The Buckley-James method for the classical accelerated failure time model has been extended to accommodate heteroscedastic survival data in two ways. The first is the weighted least squares method [Yu et al. Weighted least-squares method for right-censored data in accelerated failure time model. Biometrics. 2013;69:358-365], which estimates the heteroscedasticity nonparametrically, while the second is the local Buckley-James method [Pang et al. Local Buckley-James estimation for heteroscedastic accelerated failure time model. Stat Sin. 2015;25:863-877], which uses local Kaplan-Meier method to estimate the heteroscedasticity. However, no comparisons have been done for these two methods. Furthermore, there is no hypothesis testing procedure for this heteroscedastic accelerated failure time model. This paper is then aimed to fill these two gaps to compare the two methods theoretically and numerically with extensive simulation studies. In addition, we propose a class of hypothesis tests for the parameters to provide a complete procedure for analysing heteroscedastic survival data. Two real data examples are used for practical illustration of the comparison and the new proposed tests.

Background: The ongoing outbreak of Coronavirus disease 2019 (COVID-19) is a major challenge for mental health care systems and causes and exacerbates mental anxiety. Objective: This study sought to investigate the coping styles of stress in families and relatives of COVID-19 patients in the south of Iran, according to Lazarus and Folkman’s Transactional theory ‎of Stress coping ‎model. Methods: The present cross-sectional study was performed in the period from March 5 to July 5, 2020. Data collection was done electronically using a standard questionnaire on Lazarus and Folkman’s coping methods. Finally, the output data of the electronic questionnaire were analyzed using descriptive and inferential statistics. Results: A total of 276 people participated in the present study. There was a statistically significant difference between age and all emotion-oriented coping style domains (P <0.05), except planful problem solving (P = 0.817) and positive reappraisal (P = 0.153). The results of the present study showed that from the emotion-oriented coping, the domain of self-controlling (%55.9) received an unfavorable score, but in the problem-oriented coping (60.02%), the two domains of social support (%71.27) and positive reappraisal (70%) obtained scores above 50%. Conclusion: Families and relatives need help to improve coping with stress in the area of self-controlling. The results of the present study showed that emotion-oriented coping (self-controlling) had less effect on family stress than problem-oriented coping (domains of social support and positive reappraisal). Also, with domains of social support and positive reappraisal, the stress in the families was reduced. Factors influencing coping styles were age, literacy, source of information, and underlying disease. Since the COVID-19 pandemic condition is a unique stressful situation, it is necessary to implement psychological and educational interventions to gain the ability to control stress, especially in relatives with COVID-19.

Non-negative continuous outcomes with a substantial number of zero values and incomplete longitudinal follow-up are quite common in medical costs data. It is thus critical to incorporate the potential dependence of survival status and longitudinal medical costs in joint modeling, where censorship is death-related. Despite the wide use of conventional two-part joint models (CTJMs) to capture zero-inflation, they are limited to conditional interpretations of the regression coefficients in the model’s continuous part. In this paper, we propose a marginalized two-part joint model (MTJM) to jointly analyze semi-continuous longitudinal costs data and survival data. We compare it to the conventional two-part joint model (CTJM) for handling marginal inferences about covariate effects on average costs. We conducted a series of simulation studies to evaluate the superior performance of the proposed MTJM over the CTJM. To illustrate the applicability of the MTJM, we applied the model to a set of real electronic health record (EHR) data recently collected in Iran. We found that the MTJM yielded a smaller standard error, root-mean-square error of estimates, and AIC value, with unbiased parameter estimates. With this MTJM, we identified a significant positive correlation between costs and survival, which was consistent with the simulation results.

The expectation–maximization (EM) algorithm is a seminal method to calculate the maximum likelihood estimators (MLEs) for incomplete data. However, one drawback of this algorithm is that the asymptotic variance–covariance matrix of the MLE is not automatically produced. Although there are several methods proposed to resolve this drawback, limitations exist for these methods. In this paper, we propose an innovative interpolation procedure to directly estimate the asymptotic variance–covariance matrix of the MLE obtained by the EM algorithm. Specifically we make use of the cubic spline interpolation to approximate the first-order and the second-order derivative functions in the Jacobian and Hessian matrices from the EM algorithm. It does not require iterative procedures as in other previously proposed numerical methods, so it is computationally efficient and direct. We derive the truncation error bounds of the functions theoretically and show that the truncation error diminishes to zero as the mesh size approaches zero. The optimal mesh size is derived as well by minimizing the global error. The accuracy and the complexity of the novel method is compared with those of the well-known SEM method. Two numerical examples and a real data are used to illustrate the accuracy and stability of this novel method.

