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We explore models for the natural history of breast cancer, where the main events of interest are the start of asymptomatic detectability of the disease (through screening) and the time of symptomatic detection (through symptoms). We develop several parametric specifications based on a cure rate structure, and present the results of the analysis of data collected as part of a motivating study from Milan. Participants in the study were part of a regional breast cancer screening program, and their ten-year trajectories were obtained from administrative data available from the Italian national health care system. We first present a tractable model for which we develop the likelihood contributions of the observed trajectories and perform maximum likelihood inference on the latent process. Likelihood based inference is not feasible for more flexible models, and we implement approximate Bayesian computation (ABC) for inference. Issues that arise from the use of ABC for model choice and parameter estimation are discussed, including the problem of choosing appropriate summary statistics. The estimated parameters of the underlying disease process allow for the study of the effect of different examination schedules (age range and frequency of screening examinations) on a population of asymptomatic subjects.

Outcome values in randomized controlled trials (RCTs) may be missing not at random (MNAR), if patients with extreme outcome values are more likely to drop out (e.g., due to perceived ineffectiveness of treatment, or adverse effects). In such scenarios, estimates from complete case analysis (CCA) and multiple imputation (MI) will be biased. The trimmed means (TM) estimator operates by setting missing values to the most extreme value, and then “trimming” away equal fractions of both treatment groups, estimating the treatment effect using the remaining data. The TM estimator relies on two assumptions, which we term the “strong MNAR” and “location shift” assumptions. In this article, we derive formulae for the bias resulting from the violation of these assumptions for normally distributed outcomes. We propose an adjusted estimator, which relaxes the location shift assumption and detail how our bias formulae can be used to establish the direction of bias of CCA, MI and TM estimates under a range of plausible data scenarios, to inform sensitivity analyses. The TM approach is illustrated with simulations and in a sensitivity analysis of the CoBalT RCT of cognitive behavioural therapy (CBT) in 469 individuals with 46 months follow-up. Results were consistent with a beneficial CBT treatment effect. The MI estimates are closer to the null than the CCA estimate, whereas the TM estimate was further from the null. We propose using the TM estimator as a sensitivity analysis for data where it is suspected that extreme outcome values are missing.

Multiple endpoints and historical data borrowing may be simultaneously incorporated for enhancing efficiency and speeding up the new drug development process in the pharmaceutical industry. O'Brien's test is a widely used weighted combination test for multiplicity adjustment on multiple endpoints to control the overall type error rate in a weak sense. In this research, a modification on the O'Brien's test more specifically on the weights is considered for a trial with two primary endpoints to potentially increase power. The method can handle missing data in the current study and in the prior derivation for dynamic historical data borrowing. Simulations are conducted to compare the performances of different methods. A data example is used to illustrate the applications of the methods.

Jointly analyzing transcriptomic data and the existing biological networks can yield more robust and informative feature selection results, as well as better understanding of the biological mechanisms. Selecting and classifying node features over genome-scale networks has become increasingly important in genomic biology and genomic medicine. Existing methods have some critical drawbacks. The first is they do not allow flexible modeling of different subtypes of selected nodes. The second is they ignore nodes with missing values, very likely to increase bias in estimation. To address these limitations, we propose a general modeling framework for Bayesian node classification (BNC) with missing values. A new prior model is developed for the class indicators incorporating the network structure. For posterior computation, we resort to the Swendsen-Wang algorithm for efficiently updating class indicators. BNC can naturally handle missing values in the Bayesian modeling framework, which improves the node classification accuracy and reduces the bias in estimating gene effects. We demonstrate the advantages of our methods via extensive simulation studies and the analysis of the cutaneous melanoma dataset from The Cancer Genome Atlas.

