Conditional Independence Assumption Research Articles

Nonlinear mixed-effects modeling as a method for causal inference to predict exposures under desired within-subject dose titration schemes.

The ICH E9 (R1) guidance and the related estimand framework propose to clearly define and separate the clinical question of interest formulated as estimand from the estimation method. With that it becomes important to assess the validity of the estimation method and the assumptions that must be made. When going beyond the intention to treat analyses that can rely on randomization, causal inference is usually used to discuss the validity of estimation methods for the estimand of interest. In pharmacometrics, mixed-effects models are routinely used to analyze longitudinal clinical trial data; however, they are rarely discussed as a method for causal inference. Here, we evaluate nonlinear mixed-effects modeling and simulation (NLME M&S) in the context of causal inference as a standardization method for longitudinal data in the presence of confounders. Standardization is a well-known method in causal inference to correct for confounding by analyzing and combining results from subgroups of patients. We show that nonlinear mixed-effects modeling is a particular implementation of standardization that conditions on individual parameters described by the random effects of the mixed-effects model. As an example, we use a simulated clinical trial with within-subject dose titration. Being interested in the outcome of the hypothetical situation that patients adhere to the planned treatment schedule, we put assumptions in a causal diagram. From the causal diagram, conditional independence assumptions are derived either by conditioning on the individual parameters or on earlier outcomes. With both conditional independencies unbiased estimates can be obtained.

Shared parameter modeling of longitudinal data allowing for possibly informative visiting process and terminal event.

Joint modeling of longitudinal and time-to-event data, particularly through shared parameter models (SPMs), is a common approach for handling longitudinal marker data with an informative terminal event. A critical but often neglected assumption in this context is that the visiting/observation process is noninformative, depending solely on past marker values and visit times. When this assumption fails, the visiting process becomes informative, resulting potentially to biased SPM estimates. Existing methods generally rely on a conditional independence assumption, positing that the marker model, visiting process, and time-to-event model are independent given shared or correlated random effects. Moreover, they are typically built on an intensity-based visiting process using calendar time. This study introduces a unified approach for jointly modeling a normally distributed marker, the visiting process, and time-to-event data in the form of competing risks. Our model conditions on the history of observed marker values, prior visit times, the marker's random effects, and possibly a frailty term independent of the random effects. While our approach aligns with the shared-parameter framework, it does not presume conditional independence between the processes. Additionally, the visiting process can be defined on either a gap time scale, via proportional hazard models, or a calendar time scale, via proportional intensity models. Through extensive simulation studies, we assess the performance of our proposed methodology. We demonstrate that disregarding an informative visiting process can yield significantly biased marker estimates. However, misspecification of the visiting process can also lead to biased estimates. The gap time formulation exhibits greater robustness compared to the intensity-based model when the visiting process is misspecified. In general, enriching the visiting process with prior visit history enhances performance. We further apply our methodology to real longitudinal data from HIV, where visit frequency varies substantially among individuals.

Accuracy of CAD4TB (Computer-Aided Detection for Tuberculosis) on paediatric chest radiographs.

Computer-aided detection (CAD) systems hold promise for improving tuberculosis (TB) detection on digital chest radiographs. However, data on their performance in exclusively paediatric populations are scarce. We conducted a retrospective diagnostic accuracy study evaluating the performance of CAD4TBv7 (Computer-Aided Detection for Tuberculosis version 7) using digital chest radiographs from well-characterised cohorts of Gambian children aged <15 years with presumed pulmonary TB. The children were consecutively recruited between 2012 and 2022. We measured CAD4TBv7 performance against a microbiological reference standard (MRS) of confirmed TB, and also performed Bayesian latent class analysis (LCA) to address the inherent limitations of the MRS in children. Diagnostic performance was assessed using the area under the receiver operating characteristic curve (AUROC) and point estimates of sensitivity and specificity. A total of 724 children were included in the analysis, with confirmed TB in 58 (8%), unconfirmed TB in 145 (20%) and unlikely TB in 521 (72%). Using the MRS, CAD4TBv7 showed an AUROC of 0.70 (95% CI 0.60-0.79), and demonstrated sensitivity and specificity of 19.0% (95% CI 11-31%) and 99.0% (95% CI 98.0-100.0%), respectively. Applying Bayesian LCA with the assumption of conditional independence between tests, sensitivity and specificity estimates for CAD4TBv7 were 42.7% (95% CrI 29.2-57.5%) and 97.9% (95% CrI 96.6-98.8%), respectively. When allowing for conditional dependence between culture and Xpert assay, CAD4TBv7 demonstrated a sensitivity of 50.3% (95% CrI 32.9-70.0%) and specificity of 98.0% (95% CrI 96.7-98.9%). Although CAD4TBv7 demonstrated high specificity, its suboptimal sensitivity underscores the crucial need for optimisation of CAD4TBv7 for detecting TB in children.

