Deep-learning tools that extract prognostic factors derived from multi-omics data have recently contributed to individualized predictions of survival outcomes. However, the limited size of integrated omics-imaging-clinical datasets poses challenges. Here, we propose two biologically interpretable and robust deep-learning architectures for survival prediction of non-small cell lung cancer (NSCLC) patients, learning simultaneously from computed tomography (CT) scan images, gene expression data, and clinical information. The proposed models integrate patient-specific clinical, transcriptomic, and imaging data and incorporate Kyoto Encyclopedia of Genes and Genomes (KEGG) and Reactome pathway information, adding biological knowledge within the learning process to extract prognostic gene biomarkers and molecular pathways. While both models accurately stratify patients in high- and low-risk groups when trained on a dataset of only 130 patients, introducing a cross-attention mechanism in a sparse autoencoder significantly improves the performance, highlighting tumor regions and NSCLC-related genes as potential biomarkers and thus offering a significant methodological advancement when learning from small imaging-omics-clinical samples.

Semiparametric probabilistic index models allow for the comparison of two groups of observations, whilst adjusting for covariates, thereby fitting nicely within the framework of generalized pairwise comparisons (GPC). As with most regression approaches in this setting, the limited amount of data results in invalid inference as the asymptotic normality assumption is not met. In addition, separation issues might arise when considering small samples. In this article, we show that the parameters of the probabilistic index model can be estimated using generalized estimating equations, for which adjustments exist that lead to estimators of the sandwich variance-covariance matrix with improved finite sample properties and that can deal with bias due to separation. In this way, appropriate inference can be performed as is shown through extensive simulation studies. The known relationships between the probabilistic index and other GPC statistics allow to also provide valid inference for example, the net treatment benefit or the success odds.

This article proposes a performance measure to evaluate the detection performance of a control chart with a given sampling strategy for finite or small samples sequence and prove that the CUSUM control chart with dynamic non-random control limit and a given sampling strategy can be optimal under the measure. Numerical simulations and real data for an earthquake are provided to illustrate that for different sampling strategies, the CUSUM chart will have different monitoring performance in change-point detection. Among the six sampling strategies that take only a part of samples, the numerical comparing results illustrate that the uniform sampling strategy (uniformly dispersed sampling strategy) has the best monitoring effect.

Multilevel modeling (MLM) is commonly used in psychological research to model clustered data. However, data in applied research usually violate one of the essential assumptions of MLM-homogeneity of variance. While the fixed-effect estimates produced by the maximum likelihood method remain unbiased, the standard errors for the fixed effects are misestimated, resulting in inaccurate inferences and inflated or deflated type I error rates. To correct the bias in fixed effects standard errors and provide valid inferences, small-sample corrections such as the Kenward-Roger (KR) adjustment and the adjusted cluster-robust standard errors (CR-SEs) with the Satterthwaite approximation for t tests have been used. The current study compares KR with random slope (RS) models and the adjusted CR-SEs with ordinary least squares (OLS), random intercept (RI) and RS models to analyze small, heteroscedastic, clustered data using a Monte Carlo simulation. Results show the KR procedure with RS models has large biases and inflated type I error rates for between-cluster effects in the presence of level 2 heteroscedasticity. In contrast, the adjusted CR-SEs generally yield results with acceptable biases and maintain type I error rates close to the nominal level for all examined models. Thus, when the interest is only in within-cluster effect, any model with the adjusted CR-SEs could be used. However, when the interest is to make accurate inferences of the between-cluster effect, researchers should use the adjusted CR-SEs with RS to have higher power and guard against unmodeled heterogeneity. We reanalyzed an example in Snijders & Bosker (2012) to demonstrate the use of the adjusted CR-SEs with different models.

The part of responses that is absent in the nonequivalent groups with anchor test (NEAT) design can be managed to a planned missing scenario. In the context of small sample sizes, we present a machine learning (ML)-based imputation technique called chaining random forests (CRF) to perform equating tasks within the NEAT design. Specifically, seven CRF-based imputation equating methods are proposed based on different data augmentation methods. The equating performance of the proposed methods is examined through a simulation study. Five factors are considered: (a) test length (20, 30, 40, 50), (b) sample size per test form (50 versus 100), (c) ratio of common/anchor items (0.2 versus 0.3), and (d) equivalent versus nonequivalent groups taking the two forms (no mean difference versus a mean difference of 0.5), and (e) three different types of anchors (random, easy, and hard), resulting in 96 conditions. In addition, five traditional equating methods, (1) Tucker method; (2) Levine observed score method; (3) equipercentile equating method; (4) circle-arc method; and (5) concurrent calibration based on Rasch model, were also considered, plus seven CRF-based imputation equating methods for a total of 12 methods in this study. The findings suggest that benefiting from the advantages of ML techniques, CRF-based methods that incorporate the equating result of the Tucker method, such as IMP_total_Tucker, IMP_pair_Tucker, and IMP_Tucker_cirlce methods, can yield more robust and trustable estimates for the \"missingness\" in an equating task and therefore result in more accurate equated scores than other counterparts in short-length tests with small samples.