In the field of materials science and engineering, statistical analysis and machine learning techniques have recently been used to predict multiple material properties from an experimental design. These material properties correspond to response variables in the multivariate regression model. This study conducts a penalized maximum likelihood procedure to estimate model parameters, including the regression coefficients and covariance matrix of response variables. In particular, we employ $l_1$-regularization to achieve a sparse estimation of regression coefficients and the inverse covariance matrix of response variables. In some cases, there may be a relatively large number of missing values in response variables, owing to the difficulty in collecting data on material properties. A method to improve prediction accuracy under the situation with missing values incorporates a correlation structure among the response variables into the statistical model. The expectation and maximization algorithm is constructed, which enables application to a data set with missing values in the responses. We apply our proposed procedure to real data consisting of 22 material properties., 18 pages

Missing data are common in longitudinal cohort studies and can lead to bias, particularly in studies with informative missingness. Many common methods for handling informatively missing data in survey samples require correctly specifying a model for missingness. Although doubly robust methods exist to provide unbiased regression coefficients in the presence of missing outcome data, these methods do not account for correlation due to clustering inherent in longitudinal or cluster-sampled studies. In this work, we developed a doubly robust method to estimate the regression of an outcome on a predictor in the presence of missing multilevel data on the outcome, which results in consistent estimation of regression coefficients assuming correct specification of either (1) the probability of missingness or (2) the outcome model. This method involves specification of separate hierarchical models for missingness and for the outcome, conditional on observed auxiliary variables and cluster-specific random effects, to account for correlation among observations. We showed this proposed estimator is doubly robust and derived its asymptotic distribution, conducted simulation studies to compare the method to an existing doubly robust method developed for independent data, and applied the method to data from the China Health and Nutrition Survey, an ongoing multilevel longitudinal cohort study.

Two-phase designs can reduce the cost of epidemiological studies by limiting the ascertainment of expensive covariates or/and exposures to an efficiently selected subset (phase-II) of a larger (phase-I) study. Efficient analysis of the resulting data set combining disparate information from phase-I and phase-II, however, can be complex. Most of the existing methods, including semiparametric maximum-likelihood estimator, require the information in phase-I to be summarized into a fixed number of strata. In this paper, we describe a novel method for the analysis of two-phase studies where information from phase-I is summarized by parameters associated with a reduced logistic regression model of the disease outcome on available covariates. We then setup estimating equations for parameters associated with the desired extended logistic regression model, based on information on the reduced model parameters from phase-I and complete data available at phase-II after accounting for nonrandom sampling design. We use generalized method of moments to solve overly identified estimating equations and develop the resulting asymptotic theory for the proposed estimator. Simulation studies show that the use of reduced parametric models, as opposed to summarizing data into strata, can lead to more efficient utilization of phase-I data. An application of the proposed method is illustrated using the data from the U.S. National Wilms Tumor Study.

Many machine learning algorithms depend on weights that quantify row and column similarities of a data matrix. The choice of weights can dramatically impact the effectiveness of the algorithm. Nonetheless, the problem of choosing weights has arguably not been given enough study. When a data matrix is completely observed, Gaussian kernel affinities can be used to quantify the local similarity between pairs of rows and pairs of columns. Computing weights in the presence of missing data, however, becomes challenging. In this paper, we propose a new method to construct row and column affinities even when data are missing by building off a co-clustering technique. This method takes advantage of solving the optimization problem for multiple pairs of cost parameters and filling in the missing values with increasingly smooth estimates. It exploits the coupled similarity structure among both the rows and columns of a data matrix. We show these affinities can be used to perform tasks such as data imputation, clustering, and matrix completion on graphs.

Missing data are a major complication in longitudinal data analysis. Weighted generalized estimating equations (WGEEs, Robins et al, J Am Stat Assoc 1995;90:106-121) were developed to deal with missing response data. They have been extended for data with both missing responses and missing covariates (Chen et al, J Am Stat Assoc 2010;105:336-353). However, it may introduce more variability in dealing with the correlation structure of the responses. We propose new WGEEs for missing at random data where both response and (time-dependent) covariates may have values missing in nonmonotone missing data patterns. We also explain how to improve the estimation efficiency of WGEEs using a unified approach (Zhao and Liu, AStA Adv Stat Anal 2021;105(1):87-101). The proposed unified estimator is consistent and more efficient than the regular WGEE estimator. It is computationally simple and can be directly implemented in standard software. Simulation studies for both continuous response and binary response data are provided to examine the performance of the proposed estimators. A clinical trial example investigating the quality of life of women with early-stage breast cancer and the associated factors is analyzed.