In alcohol studies, drinking outcomes such as number of days of any alcohol drinking (DAD) over a period of time do not precisely capture the differences among subjects in a study population of interest. For example, the value of 0 on DAD could mean that the subject was continually abstinent from drinking such as lifetime abstainers or the subject was alcoholic, but happened not to use any alcohol during the period of interest. In statistics, zeros of the first kind are called structural zeros, to distinguish them from the sampling zeros of the second type. As the example indicates, the structural and sampling zeros represent two groups of subjects with quite different psychosocial outcomes. In the literature on alcohol use, although many recent studies have begun to explicitly account for the differences between the two types of zeros in modeling drinking variables as a response, none has acknowledged the implications of the different types of zeros when such modeling drinking variables are used as a predictor. This paper serves as the first attempt to tackle the latter issue and illustrate the importance of disentangling the structural and sampling zeros by using simulated as well as real study data.

Advancing cancer research needs to adapt nonlinear dynamic systems (NDS) approach in addition to the linear dynamic systems (LDS). Dynamic changes in prostate-specific antigen (PSA), a biomarker of prostate cancer showed NDS character but this character has not been examined in literature. In this study, we examine PSA guided by a NDS paradigm. Participants were urology patients diagnosed with either prostate cancer (n = 27) or benign prostate disorder (n = 352) from a tertiary hospital in northcentral Florida. Data were derived from the 2001 to 2015 electronic medical records (EMR). PSA levels (ng/mL) were analyzed with cusp catastrophe mode in which participants' age at the PSA level was used as the asymmetry variable, and testosterone levels (ng/dL) as the bifurcation variable. Modeling analyses were executed in the open source R software. LDS-based linear correlation and regression analyses were also conducted as a comparison purpose. The mean age of the participants was 66.1 (SD = 9.8) years old; the PSA range was 0.05–13.8 with mean = 1.7 (SD = 1.2) ng/mL; and the total-testosterone range was 27.00–1297.00 with mean = 318.0(SD = 191.6) ng/dL. Results from Chen-Chen cusp regression indicate better data-model fit for cusp (R 2 = 0.47) than for linear regression (R 2 = 0.027). Serum PSA was significantly associated with age (a1 = 0.2691, p < .001) and bifurcated by blood testosterone (b1 = 1.0265, p < .00) with the estimated cusp point = (age = 63, testosterone = 630 ng/mL). The estimated cusp point was close to the epidemiology data that the risk of prostate cancer started to accelerate at about ages 60–65 years; and testosterone level of 630 ng/mL, closer to the up-limit 800 ng/dL of normal range (280–800) by the American Association of Clinical Endocrinologists (AACE). In conclusion, this is the first study that examined the dynamics of PSA in men and demonstrated that serum PSA level follow the NDS. In addition to confirming the relationship between age, testosterone and PSA, findings of this analysis provide a reasonable explanation of the large PSA-range in healthy men and the small difference in mean PSA between healthy men and men with prostate cancer (1.2 vs. 2.6). There is a need to re-evaluate the role of PSA for prostate cancer screening guided by NDS paradigm.

Cusp catastrophe models are unique to advance life sciences, psychology and behavioral studies. Extensive progresses have been made to utilize this modeling technique for continuous outcome and there is no development for binary data. To fill this gap, this chapter is then aimed to develop a cusp catastrophe modelling method for binary outcome. Building upon our previous research on the nonlinear regression cusp (RegCusp) catastrophe model for continuous outcome, we propose a logistic cusp catastrophe regression (LogisticCusp). LogisticCusp is based on the principles of logistic regression for binary outcome variable y (yes/no) being expressed as a latent binary variable Y through a logit link. This latent regression provides a mathematical connection between an observed outcome variable as a binomially distributed random variable and the deterministic cusp catastrophe at its equilibrium. By connecting the two, Y in the LogisticCusp is considered as one of the true roots of the deterministic cusp catastrophe model determined using the Maxwell or Delay conventions. We validate the method using a 5-step Monte-Carlo simulation with two predictors and three parameters for both bifurcation and asymmetry control variables. We further tested the method with binge drinking behavior in youth with data from the Monitoring the Future Study. Results from 5000 Monte-Carlo simulations indicate that the parameter estimates obtained through LogisticCusp are unbiased and efficient using maximum likelihood estimation with quasi-Newton numerical search algorithm. Results from empirical testing with real data are consistent with those estimated using other methods. LogisticCusp adds a new tool for researchers to examine many issues in psychology, life sciences, and behavioral studies, particularly, issues in medicine and public health with the powerful cusp catastrophe modeling for binary outcome.

