Distinguishing case-mix from context heterogeneity in prognostic regression model synthesis settings

Prognostic regression models often synthesize data from multiple sites, whether within a multi-site study, across federated settings, or in individual participant data meta-analysis. Here, a site is any data source, such as a hospital, registry, trial, or study, and need not be a physical center. Analysts must then decide whether one regression model represents all sites or whether site-specific models are needed. Established measures such as coefficient-level tau^2 quantify heterogeneity but do not distinguish its source. We focus on diagnosing whether coefficient heterogeneity reflects case-mix or site-specific context effects. Case-mix heterogeneity can arise when linear regression terms approximate multivariable non-linear relationships in populations with different covariate distributions. Contextual heterogeneity arises when comparable patients require different regression relationships across sites. We do this by fitting site-specific local regressions in a dimension-reduced space and partitioning the smoothed coefficient surfaces into a cross-site reference and site-specific deviations. An autoencoder and custom loss structure the latent space around local prognostic relationships. We then project this partition onto the outcome scale to derive observation- and site-level summaries. We demonstrate the approach on a COPD trial with two sites. In the three leading latent slope coordinates, coefficient-surface variation was predominantly contextual. The derived observation-level outcome-scale variance partition was case-mix-leading, whereas its between-site aggregation was concentrated in contextual differences rather than case-mix shifts. A permuted-site negative control assesses whether the contextual summary can arise when site labels carry no signal. This diagnostic distinction can inform whether joint or site-specific regression models should be evaluated.

Optimizing 2D Input Representations and Sub-phase Fusion Strategies for Differential Diagnosis of Asthma and COPD Using CNN- and GRU-Based Networks

This study aims to explore the performance of the VAR model in comparison with mel-frequency cepstral coefficient (MFCC) matrices and log-mel spectrograms using deep learning. In pulmonary sound classification, spectrogram-based representations suffer from inconsistent temporal dimensions due to varying respiratory cycle durations. Along with traditional trimming/zero-padding, adaptive-length windowing was presented to fix their temporal dimensions. Their spectral and temporal dimensions were optimized by testing a range of parameters. Different convolutional neural network (CNN) architectures were employed to extract features from the two-dimensional representations obtained over the sub-phases. The extracted sub-phase features were then fused using various strategies including direct concatenation, gated recurrent unit (GRU) network and GRU with attention mechanism. Model performances were assessed through respiratory cycle-based evaluation and subject-based evaluation comprising multiple respiratory cycles. Several data augmentation techniques were also studied to cope with limitations in data size. The best cycle-based F1-score (0.877) was obtained using the MFCC matrices with thirteen coefficients and 64-point time resolution per sub-phase representation followed by direct feature concatenation, and the best subject-based F1-score (0.855) was obtained using the MFCC matrices with thirteen coefficients and 256-point time resolution per full-cycle representation, both obtained by adaptive-length windowing. Augmentation degraded the performance of models overall, yet mixup augmentation was the best among the methods tested. MFCC outperformed log-mel spectrogram and VAR model in differentiation of asthma and COPD. Sophisticated fusion strategies did not improve the diagnosis. Augmentation did not contribute, demonstrating the significance of authentic data in pulmonary sound studies.