Study designs where data have been aggregated by geographical areas are popular in environmental epidemiology. These studies are commonly based on administrative databases and, providing a complete spatial coverage, are particularly appealing to make inference on the entire population. However, the resulting estimates are often biased and difficult to interpret due to unmeasured confounders, which typically are not available from routinely collected data. We propose a framework to improve inference drawn from such studies exploiting information derived from individual-level survey data. The latter are summarized in an area-level scalar score by mimicking at ecological level the well-known propensity score methodology. The literature on propensity score for confounding adjustment is mainly based on individual-level studies and assumes a binary exposure variable. Here, we generalize its use to cope with area-referenced studies characterized by a continuous exposure. Our approach is based upon Bayesian hierarchical structures specified into a two-stage design: (i) geolocated individual-level data from survey samples are up-scaled at ecological level, then the latter are used to estimate a generalized ecological propensity score (EPS) in the in-sample areas; (ii) the generalized EPS is imputed in the out-of-sample areas under different assumptions about the missingness mechanisms, then it is included into the ecological regression, linking the exposure of interest to the health outcome. This delivers area-level risk estimates, which allow a fuller adjustment for confounding than traditional areal studies. The methodology is illustrated by using simulations and a case study investigating the risk of lung cancer mortality associated with nitrogen dioxide in England (UK).

Diverse large cohorts are necessary for dissecting subtypes of autism, and intellectual disability is one of the most robust endophenotypes for analysis. However, current cognitive assessment methods are not feasible at scale. We developed five commonly used machine learning models to predict cognitive impairment (FSIQ

PURPOSE A rapid real-time 2D accelerated method was developed for magnetic resonance imaging (MRI) using principal component analysis (PCA) in the temporal domain. This method employs a moving window of previous dynamic frames to reconstruct the current, real-time frame within this window. This technique could be particularly useful in real-time tracking applications such as in MR-guided radiotherapy, where low latency real-time reconstructions are essential. METHODS The method was tested retrospectively on 15 fully-sampled data sets of lung patient data acquired on a 3T Philips Achieva system. High frequency data are incoherently undersampled, while the central low-frequency data are always acquired to characterize the temporal fluctuations through PCA. The undersampling pattern is derived in such a way that all of k-space is acquired within a pre-determined number of frames. The missing data in the current frame are then filled in by fitting the temporal characterizations to the acquired undersampled data, using a pre-determined number of PCs. A subset of six patients was used to test the contour ability of the images. Various accelerations between 3x and 8x were tested along with the optimal number of PCs for fitting. A comparison was also performed with previous work from our group proposed by Dietz et al. as well as with a standard low resolution acquisition. In order to determine how the method would perform at lower signal to noise ratio (SNR), noise levels of 2×, 4×, and 6× were added to the 3T data. Metrics such as normalised mean square error and Dice coefficient were used to measure the reconstruction image quality and contour ability. RESULTS The proposed method demonstrated good temporal robustness as consistent metrics were detected for the duration of the imaging session. It was found that the optimal number of PCs for temporal fitting was dependent on the acceleration rate. For the data tested, five PCs were found to be optimal at the acceleration rates of 3× and 4×. This number decreases to three at accelerations of 5× and 6× and further decreases to two at an acceleration rate of 8×, likely due to greater instability with fewer acquired data points. The use of too many PCs for fitting increased the chances of noisy reconstruction which affected contourability. CONCLUSIONS The proposed 2D real-time MR acceleration method demonstrated greater robustness in the metrics over time when compared with previous real-time PCA methods using metrics such as normalised mean squared error, peak SNR and structural similarity up to an acceleration of 8x. Improved temporal robustness of image structure contourability and accurate definition was also demonstrated using several metrics including the Dice coefficient. Reconstruction of raw acquired data can be performed at approximately 50 ms per frame using an Intel core i5 CPU. The method has the advantage of being very flexible in terms of hardware requirements as it can operate successfully on a single coil channel and does not require specialized computing power to implement in real-time.

