Context.Existing samples of strong lenses have been assembled by giving priority to sample size, but this is often at the cost of a complex selection function. However, with the advent of the next generation of wide-field photometric surveys, it might become possible to identify subsets of the lens population with well-defined selection criteria, trading sample size for completeness.Aims.There are two main advantages of working with a complete sample of lenses. First, such completeness makes possible to recover the properties of the general population of galaxies, of which strong lenses are a biased subset. Second, the relative number of lenses and non-detections can be used to further constrain models of galaxy structure. The present work illustrates how to carry out a statistical strong lensing analysis that takes advantage of these features.Methods.I introduce a general formalism for the statistical analysis of a sample of strong lenses with known selection function, and then test it on simulated data. The simulation consists of a population of 105galaxies with an axisymmetric power-law density profile, a population of background point sources, and a subset of ∼103strong lenses, which form a complete sample above an observational cut.Results.The method allows the user to recover the distribution of the galaxy population in Einstein radius and mass density slope in an unbiased way. The number of non-lenses helps to constrain the model when magnification data are not available.Conclusions.Complete samples of lenses are a powerful asset with which to turn precise strong lensing measurements into accurate statements on the properties of the general galaxy population.

Continuous glucose monitoring (CGM) has become the standard of care in diabetes management with the recent advances in technology and accessibility in the last decade. An International Consensus was established to define CGM metrics and its goals in diabetes care. The 2019 International Consensus suggested 14 days of CGM sampling for the assessment of CGM metrics stating the limitations that may occur for hypoglycemia and glycemic variability metrics. Since then, several studies assessed the correlation between CGM metrics and duration of the sampling period. This review summarized the studies that investigated the relationship between 14-day CGM sampling to 90-day CGM data in >70% CGM users for all CGM metrics and highlighted possible solutions for more accurate CGM sampling durations in type 1 diabetes (T1D). Accumulating evidence showed that 14-day CGM sampling correlates well with 90-day CGM data for mean glucose, time in 70-180 mg/dL, and hyperglycemia metrics; however, it correlates weakly for hypoglycemia and glycemic variability metrics. In the studies included in this review, in adults with T1D, minimum sampling duration was 14 days for mean glucose, time in 70-180 mg/dL, and time in hyperglycemia (>180 and >250 mg/dL); however, minimum sampling duration varied between 21 to 30 days for time <70 mg/dL, 30 to 35 days for time <54 mg/dL, and 28 to 35 days for coefficient of variation. Longer than 14 days of CGM, sampling was required to properly assess hypoglycemia and glycemic variability in T1D.

<h4>Objective</h4>Consensus guidelines recommend at least 14 consecutive days of continuous glucose monitoring (CGM) with 70% completeness to represent 90-day glycemic exposure. This study quantifies bias and uncertainty introduced into downstream analyses by using CGM metrics from incomplete or reduced monitoring, relative to a 90-day complete profile.<h4>Research design and methods</h4>Using a type 1 diabetes cohort with 1,010 complete 90-day CGM profiles, we simulated incomplete profiles by varying monitoring duration and data completeness. Consensus CGM metrics were computed on incomplete and complete profiles to quantify measurement error, which was propagated into two downstream regression models: 1) CGM metric is an outcome for a binary treatment (clinical trial setting); 2) CGM metric is an explanatory variable (covariate) for another continuous outcome. Bias was quantified using observed-to-true effect size ratios and uncertainty by the sample size increase required to maintain precision.<h4>Results</h4>In the clinical trial setting, treatment effects remain unbiased but lose precision; for time in range (TIR), 14 days required ≥16% more participants versus 90 days; 30 days required ≥6.5%. When the CGM metric is a covariate, associations with outcomes are attenuated (biased toward zero up to 14% at 14 days and 6% at 30 days for TIR) and less precise.<h4>Conclusions</h4>Representing 90 days of glycemic exposure with 14 days can lead to bias and loss of precision in downstream analyses. We recommend study protocols require at least 30 days of CGM with 70% completeness. If 30 days is not feasible, studies should plan for increased sample sizes.