Consistent tests for semiparametric conditional independence

We propose new joint tests of the semiparametric conditional independence assumption and provide their asymptotic properties. To overcome the problem caused by the parameter estimation effect, we employ a convenient multiplier bootstrap to approximate the limiting distributions of the test statistics.

A note on incorrect inferences in non-binary qualitative probabilistic networks

Qualitative probabilistic networks (QPNs) combine the conditional independence assumptions of Bayesian networks with the qualitative properties of positive and negative dependence. They formalise various intuitive properties of positive dependence to allow inferences over a large network of variables. However, we will demonstrate in this paper that, due to an incorrect symmetry property, many inferences obtained in non-binary QPNs are not mathematically true. We will provide examples of such incorrect inferences and briefly discuss possible resolutions.

Relational-branchformer: Novel framework for audio-visual speech recognition

This study embraced the state-of-the-art Branchformer series architecture within the realm of automatic speech recognition, supplanting the widely utilized Conformer architecture. This substitution offers an innovative remedy tailored to audio-visual speech recognition tasks. Building upon the Branchformer architecture, enhancements were made, culminating in the proposal of the Relational-Branchformer (R-Branchformer). The convolutional attention relation module was innovatively incorporated to augment the connectivity between the local and global branches by meticulously considering their interrelations and interplays. Consequently, this module facilitates the mutual embedding of local and global contextual information, ultimately leading to a substantial enhancement in model performance. Our model was grounded in the utilization of the connectionist temporal classification (CTC) loss, wherein intermediate CTC losses were incorporated between blocks. Moreover, through the reference and enhancement of the gated interlayer collaboration module, which superseded the inter CTC module, the conditional independence assumption intrinsic to the CTC model was effectively relaxed. As a consequence, this augmentation markedly bolstered the overall performance of our model. Furthermore, the audio-visual output enhancement module was proposed, which adeptly assimilates information from both audio and visual modalities to enrich the representation of audio-visual information. Consequently, the R-Branchformer model achieved remarkable word error rates of 1.7% and 1.5% on the LRS2 and LRS3 test sets, respectively, exemplifying its state-of-the-art performance in audio-visual speech recognition tasks.

Is private education worth it? Evidence from school-to-work transitions in Chile

Using comprehensive longitudinal data from Chile, we examine the impact of attending a private high school on labor market outcomes. The empirical strategy exploits conditional independence assumptions and leverages the effects of self-selection based on ability. We establish that private high schools boost average adult earnings by 99–144 dollars a month (relative to public schools), equivalent to a 15%–22% premium. We then explore potential channels behind these effects. Both academic and non-academic factors emerge as mediators. Our findings highlight the importance of financial resources, as education investments have long-term impacts on private high school students, while yielding negligible effects for those attending public and voucher schools. Finally, we document the prominent role of firms as mediators of the private school advantages during the school-to-work transition. Our analysis provides new insights into the association between school choice and income disparities, even after controlling for pre-labor market academic performance.

Nonparametric receiver operating characteristic curve analysis with an imperfect gold standard.

