Statistical Causal Discovery in Developing Adverse Outcome Pathway (AOP).

Process Fault Diagnosis Method Based on MSPC and LiNGAM and its Application to Tennessee Eastman Process

This paper considers the use of two machine learning algorithms to identify the causal relationships among retail prices, manufacturer prices, and number of packages sold. The two algorithms are PC and Linear Non-Gaussian Acyclic Models (LiNGAM). The dataset studied comprises scanner data collected from the retail sales of carbonated soft drinks in the Chicago area. The PC algorithm is not able to assign direction among retail price, manufacturer price and quantity sold, whereas the LiNGAM algorithm is able to decide in every case, i.e., retail price leads manufacturer price and quantity sold.

Recently, there is a growing need for statistical learning of causal structures in data with many variables. A structural equation model called Linear Non-Gaussian Acyclic Model (LiNGAM) has been extensively studied to uniquely estimate causal structures in data. The key assumptions are that external influences are independent and follow non-Gaussian distributions. However, LiNGAM does not capture temporal structural changes in observed data. In this paper, we consider learning causal structures in longitudinal data that collects samples over a period of time. In previous studies of LiNGAM, there was no model specialized to handle longitudinal data with multiple samples. Therefore, we propose a new model called longitudinal LiNGAM and a new estimation method using the information on temporal structural changes and non-Gaussianity of data. The new approach requires less assumptions than previous methods.

Considerations of sample size in medical research

Altered-LiNGAM (ALiNGAM) for solving nonlinear causal models when data is nonlinear and noisy

BackgroundUnderstanding the determinants of global quality of life in cancer patients is crucial for improving their overall well-being. While correlations between various factors and quality of life have been established, the causal relationships remain largely unexplored. This study aimed to identify the causal factors influencing global quality of life in cancer patients and compare them with known correlative factors.MethodsWe conducted a retrospective analysis of European Organization for Research and Treatment of Cancer Quality of Life Questionnaire data, alongside demographic and disease-related features, collected from new cancer patients during their initial visit to an oncology outpatient clinic. Correlations with global quality of life were identified using univariate and multivariate regression analyses. Causal inference analysis was performed using two approaches. First, we employed the Dowhy Python library for causal analysis, incorporating prior information and manual characterization of an acyclic graph. Second, we utilized the Linear Non-Gaussian Acyclic Model (LiNGAM) machine learning algorithm from the Lingam Python library, which automatically generated an acyclic graph without prior information. The significance level was set at p < 0.05.ResultsMultivariate analysis of 469 new admissions revealed that disease stage, role functioning, emotional functioning, social functioning, fatigue, pain and diarrhea were linked with global quality of life. The most influential direct causal factors were emotional functioning, social functioning, and physical functioning, while the most influential indirect factors were physical functioning, emotional functioning, and fatigue. Additionally, the most prominent total causal factors were identified as type of cancer (diagnosis), cancer stage, and sex, with total causal effect ratios of -9.47, -4.67, and − 1.48, respectively. The LiNGAM algorithm identified type of cancer (diagnosis), nausea and vomiting and social functioning as significant, with total causal effect ratios of -9.47, -0.42, and 0.42, respectively.ConclusionsThis study identified that causal factors for global quality of life in new cancer patients are distinct from correlative factors. Understanding these causal relationships could provide valuable insights into the complex dynamics of quality of life in cancer patients and guide targeted interventions to improve their well-being.