Missing values exist in nearly all clinical studies because data for a variable or question are not collected or not available. Inadequate handling of missing values can lead to biased results and loss of statistical power in analysis. Existing models usually do not consider privacy concerns or do not utilise the inherent correlations across multiple features to impute the missing values. In healthcare applications, we are usually confronted with high dimensional and sometimes small sample size datasets that need more effective augmentation or imputation techniques. Besides, imputation and augmentation processes are traditionally conducted individually. However, imputing missing values and augmenting data can significantly improve generalisation and avoid bias in machine learning models. A Bayesian approach to impute missing values and creating augmented samples in high dimensional healthcare data is proposed in this work. We propose folded Hamiltonian Monte Carlo (F-HMC) with Bayesian inference as a more practical approach to process the cross-dimensional relations by applying a random walk and Hamiltonian dynamics to adapt posterior distribution and generate large-scale samples. The proposed method is applied to a cancer symptom assessment dataset and confirmed to enrich the quality of data in precision, accuracy, recall, F1 score, and propensity metric.

example, statistical inference). In the absence of sufficient evidence, drawing conclusions based on induction is unwarranted and fallacious. With the A fallacy is the use of invalid or otherwise faulty reasoning in the construction of an argument that may appear to be well-reasoned if unnoticed. The term was introduced in the Western intellectual tradition by the Aristotelian De Sophisticis Elenchis. Fallacies in reasoning may be invoked intentionally to manipulate or persuade by deception, unintentionally because of human limitations such as A… X is true for A. X is true for B. Therefore, X is true for C, D, etc. While never a valid logical deduction, if such an inference can be made on statistical grounds, it may nonetheless be convincing. This is because with enough empirical evidence, the generalization is no longer a hasty one.

other forms of discourse. A fallacious argument may nevertheless have a true conclusion; the defect lies in the inadequate reasoning offered in support A fallacy is an error in reasoning that undermines an argument's support for its conclusion. In academic usage, the term usually applies to arguments, although it is sometimes used more broadly for errors in reasoning in explanations, definitions, questions, or other forms of discourse. A fallacious argument may nevertheless have a true conclusion; the defect lies in the inadequate reasoning offer A fallacy is an error in reasoning that undermines an argument's support for its conclusion. In academic usage, the term usually applies to arguments, although it is sometimes used more broadly for errors in reasoning in explanations, definitions, questions, or other forms of discourse. A fallacious argument may nevertheless have a true conclusion; the defect lies in the inadequate reasoning offered in support of it. Fallacies are commonly divided into formal and informal fallacies. A formal fallacy is a defect in an argument's logical form that makes a deductive argument invalid. Informal fallacies cannot ordinarily be identified from form alone, since their assessment depends on such factors as content, evidence, context, and the purpose of the argument. They are often grouped under headings such as relevance, ambiguity, presumption, faulty generalization, and faulty causal reasoning, although the classification and boundaries of individual fallacies vary among authors. Fallacies may be used deliberately to persuade, but they can also arise unintentionally through cognitive bias, ambiguity, or faulty inference. In deductive… Appeal to probability – taking something for granted because it would probably be the case (or might possibly be the case). Argument from fallacy (also known as the fallacy fallacy) – the assumption that, if a particular argument for a "conclusion" is fallacious, then the conclusion by itself is false. Base rate fallacy – making a probability judgement based on conditional probabilities, without taking into account the effect of prior probabilities. Conjunction fallacy – the assumption that an outcome simultaneously satisfying multiple conditions is more probable than an outcome satisfying a single one of them. Masked-man fallacy (illicit substitution of identicals) – the substitution of identical designators in a true statement can lead to a false one.

As alternatives to the time-to-first-event analysis of composite endpoints, the {\it net benefit} (NB) and the {\it win ratio} (WR) -- which assess treatment effects using prioritized component outcomes based on clinical importance -- have been proposed. However, statistical inference of NB and WR relies on a large-sample assumptions, which can lead to an invalid test statistic and inadequate, unsatisfactory confidence intervals, especially when the sample size is small or the proportion of wins is near 0 or 1. In this paper, we develop a systematic approach to address these limitations in a paired-sample design. We first introduce a new test statistic under the null hypothesis of no treatment difference. Then, we present the formula to calculate the sample size. Finally, we develop the confidence interval estimations of these two estimators. To estimate the confidence intervals, we use the {\it method of variance estimates recovery} (MOVER), that combines two separate individual-proportion confidence intervals into a hybrid interval for the estimand of interest. We assess the performance of the proposed test statistic and MOVER confidence interval estimations through simulation studies. We demonstrate that the MOVER confidence intervals are as good as the large-sample confidence intervals when the sample is large and when the proportions of wins is bounded away from 0 and 1. Moreover, the MOVER intervals outperform their competitors when the sample is small or the proportions are at or near the boundaries 0 and 1. We illustrate the method (and its competitors) using three examples from randomized clinical studies.