This article addresses the challenge of estimating receiver operating characteristic (ROC) curves and the areas under these curves (AUC) in the context of an imperfect gold standard, a common issue in diagnostic accuracy studies. We delve into the nonparametric identification and estimation of ROC curves and AUCs when the reference standard for disease status is prone to error. Our approach hinges on the known or estimable accuracy of this imperfect reference standard and the conditional independent assumption, under which we demonstrate the identifiability of ROC curves and propose a nonparametric estimation method. In cases where the accuracy of the imperfect reference standard remains unknown, we establish that while ROC curves are unidentifiable, the sign of the difference between two AUCs is identifiable. This insight leads us to develop a hypothesis-testing method for assessing the relative superiority of AUCs. Compared to the existing methods, the proposed methods are nonparametric so that they do not rely on the parametric model assumptions. In addition, they are applicable to both the ROC/AUC analysis of continuous biomarkers and the AUC analysis of ordinal biomarkers. Our theoretical results and simulation studies validate the proposed methods, which we further illustrate through application in two real-world diagnostic studies.

A naïve Bayes regularized logistic regression estimator for low-dimensional classification

To reduce the estimator's variance and prevent overfitting, regularization techniques have attracted great interest from the statistics and machine learning communities. Most existing regularized methods rely on the sparsity assumption that a model with fewer parameters predicts better than one with many parameters. This assumption works particularly well in high-dimensional problems. However, the sparsity assumption may not be necessary when the number of predictors is relatively small compared to the number of training instances. This paper argues that shrinking the coefficients towards a low-variance data-driven estimate could be a better regularization strategy for such situations. For low-dimensional classification problems, we propose a naïve Bayes regularized logistic regression (NBRLR) that shrinks the logistic regression coefficients toward the naïve Bayes estimate to provide a reduction in variance. Our approach is primarily motivated by the fact that naïve Bayes is functionally equivalent to logistic regression if naïve Bayes' conditional independence assumption holds. Under standard conditions, we prove the consistency of the NBRLR estimator. Extensive simulation and empirical experimental results show that NBRLR is a competitive alternative to various state-of-the-art classifiers, especially on low-dimensional datasets.

Image classification with symbolic hints using limited resources.

Typical machine learning classification benchmark problems often ignore the full input data structures present in real-world classification problems. Here we aim to represent additional information as "hints" for classification. We show that under a specific realistic conditional independence assumption, the hint information can be included by late fusion. In two experiments involving image classification with hints taking the form of text metadata, we demonstrate the feasibility and performance of the fusion scheme. We fuse the output of pre-trained image classifiers with the output of pre-trained text models. We show that calibration of the pre-trained models is crucial for the performance of the fused model. We compare the performance of the fusion scheme with a mid-level fusion scheme based on support vector machines and find that these two methods tend to perform quite similarly, albeit the late fusion scheme has only negligible computational costs.

Promises of parallel outcomes

Summary A key challenge in causal inference from observational studies is the identification and estimation of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel approach for causal inference that leverages information in multiple outcomes to deal with unmeasured confounding. An important assumption in our approach is conditional independence among multiple outcomes. In contrast to existing proposals in the literature, the roles of multiple outcomes in the conditional independence assumption are symmetric; hence, the name parallel outcomes. We show nonparametric identifiability with at least three parallel outcomes and provide parametric estimation tools under a set of linear structural equation models. Our proposal is evaluated through a set of synthetic and real data analyses.

A copula formulation for multivariate latent Markov models

AbstractWe specify a general formulation for multivariate latent Markov models for panel data, where outcomes are possibly of mixed-type (categorical, discrete, continuous). Conditionally on a time-varying discrete latent variable and covariates, the joint distribution of outcomes simultaneously observed is expressed through a parametric copula. We therefore do not make any conditional independence assumption. The observed likelihood is maximized by means of an expectation–maximization algorithm. In a simulation study, we argue how modeling the residual contemporary dependence might be crucial in order to avoid bias in the parameter estimates. We illustrate through an original application to assessment of poverty through direct and indirect indicators in a cohort of Italian households.