294 Background: Economic evaluations in oncology aim to assess the value of new therapies in the long term based on clinical trial data that often have restricted follow-up times (&lt; 5 years) and small sample sizes (&lt; 500 patients). This requires the use of extrapolation assumptions on long-term survival that go beyond the observed data. In this analysis, differences in survival extrapolation methods are tested in samples of sizes and follow-up reflecting typical clinical trials against a background of known survival in prostate cancer from a US based cancer registry. Methods: Data from the National Cancer Institute's Surveillance Epidemiology and End Results (SEER) registry on long-term survival in patients with stage IV prostate cancer were employed. The data set comprised those patients diagnosed between 1988 and 2003, with follow-up data available until 2012. Additional survival for those who received surgery (compared to those who did not), was estimated based on extrapolations using standard parametric statistical models (exponential, Weibull, log-logistic, log-normal, Gamma) fitted to the observed data. Survival analyses were run for 5 sample size scenarios (n = 27,670, 1000, 500, 200, 50) and 6 follow-up scenarios (follow-up years = 25, 20, 10, 5, 2, 1) yielding 30 combination scenarios. Performance of the methods was tested relative to the maximum follow-up, maximum sample size scenario (i.e. reference case) from the SEER registry. Results: Log-logistic and log-normal models were associated with flat tails which led to inflated survival estimations. For scenarios with smaller sizes, gamma models often did not converge. Exponential models were the most frequently reported as best model fit (in approximately 50% of scenarios). Also, gains in OS were consistent when exponential models were selected, and closely matched gain in OS from the reference case. Conclusions: Since clinical trials in oncology are often associated with small patient sample sizes and restricted follow-up, selecting an exponential model may lead to the most consistent and stable results based on the experiment constructed here. Further research should confirm these results for other types of cancer.

The discovery of causal relationships from the observational data is an important task. To identify the unique causal structure belonging to a Markov equivalence class, a number of algorithms, such as the linear non-Gaussian acyclic model (LiNGAM), have been proposed. However, two challenges remain to be met: 1) these algorithms fail to work on the data which follow linear structural equation model with Gaussian noise and 2) they misjudge the causal direction when the data contain additional measurement errors. In this paper, we propose an entropy-based two-phase iterative algorithm for arbitrary distribution data with additional measurement errors under some mild assumptions. In the first phase of the algorithm, based on the property that entropy can measure the amount of information behind the data with arbitrary distribution, we design a general approach for the identification of exogenous variable on both Gaussian and non-Gaussian data, and we give the corresponding theoretical derivation. In the second phase, to eliminate the effects of measurement errors, we revise the value of the exogenous variable by removing its measurement error and further use the revised value to remove its effect on the remaining variables. Experimental results on real-world causal structures are presented to demonstrate the effectiveness and stability of our method. We also apply the proposed algorithm on the mobile-base-station data with measurement errors, and the results further prove the effectiveness of our algorithm.

Relatively few empirical studies have examined the performance of enumeration indices in correctly identifying longitudinal population heterogeneity when present, and these studies have produced mixed results. In light of these findings, Muthén (2003) suggested that the inclusion of time-invariant (antecedent) and time-varying (concurrent) covariates, as well as allowing the extracted growth mixture classes to predict a distal outcome (consequent covariate), could improve the performance of enumeration indices. This Monte Carlo simulation study examined the performance of a large set of enumeration indices within these generalized growth mixture model (GGMM) conditions, as suggested by Muthén, by manipulating 4 design conditions: (a) sample size, (b) separation distance between adjacent latent growth trajectories, (c) growth trajectory membership proportions, and (d) the amount of mixture model variance explained by the covariates. The findings suggest: (a) at smaller (N = 500) sample sizes, enumeration indices were much more likely to select an incorrect model than the correct one, (b) at larger (N = 3,000) sample sizes, correct model identification occurred only in the largest separation distance and trajectory membership equality conditions, and (c) the inclusion of covariates had a negligible effect at smaller sample sizes, but covariate inclusion had a more favorable effect on data generation model identification in the largest sample size, largest trajectory separation distance, and equal trajectory membership proportions conditions. Suggestions for researchers and future empirical study possibilities are discussed.

The advancement of multichannel functional near-infrared spectroscopy (fNIRS) has enabled measurements across a wide range of brain regions. This increase in multiplicity necessitates the control of family-wise errors in statistical hypothesis testing. To address this issue, the effective multiplicity ( ) method designed for channel-wise analysis, which considers the correlation between fNIRS channels, was developed. However, this method loses reliability when the sample size is smaller than the number of channels, leading to a rank deficiency in the eigenvalues of the correlation matrix and hindering the accuracy of calculations. We aimed to reevaluate the effectiveness of the method for fNIRS data with a small sample size. In experiment 1, we used resampling simulations to explore the relationship between sample size and values. Based on these results, experiment 2 employed a typical exponential model to investigate whether valid could be predicted from a small sample size. Experiment 1 revealed that the values were underestimated when the sample size was smaller than the number of channels. However, an exponential pattern was observed. Subsequently, in experiment 2, we found that valid values can be derived from sample sizes of 30 to 40 in datasets with 44 and 52 channels using a typical exponential model. The findings from these two experiments indicate the potential for the effective application of correction in fNIRS studies with sample sizes smaller than the number of channels.