Population genetic studies in non-model systems increasingly use next-generation sequencing to obtain more loci, but such methods also generate more missing data that may affect downstream analyses. Here we focus on the principal component analysis (PCA) which has been widely used to explore and visualize population structure with mean-imputed missing data. We simulated data of different population models with various total missingness (1%, 10%, 20%) introduced either randomly or biased among individuals or populations. We found that individuals biased with missing data would be dragged away from their real population clusters to the origin of PCA plots, making them indistinguishable from true admixed individuals and potentially leading to misinterpreted population structure. We also generated empirical data of the big brown bat (Eptesicus fuscus) using restriction site-associated DNA sequencing (RADseq). We filtered three data sets with 19.12%, 9.87%, and 1.35% total missingness, all showing nonrandom missing data with biased individuals dragged towards the PCA origin, consistent with results from simulations. We highlight the importance of considering missing data effects on PCA in non-model systems where nonrandom missing data are common due to varying sample quality. To help detect missing data effects, we suggest to (1) plot PCA with a colour gradient showing per sample missingness, (2) interpret samples close to the PCA origin with extra caution, (3) explore filtering parameters with and without the missingness-biased samples, and (4) use complementary analyses (e.g., model-based methods) to cross-validate PCA results and help interpret population structure.

We rank counties in the United States with respect to population health. We utilize the five observable county health variables used to construct the University of Wisconsin Population Health Institute's County Health Rankings (CHRs). Our method relies on a Bayesian factor analysis model that estimates data-driven weights for our rankings, incorporates county population sizes into the level of rank uncertainty, and allows for spillovers of health stock across county lines. We find that demographic and economic variation explains a large portion of the variation in health rankings. We address the importance of uncertainty caused by imputation of missing data and show that there is a substantial quantity of uncertainty in rankings throughout the rank distribution. Analyzing the health of counties both within and across state lines shows notable degrees of disparity in county health. While we find some disagreement between the ranks of our model and the CHRs, we show that there is additional information gained by utilizing the rankings produced by both methods.

Aim Increasing evidence points to the value of coordinated specialty care (CSC) for early intervention in psychotic disorders. This report characterizes clinical and socio-demographic features of patients at CSC programs in Massachusetts (MA), assessed by a standardized battery incorporated into "real-world" clinical care. Methods The MA psychosis network for early treatment developed a pilot battery to coordinate assessments across six CSC clinics. Programs reported baseline, 6-month, and 12-month data from a sample of 287 patients with intake dates ranging from April 2015 to December 2020. Results Patients showed improvements in functioning, emergency service use and several symptom domains at 6 and 12 months. Missing data proved to be a limitation. Conclusions Patients improved on several meaningful domains within the first year of CSC treatment. Future implementation efforts in cross-program data collection should consider strategies to circumvent limitations related to heterogeneity between clinics, patient discharge and clinics' capacity for data collection.

Purpose Magnetic resonance (MR) imaging is an essential diagnostic tool in clinical medicine. Recently, a variety of deep-learning methods have been applied to segmentation tasks in medical images, with promising results for computer-aided diagnosis. For MR images, effectively integrating different pulse sequences is important to optimize performance. However, the best way to integrate different pulse sequences remains unclear. In addition, networks trained with a certain subset of pulse sequences as input are unable to perform when given a subset of those pulse sequences. In this study, we evaluate multiple architectural features and characterize their effects in the task of metastasis segmentation while creating a method to robustly train a network to be able to work given any strict subset of the pulse sequences available during training. Methods We use a 2.5D DeepLabv3 segmentation network to segment metastases lesions on brain MR's with four pulse sequence inputs. To study how we can best integrate MR pulse sequences for this task, we consider (1) different pulse sequence integration schemas, combining our features at early, middle, and late points within a deep network, (2) different modes of weight sharing for parallel network branches, and (3) a novel integration level dropout layer, which will allow the networks to be robust to performing inference on input with only a subset of pulse sequences available at the training. Results We find that levels of integration and modes of weight sharing that favor low variance work best in our regime of small amounts of training data (n = 100). By adding an input-level dropout layer, we could preserve the overall performance of these networks while allowing for inference on inputs with missing pulse sequences. We illustrate not only the generalizability of the network but also the utility of this robustness when applying the trained model to data from a different center, which does not use the same pulse sequences. Finally, we apply network visualization methods to better understand which input features are most important for network performance. Conclusions Together, these results provide a framework for building networks with enhanced robustness to missing data while maintaining comparable performance in medical imaging applications.

