Gaussian Bayesian network model of healthcare, food and energy sectors in the pandemic: Türkiye case

Healthcare, food, and energy are the basic needs of life in the globalizing world. Humankind's quest to maintain a healthy life and find ways to meet its needs has continued since its existence. The causal relations between the healthcare, food, and energy sectors are explored using data from the pandemic when COVID-19 was a global risk, and human health sustainability underwent a complicated process. It aims to examine the interaction between the healthcare, food, and energy sectors and model the causal relationship within the framework of probabilistic dependencies. For this purpose, the relationships between these sectors during the pandemic are modeled via Bayesian Networks (BNs). This highly successful inference method makes the complex structure of causal relationships graphically understandable. The data consists of stock returns at the end of the business day between March 11, 2020, when the pandemic was declared, and December 26, 2022. Data on 13 stocks actively traded on the Istanbul Stock Exchange (BIST) during the 700 days were obtained from tr.investing.com. Causal modeling uses Gaussian Bayesian Networks (GBNs) for continuous variables. To make the inferences drawn from the data more successful and minimize the loss of information, the GBN model is built with continuous variables. The posterior Probability Density Functions (PDFs) of the stocks in the network are constructed over the structure of the Directed Acyclic Graphs (DAG) of the BNs, and inferences are made by querying possible cases (tips). Markov Chain Monte Carlo (MCMC) simulations are performed with the posterior PDFs, and measures of the central tendency of the stocks are calculated. GBNs are used to generate daily return estimates for ULKER with the lowest MSE (1.06e-03) and RMSE (3.22e-02) values and ULUUN with the highest MSE (3.43e-03) and RMSE (5.83e-02) values.

Subgroup analyses in randomized controlled trials frequently categorized continuous subgroup information

BACKGROUND AND OBJECTIVES

To investigate how subgroup analyses of published Randomized Controlled Trials (RCTs) are performed when subgroups are created from continuous variables.

METHODS

We carried out a review of RCTs published in 2016-2021 that included subgroup analyses. Information was extracted on whether any of the subgroups were based on continuous variables and, if so, how they were analyzed.

RESULTS

Out of 428 reviewed papers, 258 (60.4%) reported RCTs with a subgroup analysis. Of these, 178/258 (69%) had at least one subgroup formed from a continuous variable and 14/258 (5.4%) were unclear. The vast majority (169/178, 94.9%) dichotomized the continuous variable and treated the subgroup as categorical. The most common way of dichotomizing was using a pre-specified cutpoint (129/169, 76.3%), followed by a data-driven cutpoint (26/169, 15.4%), such as the median.

CONCLUSION

It is common for subgroup analyses to use continuous variables to define subgroups. The vast majority dichotomize the continuous variable and, consequently, may lose substantial amounts of statistical information (equivalent to reducing the sample size by at least a third). More advanced methods that can improve efficiency, through optimally choosing cutpoints or directly using the continuous information, are rarely used.

Meta-analysis for individual participant data with a continuous exposure: A case study

OBJECTIVE

Methods for meta-analysis of studies with individual participant data and continuous exposure variables are well described in the statistical literature but are not widely used in clinical and epidemiological research. The purpose of this case study is to make the methods more accessible.

STUDY DESIGN AND SETTING

A two-stage process is demonstrated. Response curves are estimated separately for each study using fractional polynomials. The study-specific curves are then averaged pointwise over all studies at each value of the exposure. The averaging can be implemented using fixed effects or random effects methods.

RESULTS

The methodology is illustrated using samples of real data with continuous outcome and exposure data and several covariates. The sample data set, segments of Stata and R code, and outputs are provided to enable replication of the results.

CONCLUSION

These methods and tools can be adapted to other situations, including for time-to-event or categorical outcomes, different ways of modelling exposure-outcome curves, and different strategies for covariate adjustment.

Quantity discrimination in fish species: fish use non-numerical continuous quantity traits to select shoals

Fish typically prefer to live in big shoals due to the associated ecological benefits. Shoaling is a behavior that depends on the ability to quantitatively discriminate. The fundamental mechanism involved in quantity discrimination determines whether fish can discriminate a shoal using numerical discrete cues (e.g., number of shoal members), non-numerical continuous traits (e.g., total body surface area) or both; however, the mechanism is currently a controversial topic. In the present study, we used a spontaneous choice experiment to test whether guppy (Poecilia reticulata), zebrafish (Danio rerio), Chinese crucian carp (Carassius auratus) and qingbo (Spinibarbus sinensis) rely on continuous (i.e., body surface area) or discrete (i.e., number of shoal members) information for shoal selection by altering the body surface area (cumulative body surface area ratio of 3:2 or 1:1) between two stimulus shoals with a different number of members (2 individuals vs 3 individuals). All four fish species preferred to shoal with the stimulus shoal with the larger cumulative surface area even if the shoal had fewer members; however, fish showed no shoal preference when the cumulative surface body areas of both stimulus shoals were equal. Furthermore, qingbo did not numerically discriminate between a shoal with 1 individual and a shoal with 3 individuals when the cumulative surface areas of both stimulus shoals were equal; however, qingbo showed a preference for the shoal with the larger cumulative surface area when the two stimulus shoals each had 3 individuals. In conclusion, the present study demonstrated that all four fish species relied only on non-numerical continuous quantity information for shoal selection, at least under a difficult task (i.e., 2 vs 3).