Micro-Macro Mediation Analysis in Social Networks

Mediation analysis is increasingly used in the social sciences. Extension to social network data, however, has proved difficult because statistical network models are formulated at a lower level of analysis (the dyad) than many outcomes of interest. This study introduces a general approach for micro-macro mediation analysis in social networks. The author defines the average mediated micro effect (AMME) as the indirect effect of a network selection process on an individual, group, or organizational outcome through its effect on an intervening network variable. The author shows that the AMME can be nonparametrically identified using a wide range of common statistical network and regression modeling strategies under the assumption of conditional independence among multiple mediators. Nonparametric and parametric algorithms are introduced to generically estimate the AMME in a multitude of research designs. The author illustrates the utility of the method with an applied example using cross-sectional National Longitudinal Study of Adolescent to Adult Health data to examine the friendship selection mechanisms that indirectly shape adolescent school performance through their effect on network structure.

No Eleventh Conditional Ingleton Inequality

A rational probability distribution on four binary random variables X , Y , Z , U is constructed which satisfies the conditional independence relations [ X ⊥ ⊥ Y ] , [ X ⊥ ⊥ Z | U ] , [ Y ⊥ ⊥ U | Z ] and [ Z ⊥ ⊥ U | X Y ] but whose entropy vector violates the Ingleton inequality. This settles a recent question of Studený (IEEE Trans. Inf. Theory vol. 67, no. 11) and shows that there are, up to symmetry, precisely ten inclusion-minimal sets of conditional independence assumptions on four discrete random variables which make the Ingleton inequality hold. The last case in the classification of which of these inequalities are essentially conditional is also settled.

Alleviating conditional independence assumption of naive Bayes

Alleviating conditional independence assumption of naive Bayes

Adjusted Residuals for Evaluating Conditional Independence in IRT Models for Multistage Adaptive Testing.

The key assumption of conditional independence of item responses given latent ability in item response theory (IRT) models is addressed for multistage adaptive testing (MST) designs. Routing decisions in MST designs can cause patterns in the data that are not accounted for by the IRT model. This phenomenon relates to quasi-independence in log-linear models for incomplete contingency tables and impacts certain types of statistical inference based on assumptions on observed and missing data. We demonstrate that generalized residuals for item pair frequencies under IRT models as discussed by Haberman and Sinharay (J Am Stat Assoc 108:1435-1444, 2013. https://doi.org/10.1080/01621459.2013.835660 ) are inappropriate for MST data without adjustments. The adjustments are dependent on the MST design, and can quickly become nontrivial as the complexity of the routing increases. However, the adjusted residuals are found to have satisfactory Type I errors in a simulation and illustrated by an application to real MST data from the Programme for International Student Assessment (PISA). Implications and suggestions for statistical inference with MST designs are discussed.

Spam filter based on naive bayes algorithm

The widespread use of Electronic Mail (E-mail) has led to a significant increase in spam, which has severely impeded the growth and well-being of the Internet. To mitigate this issue, the implementation of email filtering techniques has become necessary, requiring the use of specific technological tools. Presently, the K-Nearest Neighbor (KNN), Support Vector Machine (SVM), and Naive Bayes (NB) algorithms are commonly used in probability statistical classification methods for email filtering. Among these, the NB algorithm is the most classical, with its rich mathematical theory as the basis, high classification efficiency, and straightforward algorithmic approach. However, the algorithm relies on the conditional independence assumption, making the accuracy susceptible to the correlation between attributes. This study focuses on email filtering techniques based on the NB algorithm, conducting experiments to evaluate the classification accuracy and proposing feasible improvements to weaken the independence assumption. The experimental results demonstrated the effectiveness of the employed method.