Research findings are inconsistent regarding a positive association between the passage of state medical marijuana laws (MML) and the adolescent access and the use of marijuana. We utilized a novel analytical approach to examine this issue with multiyear data from the 1997–2013 Youth Risk Behavior Surveillance System of the State of Michigan. After controlling for the historically declining trend in marijuana use prior to the passages of MML in Michigan, we found that marijuana use among adolescents had increased subsequent to the passage of state MML. The study findings suggest the need for considering the increased risk of marijuana use in adolescents, as more states have implemented laws permitting marijuana use.

ABSTRACTIntroductionThe complex relationships among HIV knowledge, condom‐use skills, self‐efficacy, peer influence and intention to use condoms have been rigorously investigated. However, studies guided by a linear behavior change model often explain only a limited amount of variances. This study aims to advance our understanding of the relationships through a nonlinear quantum change paradigm.MethodsData (n = 1970, 40.61% male, mean age 16.94 ± 0.74) from a behavioral intervention program among high school students in the Bahamas were analyzed with a chained cusp catastrophe model in two steps. In the first step, self‐efficacy was analyzed as the outcome with HIV knowledge/condom‐use skills as asymmetry variables and peer influence as bifurcation variable. In the second step, condom‐use intention was analyzed as the outcome while self‐efficacy (outcome in the first step) was used as bifurcation variable allowing peer influence as bifurcation, and HIV knowledge/condom‐use skills were included as asymmetry. Cusp modeling analysis was conducted along with equivalent linear models.ResultsThe cusp model performed better than the linear and logistic models. Cusp modeling analyses revealed that peer influence significantly bifurcated the relationships between HIV knowledge/condom‐use skills and self‐efficacy; while both self‐efficacy and peer influence significantly bifurcated the relationship between HIV knowledge/condom‐use skills and condom‐use intention.ConclusionOur findings support the central role of self‐efficacy and peer influence as two chains in bridging the complex quantum relationships between HIV knowledge/condom‐use skills and condom‐use intention among adolescents. The nonlinear cusp catastrophe modeling provided a new method to advance HIV behavioral research.

It has became more popular in the recent statistical literature to see Bayesian approaches for clinical trials, such as assurance calculations for study designs and the use of posterior probability for data analyses. When applying Bayesian analysis to clinical trial data, one common question is to use informative priors or noninformative priors. In order to explore this question, we looked for existing clinical trial data with a simple structure and a simple clinical endpoint so that the Bayesian re-analyses can be easily performed. We came across the published Phase III Macugen (R) data that were suitable for this exploration. In this manuscript, the Macugen Phase III development program was described, the primary data for the two Phase III pivotal studies were re-analyzed using Bayesian applications with informative priors and noninformative priors. These re-analysis results were summarized, compared, and discussed.

The lifetime information of highly reliable products is usually very difficult to be obtained within an affordable amount experimental time through using traditional life testing methods. Because the benefit of lower manufacturing cost for many highly reliable products, manufacturers can offer more highly reliable products for implementing an accelerated degradation test under constant-stress loading conditions. In this chapter, lumen degradation measurements of high power light emitting diodes based on their cumulative damage are studied. The measurements are collected by the constant-stress accelerated degradation testing method with the stress loadings of ambient temperature and drive current. Each cumulative damage process is model by a Wiener process, of which drift parameter depends on the two stress loadings. General statistical inference of the model parameters and percentiles of the lifetime distribution of light emitting diodes is addressed, and approximate lower confidence bounds of the lifetime percentiles are evaluated using the Fisher information of maximum likelihood estimators. Based on the obtained maximum likelihood estimates of the model parameters, an optimal strategy for implementing a constant-stress accelerated degradation test is established. The optimal strategy can reach a compromised decision between the experimental budget and estimation precision of reliability analysis. An algorithm is provided to search for the proposed optimal strategy. The proposed method is illustrated with an example of light emitting diodes.

A well-designed clinical trial requires an appropriate sample size with adequate statistical power to address trial objectives. The statistical power is traditionally defined as the probability of rejecting the null hypothesis with a pre-specified true clinical treatment effect. This power is a conditional probability conditioned on the true but actually unknown effect. In practice, however, this true effect is never a fixed value. Thus, we discuss a newly proposed alternative to this conventional statistical power: statistical assurance, defined as the unconditional probability of rejecting the null hypothesis. This kind of assurance can then be obtained as an expected power where the expectation is based on the prior probability distribution of the unknown treatment effect, which leads to the Bayesian paradigm. In this article, we outline the transition from conventional statistical power to the newly developed assurance and discuss the computations of assurance using Monte Carlo simulation-based approach.