In the causal analysis of observational data, the positivity assumption requires that all treatments of interest be observed in every patient subgroup. Violations of this assumption are indicated by nonoverlap in the data in the sense that patients with certain covariate combinations are not observed to receive a treatment of interest, which may arise from contraindications to treatment or small sample size. In this paper, we emphasize the importance and implications of this often-overlooked assumption. Further, we elaborate on the challenges nonoverlap poses to estimation and inference and discuss previously proposed methods. We distinguish between structural and practical violations and provide insight into which methods are appropriate for each. To demonstrate alternative approaches and relevant considerations (including how overlap is defined and the target population to which results may be generalized) when addressing positivity violations, we employ an electronic health record-derived data set to assess the effects of metformin on colon cancer recurrence among diabetic patients.

# CONSIDER COST AND FEASIBILITY WHEN CHOOSING SAMPLE SIZE {#article-title-2} to the editor: I commend the authors for advocating alternatives to the usual convention-bound sample size methods ([5][1]). Problems with the conventional methods extend beyond special settings, because in practice

Parasite prevalence and sample size: misconceptions and solutions

Thermal traits, such as upper and lower critical thermal limits, are vital indicators of the vulnerability of populations and species to environmental change. Thus, accurate estimates of these traits are needed to explain biological patterns and forecast responses to the changing thermal environment. However, many thermal trait studies measure relatively few individuals to estimate traits for whole populations or species. To ascertain if, and how, sample size affects the accuracy of reported trait means and variances, we applied a subsampling and equivalency testing approach to empirical and simulated trait data to investigate the accuracy of trait estimates relative to sample size and the skew and variance of the trait distribution in the source population. Simulation results indicated that only 7.9% of the 428 critical thermal limit traits documented in a recent synthesis of thermal trait data reported sufficiently large sample sizes, relative to variance, to ensure confidence in the reported mean trait value with negligible (±0.25°C) error. Greater inter‐individual trait variance in the source population requires a larger number of individuals to be measured to accurately estimate the mean and variance of that trait. This pattern is mitigated somewhat by the tendency of thermal traits to exhibit skew‐normal distributions. As measurements of few individuals from a population are unlikely to provide accurate estimates of thermal traits, the propensity towards small sample sizes in thermal trait studies is concerning. Macrophysiological syntheses often use these data to describe, explain and predict broad‐scale ecological patterns. Thus, insufficient sample sizes in the original studies could diminish the robustness of these patterns and predictions. For future studies, we recommend that preliminary data be used to estimate trait variance and calculate minimum sample sizes. If small sample sizes are unavoidable, larger error around the measured trait mean must be assumed and accounted for in subsequent analyses. A free Plain Language Summary can be found within the Supporting Information of this article.

With recent success in supervised learning, artificial intelligence (AI) and machine learning (ML) can play a vital role in precision medicine. Deep learning neural networks have been used in drug discovery when larger data is available. However, applications of machine learning in clinical trials with small sample size (around a few hundreds) are limited. We propose a Similarity-Principle-Based Machine Learning (SBML) method, which is applicable for small and large sample size problems. In SBML, the attribute-scaling factors are introduced to objectively determine the relative importance of each attribute (predictor). The gradient method is used in learning (training), that is, updating the attribute-scaling factors. We evaluate SBML when the sample size is small and investigate the effects of tuning parameters. Simulations show that SBML achieves better predictions in terms of mean squared errors for various complicated nonlinear situations than full linear models, optimal and ridge regressions, mixed effect models, support vector machine and decision tree methods.