The ISNI (index of sensitivity to local nonignorability) method quantifies local sensitivity of parametric inferences to nonignorable missingness in an outcome variable. Here we extend ISNI to the situations where both outcomes and predictors can be missing and where the missingness mechanism can be either parametric or semi-parametric. We define the quantity MinNI (minimum nonignorability) to be an approximation to the norm of the smallest value of the transformed nonignorability that gives a nonnegligible displacement of the estimate of the parameter of interest. We illustrate our method in a complete data set from which we synthetically delete observations according to various patterns. We then apply the method to real-data examples involving the normal linear model and conditional logistic regression.

INTRODUCTION: Population-based biomarker surveys are the gold standard for estimating HIV prevalence but are susceptible to substantial non-participation (up to 30%). Analytical missing data methods, including inverse-probability weighting (IPW) and multiple imputation (MI), are biased when data are missing-not-at-random, for example when people living with HIV more frequently decline participation. Heckman-type selection models can, under certain assumptions, recover unbiased prevalence estimates in such scenarios. METHODS: We pooled data from 142,706 participants aged 15-49 years from nationally representative cross-sectional Population-based HIV Impact Assessments in seven countries in sub-Saharan Africa, conducted between 2015 and 2018 in Tanzania, Uganda, Malawi, Zambia, Zimbabwe, Lesotho and Eswatini. We compared sex-stratified HIV prevalence estimates from unadjusted, IPW, MI and selection models, controlling for household and individual-level predictors of non-participation, and assessed the sensitivity of selection models to the copula function specifying the correlation between study participation and HIV status. RESULTS: In total, 84.1% of participants provided a blood sample to determine HIV serostatus (range: 76% in Malawi to 95% in Uganda). HIV prevalence estimates from selection models diverged from IPW and MI models by up to 5% in Lesotho, without substantial precision loss. In Tanzania, the IPW model yielded lower HIV prevalence estimates among males than the best-fitting copula selection model (3.8% vs. 7.9%). CONCLUSIONS: We demonstrate how HIV prevalence estimates from selection models can differ from those obtained under missing-at-random assumptions. Further benefits include exploration of plausible relationships between participation and outcome. While selection models require additional assumptions and careful specification, they are an important tool for triangulating prevalence estimates in surveys with substantial missing data due to non-participation.

Inbreeding can lead to a loss of heterozygosity in a population and when combined with genetic drift may reduce the adaptive potential of a species. However, there is uncertainty about whether resequencing data can provide accurate and consistent inbreeding estimates. Here, we performed an in-depth inbreeding analysis for hihi (Notiomystis cincta), an endemic and nationally vulnerable passerine bird of Aotearoa New Zealand. We first focused on subsampling variants from a reference genome male, and found that low-density data sets tend to miss runs of homozygosity (ROH) in some places and overestimate ROH length in others, resulting in contrasting homozygosity landscapes. Low-coverage resequencing and 50 K SNP array densities can yield comparable inbreeding results to high-coverage resequencing approaches, but the results for all data sets are highly dependent on the software settings employed. Second, we extended our analysis to 10 hihi where low-coverage whole genome resequencing, RAD-seq and SNP array genotypes are available. We inferred ROH and individual inbreeding to evaluate the relative effects of sequencing depth versus SNP density on estimating inbreeding coefficients and found that high rates of missingness downwardly bias both the number and length of ROH. In summary, when using genomic data to evaluate inbreeding, studies must consider that ROH estimates are heavily dependent on analysis parameters, data set density and individual sequencing depth.