A Flexible Probabilistic Framework With Concurrent Analysis of Continuous and Categorical Data for Industrial Fault Detection and Diagnosis

Operational data from industrial processes typically consist of continuous and categorical variables. They reveal different aspects of the operational conditions, and both are useful for comprehensive fault detection and diagnosis (FDD). However, due to the multiple production modes, the variables usually do not follow Gaussian or Bernoulli distributions. Furthermore, their correlations can be different across normal and various faulty classes. Thus, the main challenge lies in how to properly fuse the complementary information in the two types of variables and accurately characterize the complicated distribution for each class. This work proposes a flexible probabilistic framework that can concurrently analyze continuous and categorical variables for FDD. Our framework specifies a finite mixture model for each class. Thus, it can handle non-Gaussian and non-Bernoulli variables and capture their correlations under the conditional independence assumption. We then introduce the variational inference for parameter estimation, which makes our framework adaptive to the different distributions of various classes. Furthermore, a unified statistical index is designed for two types of variables, giving our method extra capability to distinguish unknown faults. Finally, the effectiveness of our method is validated on the Tennessee Eastman (TE) process and a practical industrial plant process. The average <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F1</i> score of our method is improved by 3.4/3.9 percentage points in the single-mode/multimode situation on the TE process compared with traditional mixture discriminant analysis. In the industrial plant process, when unknown faults are added, the average <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F1</i> score of our method is 91.1% and only 1.2 percentage points lower than that on the test set without unknown faults.

Testing conditional independence in casual inference for time series data

In this paper, we propose a new procedure to test conditional independence assumption in studying casual inference for time series data. The conditional independence assumption is transformed to a nonparametric conditional moment test with the help of auxiliary variables which are allowed to affect policy choice but the dependence can be fully captured by potential outcomes and observable controls. When the policy choice is binary, a nonparametric statistic test is developed further for testing the conditional independence assumption conditional on policy propensity score. Under some regular conditions, we show that the proposed test statistics are asymptotically normal under the null hypotheses for time series data. In addition, the performances of the proposed methods are illustrated through Monte Carlo simulations and a real example considered in Angrist and Kuersteiner (2011).

A Bayesian latent class extension of naive Bayesian classifier and its application to the classification of gastric cancer patients

BackgroundThe Naive Bayes (NB) classifier is a powerful supervised algorithm widely used in Machine Learning (ML). However, its effectiveness relies on a strict assumption of conditional independence, which is often violated in real-world scenarios. To address this limitation, various studies have explored extensions of NB that tackle the issue of non-conditional independence in the data. These approaches can be broadly categorized into two main categories: feature selection and structure expansion.In this particular study, we propose a novel approach to enhancing NB by introducing a latent variable as the parent of the attributes. We define this latent variable using a flexible technique called Bayesian Latent Class Analysis (BLCA). As a result, our final model combines the strengths of NB and BLCA, giving rise to what we refer to as NB-BLCA. By incorporating the latent variable, we aim to capture complex dependencies among the attributes and improve the overall performance of the classifier.MethodsBoth Expectation-Maximization (EM) algorithm and the Gibbs sampling approach were offered for parameter learning. A simulation study was conducted to evaluate the classification of the model in comparison with the ordinary NB model. In addition, real-world data related to 976 Gastric Cancer (GC) and 1189 Non-ulcer dyspepsia (NUD) patients was used to show the model's performance in an actual application. The validity of models was evaluated using the 10-fold cross-validation.ResultsThe presented model was superior to ordinary NB in all the simulation scenarios according to higher classification sensitivity and specificity in test data. The NB-BLCA model using Gibbs sampling accuracy was 87.77 (95% CI: 84.87-90.29). This index was estimated at 77.22 (95% CI: 73.64-80.53) and 74.71 (95% CI: 71.02-78.15) for the NB-BLCA model using the EM algorithm and ordinary NB classifier, respectively.ConclusionsWhen considering the modification of the NB classifier, incorporating a latent component into the model offers numerous advantages, particularly within medical and health-related contexts. By doing so, the researchers can bypass the extensive search algorithm and structure learning required in the local learning and structure extension approach. The inclusion of latent class variables allows for the integration of all attributes during model construction. Consequently, the NB-BLCA model serves as a suitable alternative to conventional NB classifiers when the assumption of independence is violated, especially in domains pertaining to health and medicine.