Quantity discrimination in angelfish (Pterophyllum scalare) is maintained after a 30-s retention interval in the large but not in the small number range

The ability to discriminate between sets that differ in the number of elements can be useful in different contexts and may have survival and fitness consequences. As such, numerical/quantity discrimination has been demonstrated in a diversity of animal species. In the laboratory, this ability has been analyzed, for example, using binary choice tests. Furthermore, when the different number of items first presented to the subjects are subsequently obscured, i.e., are not visible at the moment of making a choice, the task requires memory for the size of the sets. In previous work, angelfish (Pterophyllum scalare) have been found to be able to discriminate shoals differing in the number of shoal members both in the small (less than 4) and the large (4 or more) number range, and they were able to perform well even when a short memory retention interval (2-15 s) was imposed. In the current study, we increased the retention interval to 30 s during which the shoals to choose between were obscured, and investigated whether angelfish could show preference for the larger shoal they saw before this interval. Subjects were faced with a discrimination between numerically small shoals (≤4 fish) and also between numerically large (≥4 fish) shoals of conspecifics. We found angelfish not to be able to remember the location of larger versus smaller shoals in the small number range, but to exhibit significant memory for the larger shoal in the large number range as long as the ratio between these shoals was at least 2:1. These results, together with prior findings, suggest the existence of two separate quantity estimation systems, the object file system for small number of items that does not work with the longer retention interval and the analogue magnitude system for larger number of items that does.

A comparison of methods to adjust for continuous covariates in the analysis of randomised trials

BACKGROUND

Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy.

METHODS

We compared several methods of adjustment to determine which is best when the association between covariate and outcome is unknown. We assessed (a) dichotomisation or categorisation; (b) assuming a linear association with outcome; (c) using fractional polynomials with one (FP1) or two (FP2) polynomial terms; and (d) using restricted cubic splines with 3 or 5 knots. We evaluated each method using simulation and through a re-analysis of trial datasets.

RESULTS

Methods which kept covariates as continuous typically had higher power than methods which used categorisation. Dichotomisation, categorisation, and assuming a linear association all led to large reductions in power when the true association was non-linear. FP2 models and restricted cubic splines with 3 or 5 knots performed best overall.

CONCLUSIONS

For the analysis of randomised trials we recommend (1) adjusting for continuous covariates even if their association with outcome is unknown; (2) keeping covariates as continuous; and (3) using fractional polynomials with two polynomial terms or restricted cubic splines with 3 to 5 knots when a linear association is in doubt.

Spontaneous versus trained numerical abilities. A comparison between the two main tools to study numerical competence in non-human animals

A large body of experimental evidence shows that animals as diverse as mammals, birds, and fish are capable of processing numerical information. Considerable differences have been reported in some cases among species and a wide debate currently surrounds the issue of whether all vertebrates share the same numerical systems or not. Part of the problem is due to the fact that these studies often use different methods, a circumstance that potentially introduces confounding factors in a comparative analysis. In most studies, two main methodological approaches have been used: spontaneous choice tests and training procedures. The former approach consists of presenting to the subjects two groups of biologically-relevant stimuli (e.g., food items or social companions) differing in numerosity with the assumption that if they are able to discriminate between the two quantities, they are expected to spontaneously select the larger/smaller quantity. In the latter approach, subjects undergo extensive training in which some neutral stimuli (e.g., a quantity of dots) are associated with a reward and the capacity to learn a numerical rule is taken as evidence of numerical abilities. We review the literature on this topic, highlighting the relevance, and potential weaknesses in controlling confounding factors obtained with either approach.

On the Use of Fractional Polynomial Models to Assess Preventive Aspect of Variables: An Example in Prevention of Mortality Following HIV Infection

BACKGROUND

Identification of disease risk factors can help in the prevention of diseases. In assessing the predictive value of continuous variables, a routine procedure is to categorize the factors. This yield to inability to detect non-linear relationship, if exist. Multivariate fractional polynomial (MFP) modeling is a flexible method to reveal non-linear associations. We aim to demonstrate the impact of choice of risk function on the significance of variables.

METHODS

We selected 6508 HIV-infected persons registered in the Australia National HIV Registry between 1980 and 2003 to assess the predictors associated with the risk of death after HIV infection prior to AIDS. First, CD4 count as a categorical factor with three other categorical variables (age, sex, and HIV exposure category) was entered into the Cox regression model. Second, CD4 counts as a continuous variable along with other categorical variables were entered into the fractional polynomial (FP) model.

RESULTS

Both the Cox and FP models showed age ≥ 40 years and hemophiliac patients were significantly associated with increased risk of death. In the categorized model, the CD4 variable did not reach the significance level. However, this variable was highly significant in the MFP model. The FP model showed slightly better performance in terms of discrimination ability and goodness of fit.

CONCLUSIONS

The FP model is a flexible method in detecting the predictive effect of continuous variables. This method enhances the ability to assess the predictive ability of variables and improves model performance.