Ecological and evolutionary research questions are increasingly requiring the integration of research fields along with larger data sets to address fundamental local‐ and global‐scale problems. Unfortunately, these agendas are often in conflict with limited funding and a need to balance animal welfare concerns. Planned missing data design (PMDD), where data are randomly and deliberately missed during data collection, combined with missing data procedures, can be useful tools when working under greater research constraints. Here, we review how PMDD can be incorporated into existing experimental designs by discussing alternative design approaches and demonstrate with simulated data sets how missing data procedures work with incomplete data. PMDDs can provide researchers with a unique toolkit that can be applied during the experimental design stage. Planning and thinking about missing data early can (1) reduce research costs by allowing for the collection of less expensive measurement variables; (2) provide opportunities to distinguish predictions from alternative hypotheses by allowing more measurement variables to be collected; and (3) minimize distress caused by experimentation by reducing the reliance on invasive procedures or allowing data to be collected on fewer subjects (or less often on a given subject). PMDDs and missing data methods can even provide statistical benefits under certain situations by improving statistical power relative to a complete case design. The impacts of unplanned missing data, which can cause biases in parameter estimates and their uncertainty, can also be ameliorated using missing data procedures. PMDDs are still in their infancy. We discuss some of the difficulties in their implementation and provide tentative solutions. While PMDDs may not always be the best option, missing data procedures are becoming more sophisticated and more easily implemented and it is likely that PMDDs will be effective tools for a wide range of experimental designs, data types and problems in ecology and evolution.

To optimize cyclosporine A (CsA) dosing regimen in pediatric patients undergoing hematopoietic stem cell transplantation (HSCT), we aimed to provide clinicians with a validated decision support tool for determining the most suitable first dose of intravenous CsA. We used a 10-year monocentric data set of pediatric patients undergoing HSCT. Discretization of all variables was performed according to literature or thanks to algorithms using Shannon entropy (from information theory) or equal width intervals. The first 8 years were used to build the Bayesian network model. This model underwent a 10-fold cross-validation, and then a prospective validation with data of the last 2 years. There were 3.3% and 4.1% of missing values in the training and the validation data set, respectively. After prospective validation, the Tree-Augmented Naïve Bayesian network shows interesting prediction performances with an average area under the receiver operating characteristic curve of 0.804, 32.8% of misclassified patients, a true-positive rate of 0.672, and a false-positive rate of 0.285. This validated model allows good predictions to propose an optimized and personalized initial CsA dose for pediatric patients undergoing HSCT. The clinical impact of its use should be further evaluated.

Multiple public health and medical research studies have applied matched-pair cluster randomization design to the evaluation of the intervention and/or prevention effects. One of the most common and severe problems faced by researchers when conducting cluster randomized trials (CRTs) is incomplete observations, which are associated with various reasons causing the individuals to discontinue participating in the trials. Although statistical methods to remedy the problems of missing data have already been proposed, there are still methodological gaps in research concerning the determination of sample size in matched-pair CRTs with incomplete binary outcomes. One conventional method for adjusting for missing data in the sample size determination is to divide the sample size under complete data by the expected follow-up rate. However, such crude adjustment ignores the impact of the structure and strength of correlations regarding both outcome data and missing data mechanism. This article provides a closed-form sample size formula for matched-pair CRTs with incomplete binary outcomes, which appropriately accounts for different missing patterns and magnitudes as well as the effects of matching and clustering on the outcome and missing data. The generalized estimating equation (GEE) approach treats incomplete observations as missing data in a marginal logistic regression model, which flexibly accommodates various types of intraclass correlation, missing patterns, and missing proportions. In the presence of missing data, the proposed GEE sample size method provides higher accuracy as compared with the conventional method. The performance of the proposed method is assessed by simulation studies. This article also illustrates how the proposed method can be used to design a real-world matched-pair CRT to examine the effect of a team-based approach on controlling blood pressure (BP).

Chebyshev polynomials are used to extract from the data collected under non‐anechoic environment a radiation pattern for the same antenna radiating in free space conditions. The Cauchy method based on Gegenbauer polynomials is presented for antenna near‐field extrapolation and the far‐field estimation. Some numerical results are given to demonstrate the applicability of the proposed scheme in antenna near‐field extrapolation and far‐field estimation. Total least square (TLS) and singular value decomposition also suppress partially the effects of noise in the known data for extrapolation. The TLS solution for best data fitting shows an excellent performance for minimizing errors of interpolation in. TLS can also work well for extrapolating missing data on a small interval, which is quite similar to an interpolation problem with several sample points removed. However, an interesting result of zenith‐directed reflector antenna configuration is that the hole was able to be expanded significantly without increasing the error of the interpolation.