This book compiles and presents new developments in statistical causal inference. The accompanying data and computer programs are publicly available so readers may replicate the model development and

BACKGROUND AND PURPOSE:The psychometric properties of the Kansas City Cardiomyopathy Questionnaire (KCCQ) have been examined primarily in community-dwelling patients with heart failure (HF). The objective of this research was to examine the properties of the KCCQ administered to patients hospitalized with HF (N = 233).METHODS:Confirmatory factor analysis, Cronbach's alphas, and correlations were performed to examine the scale's dimensions, reliability, and validity.RESULTS:Confirmatory factor analysis indicated a 5-factor solution (63.6% of the variance). The Cronbach's alpha levels were greater than .70, except for the self-efficacy dimension (.60). Convergent validity was not verified between the KCCQ and several illness severity measures.CONCLUSIONS:The psychometric properties of the KCCQ may be different based on the population in which the KCCQ is administered, which may have clinical implications.

The Cusp Catastrophe Model provides a promising approach for health and behavioral researchers to investigate both continuous and quantum changes in one modeling framework. However, application of the model is hindered by unresolved issues around a statistical model fitting to the data. This paper reports our exploratory work in developing a new approach to statistical cusp catastrophe modeling. In this new approach, the Cusp Catastrophe Model is cast into a statistical nonlinear regression for parameter estimation. The algorithms of the delayed convention and Maxwell convention are applied to obtain parameter estimates using maximum likelihood estimation. Through a series of simulation studies, we demonstrate that (a) parameter estimation of this statistical cusp model is unbiased, and (b) use of a bootstrapping procedure enables efficient statistical inference. To test the utility of this new method, we analyze survey data collected for an NIH-funded project providing HIV-prevention education to adolescents in the Bahamas. We found that the results can be more reasonably explained by our approach than other existing methods. Additional research is needed to establish this new approach as the most reliable method for fitting the cusp catastrophe model. Further research should focus on additional theoretical analysis, extension of the model for analyzing categorical and counting data, and additional applications in analyzing different data types.

Abstract Background: Comparatively few studies have examined the biological mechanisms that may underlie the reported racial disparities in antenatal and postpartum depression. Objective: To examine the associations among race, depressive symptoms and the proinflammatory cytokines interleukin (IL)-6 and tumor necrosis factor (TNF)-α across the perinatal period in a diverse sample of healthy pregnant women at elevated psychosocial risk. Methods: 171 subjects were enrolled. Women were interviewed and blood samples drawn at 18 and 32 weeks gestation and 6 weeks and 6 months postpartum. Depressive symptoms were measured using the Edinburgh Postnatal Depression Scale. Serum levels of IL-6 and TNF-α were assayed using high sensitivity enzyme-linked immunosorbent assay kits. Results: Compared with non-African American (AA) women, AA women had significantly higher levels of IL-6 (est. diff = 0.521, p = 0.02, confidence interval (CI): 0.088–0.954) but not TNF-α across all time points (est. diff = −0.060, p = 0.80, CI: −0.517 to 0.397). IL-6 was not associated with depressive symptoms but differences in IL-6 were accounted for by greater Body Mass Index in AA women. Conclusions: Compared with non-AA women, AA women entered pregnancy with elevated inflammatory cytokine levels that persisted across the perinatal period. This group difference in inflammation did not suggest increased risk for depression, but suggests other implications for long-term health.

Background Although health outcomes may have fundamentally nonlinear relationships with relevant behavioral, psychological, cognitively, or biological predictors, most analytical models assume a linear relationship. Furthermore, some health outcomes may have multimodal distributions, but most statistical models in common use assume a unimodal, normal distribution. Suitable nonlinear models should be developed to explain health outcomes.Objective The aim of this study is to provide an overview of a cusp catastrophe model for examining health outcomes and to present an example using grip strength as an indicator of a physical functioning outcome to illustrate how the technique may be used. Results using linear regression, nonlinear logistic model, and the cusp catastrophe model were compared.Methods Data from 935 participants from the Survey of Midlife Development in the United States (MIDUS) were analyzed. The outcome was grip strength; executive function and the inflammatory cytokine interleukin-6 were predictor variables.Results Grip strength was bimodally distributed. On the basis of fit and model selection criteria, the cusp model was superior to the linear model and the nonlinear logistic regression model. The cusp catastrophe model identified interleukin-6 as a significant asymmetry factor and executive function as a significant bifurcation factor.Conclusion The cusp catastrophe model is a useful alternative for explaining the nonlinear relationships commonly seen between health outcome and its predictors. Considerations for the use of cusp catastrophe model in nursing research are discussed and recommended.