable amount of time. The study reveals that apolipo-protein plays a significant role in assessing a patient's disease severity. A detailed simulation has also been carried out for justifying the performance of our approach.

Subrata Rana

Papers

Analysis of ordinal longitudinal data under nonignorable missingness and misreporting: An application to Alzheimer’s disease study

Clustered data analysis under miscategorized ordinal outcomes and missing covariates

On analyzing ordinal data when responses and covariates are both missing at random.

Evaluation of Alzheimer's disease progression based on clinical dementia rating scale with missing responses and covariates.