Hyperspectral remote sensing images (HRSI) have the characteristics of foreign objects with the same spectrum. As it is difficult to label samples manually, the hyperspectral remote sensing images are understood to be typical \"small sample\" datasets. Deep neural networks can effectively extract the deep features from the HRSI, but the classification accuracy mainly depends on the training label samples. Therefore, the stacked convolutional autoencoder network and transfer learning strategy are employed in order to design a new stacked convolutional autoencoder network model transfer (SCAE-MT) for the purposes of classifying the HRSI in this paper. In the proposed classification method, the stacked convolutional au-to-encoding network is employed in order to effectively extract the deep features from the HRSI. Then, the transfer learning strategy is applied to design a stacked convolutional autoencoder network model transfer under the small and limited training samples. The SCAE-MT model is used to propose a new HRSI classification method in order to solve the small samples of the HRSI. In this study, in order to prove the effectiveness of the proposed classification method, two HRSI datasets were chosen. In order to verify the effectiveness of the methods, the overall classification accuracy (OA) of the convolutional self-coding network classification method (CAE), the stack convolutional self-coding network classification method (SCAE), and the SCAE-MT method under 5%, 10%, and 15% training sets are calculated. When compared with the CAE and SCAE models in 5%, 10%, and 15% training datasets, the overall accuracy (OA) of the SCAE-MT method was improved by 2.71%, 3.33%, and 3.07% (on average), respectively. The SCAE-MT method is, thus, clearly superior to the other methods and also shows a good classification performance.

It is well known that crop classification is essential for genetic resources and phenotype development. Compared with traditional methods, convolutional neural networks can be utilized to identify features automatically. Nevertheless, crops and scenarios are quite complex, which makes it challenging to develop a universal classification method. Furthermore, manual design demands professional knowledge and is time-consuming and labor-intensive. In contrast, auto-search can create network architectures when faced with new species. Using rapeseed images for experiments, we collected eight types to build datasets (rapeseed dataset (RSDS)). In addition, we proposed a novel target-dependent search method based on VGGNet (target-dependent neural architecture search (TD-NAS)). The result shows that test accuracy does not differ significantly between small and large samples. Therefore, the influence of the dataset size on generalization is limited. Moreover, we used two additional open datasets (Pl@ntNet and ICL-Leaf) to test and prove the effectiveness of our method due to three notable features: (a) small sample sizes, (b) stable generalization, and (c) free of unpromising detections.

Researchers frequently use Mokken scale analysis (MSA), which is a nonparametric approach to item response theory, when they have relatively small samples of examinees. Researchers have provided some guidance regarding the minimum sample size for applications of MSA under various conditions. However, these studies have not focused on item-level measurement problems, such as violations of monotonicity or invariant item ordering (IIO). Moreover, these studies have focused on problems that occur for a complete sample of examinees. The current study uses a simulation study to consider the sensitivity of MSA item analysis procedures to problematic item characteristics that occur within limited ranges of the latent variable. Results generally support the use of MSA with small samples (N around 100 examinees) as long as multiple indicators of item quality are considered.

It has been reported that about half of biological discoveries are irreproducible. These irreproducible discoveries were partially attributed to poor statistical power. The poor powers are majorly owned to small sample sizes. However, in molecular biology and medicine, due to the limit of biological resources and budget, most molecular biological experiments have been conducted with small samples. Two-sample t-test controls bias by using a degree of freedom. However, this also implicates that t-test has low power in small samples. A discovery found with low statistical power suggests that it has a poor reproducibility. So, promotion of statistical power is not a feasible way to enhance reproducibility in small-sample experiments. An alternative way is to reduce type I error rate. For doing so, a so-called t α -test was developed. Both theoretical analysis and simulation study demonstrate that t α -test much outperforms t-test. However, t α -test is reduced to t-test when sample sizes are over 15. Large-scale simulation studies and real experiment data show that t α -test significantly reduced type I error rate compared to t-test and Wilcoxon test in small-sample experiments. t α -test had almost the same empirical power with t-test. Null p-value density distribution explains why t α -test had so lower type I error rate than t-test. One real experimental dataset provides a typical example to show that t α -test outperforms t-test and a microarray dataset showed that t α -test had the best performance among five statistical methods. In addition, the density distribution and probability cumulative function of t α -statistic were given in mathematics and the theoretical and observed distributions are well matched.

OBJECTIVE: Computer-aided MRI analysis is helpful for early detection of Alzheimer\'s disease(AD). Recently, 3D convolutional neural networks(CNN) are widely used to analyse MRI images. However, 3D CNN requires huge memory cost. In this paper, we introduce cascaded CNN and long and short-term memory (LSTM) networks. We also use knowledge distillation to improve the accuracy of the model using small medical image dataset.
METHODS: We propose a cascade structure, CNN-LSTM. CNN is used as the function of feature extraction, and LSTM is used as the classifier. In this way, the correlation between different slices can be considered and the calculation cost caused by 3D data can be reduced. To overcome the problem of limited image training data, transfer learning is a more reasonable way of feature extraction. We use the knowledge distillation algorithm to improve the performance of student models for AD diagnosis through a powerful teacher model to guide the work of student models.
RESULTS: The accuracy of the proposed model is improved using knowledge distillation. The results show that the accuracy of the student models reached 85.96% after the guidance of the teacher models, an increase by 3.83%.
CONCLUSIONS: We propose cascaded CNN-LSTM to classify 3D ADNI data, and use knowledge distillation to improve the model accuracy when trained with small size dataset. It can process 3D data efficiently as well as reduce the computational cost.