Explained variation and degrees of necessity and of sufficiency for competing risks survival data

In this contribution, the Schemper-Henderson measure of explained variation for survival outcomes is extended to accommodate competing events (CEs) in addition to events of interest. The extension is achieved by moving from the unconditional and conditional survival functions of the original measure to unconditional and conditional cumulative incidence functions, the latter obtained, for example, from Fine and Gray models. In the absence of CEs, the original measure is obtained as a special case. We define explained variation on the population level and provide two different types of estimates. Recently, the authors have achieved a multiplicative decomposition of explained variation into degrees of necessity and degrees of sufficiency. These measures are also extended to the case of competing risks survival data. A SAS macro and an R function are provided to facilitate application. Interesting empirical properties of the measures are explored on the population level and by an extensive simulation study. Advantages of the approach are exemplified by an Austrian study of breast cancer with a high proportion of CEs.

The Power of Peer Leaders: Exploring the Link between Peer Leadership Behaviors and Sustainable Work Outcomes

Most leadership studies primarily focus on formal leaders, often overlooking the influence of leaders within the team. While prior research has shown that peer leaders can have a beneficial impact on various team outcomes, it is yet unclear which peer leadership behaviors precisely foster a supportive and sustainable work environment. Building upon the recent identification of 10 peer leadership roles and 37 underlying functions, the current study aims to investigate the relationships between these peer leadership roles and functions and key outcomes (i.e., job satisfaction, team cohesion, team effectiveness, and OCB). A total of 31 organizational teams, comprising 182 employees from diverse sectors, participated in a quantitative survey. Employing multilevel modeling analysis, the findings demonstrated that each leadership role and nearly every function predicted at least one outcome, highlighting their significance within organizational teams. Additionally, Necessary Condition Analysis revealed that specific roles and functions were necessary for generating one or more outcomes. Finally, we found that most of the significant relationships remained consistent across teams, regardless of their size, tenure, or level of team identification. These findings refine our understanding of shared leadership and how peer leaders can create a sustainable workplace by fostering employee well-being and productivity in organizational teams.

Evaluating Restrictive Models in Educational and Behavioral Research: Local Misfit Overrides Model Tenability

The frequent practice of overall fit evaluation for latent variable models in educational and behavioral research is reconsidered. It is argued that since overall plausibility does not imply local plausibility and is only necessary for the latter, local misfit should be considered a sufficient condition for model rejection, even in the case of omnibus model tenability. The argument is exemplified with a comparison of the widely used one-parameter and two-parameter logistic models. A theoretically and practically relevant setting illustrates how discounting local fit and concentrating instead on overall model fit may lead to incorrect model selection, even if a popular information criterion is also employed. The article concludes with the recommendation for routine examination of particular parameter constraints within latent variable models as part of their fit evaluation.

Degrees of necessity and of sufficiency: Further results and extensions, with an application to covid-19 mortality in Austria

The purpose of this paper is to extend to ordinal and nominal outcomes the measures of degree of necessity and of sufficiency defined by the authors for dichotomous and survival outcomes in a previous paper. A cause, represented by certain values of prognostic factors, is considered necessary for an event if, without the cause, the event cannot develop. It is considered sufficient for an event if the event is unavoidable in the presence of the cause. The degrees of necessity and sufficiency, ranging from zero to one, are simple, intuitive functions of unconditional and conditional probabilities of an event such as disease or death. These probabilities often will be derived from logistic regression models; the measures, however, do not require any particular model. In addition, we study in detail the relationship between the proposed measures and the related explained variation summary for dichotomous outcomes, which are the common root for the developments for ordinal, nominal, and survival outcomes. We introduce and analyze the Austrian covid-19 data, with the aim of quantifying effects of age and other potentially prognostic factors on covid-19 mortality. This is achieved by standard regression methods but also in terms of the newly proposed measures. It is shown how they complement the toolbox of prognostic factor studies, in particular when comparing the importance of prognostic factors of different types. While the full model's degree of necessity is extremely high (0.933), its low degree of sufficiency (0.179) is responsible for the low proportion of explained variation (0.193).

A Method for Examining the Equating of Psychometric Scales and Tests: An Application Using Dementia Screening Test Batteries

Equating of psychometric scales and tests is frequently required and conducted in educational, behavioral, and clinical research. Construct comparability or equivalence between measuring instruments is a necessary condition for making decisions about linking and equating resulting scores. This article is concerned with a widely applicable method for examining if two scales or tests cannot be equated. A latent variable modeling method is discussed that can be used to evaluate whether the tests or parts thereof measure latent constructs that are distinct from each other. The approach can be routinely used before an equating procedure is undertaken, in order to assess whether equating could be meaningfully carried out to begin with. The procedure is readily applicable in empirical research using popular software. The method is illustrated with data from dementia screening test batteries administered as part of two studies designed to evaluate a wide range of biomarkers throughout the process of normal aging to dementia or Alzheimer's disease.

Sugar-Sweetened Beverages, Type 2 Diabetes and Factual Causation in Negligence

In this article we consider whether sugar-sweetened beverages (SSBs) (factually) cause type 2 diabetes for the purposes of negligence. In so doing we demonstrate how factual causation is confounded by other contributing factors such as genetics, lack of physical activity and other diet behaviours (eg low-fibre and high-fat diets). That said, a plaintiff is not necessarily deprived of the opportunity to prove causation merely because there are multiple contributing factors to the harm. While difficult, it is possible for type 2 diabetes to be categorised as an "exceptional circumstance", in which it must be shown that SSBs "materially contributed" to or were a "necessary element" of, the development of type 2 diabetes.

Quantifying degrees of necessity and of sufficiency in cause-effect relationships with dichotomous and survival outcomes

We suggest measures to quantify the degrees of necessity and of sufficiency of prognostic factors for dichotomous and for survival outcomes. A cause, represented by certain values of prognostic factors, is considered necessary for an event if, without the cause, the event cannot develop. It is considered sufficient for an event if the event is unavoidable in the presence of the cause. Necessity and sufficiency can be seen as the two faces of causation, and this symmetry and equal relevance are reflected by the suggested measures. The measures provide an approximate, in some cases an exact, multiplicative decomposition of explained variation as defined by Schemper and Henderson for censored survival and for dichotomous outcomes.

The measures, ranging from zero to one, are simple, intuitive functions of unconditional and conditional probabilities of an event such as disease or death. These probabilities often will be derived from logistic or Cox regression models; the measures, however, do not require any particular model.

The measures of the degree of necessity implicitly generalize the established attributable fraction or risk for dichotomous prognostic factors and dichotomous outcomes to continuous prognostic factors and to survival outcomes. In a setting with multiple prognostic factors, they provide marginal and partial results akin to marginal and partial odds and hazard ratios from multiple logistic and Cox regression.

Properties of the measures are explored by an extensive simulation study. Their application is demonstrated by three typical real data examples.