Reducing sample size needed for cox-proportional hazards model analysis using more efficient sampling method

Abstract

In general, survival data are time-to-event data, such as time to death, time to appearance of a tumor, or time to recurrence of a disease. Models for survival data have frequently been based on the proportional hazards model, proposed by Cox. The Cox model has intensive application in the field of social, medical, behavioral and public health sciences. In this paper we propose a more efficient sampling method of recruiting subjects for survival analysis. We propose using a Moving Extreme Ranked Set Sampling (MERSS) scheme with ranking based on an easy-to-evaluate baseline auxiliary variable known to be associated with survival time. This paper demonstrates that this approach provides a more powerful testing procedure as well as a more efficient estimate of hazard ratio than that based on simple random sampling (SRS). Theoretical derivation and simulation studies are provided. The Iowa 65+ Rural study data are used to illustrate the methods developed in this paper.     

Couples’ time together: complementarities in production versus complementarities in consumption

Economists have previously suggested that gains from marriage can be generated by complementarities in production (gains from specialization and exchange) or by complementarities in consumption (gains from joint consumption of household public goods and joint time consumption). This paper uses the American Time Use Survey (ATUS) from 2003 to 2011 to test whether couples that engage in less specialization (are more similar in hours of market work) spend more time together. We find that among married couples without young children, those with a greater difference in weekly hours of work between husband and wife spend less time together on non-working weekend days. Importantly, we find that this relationship is quite symmetric between couples in which the husband works greater hours and couples in which the wife works greater hours. We do not find evidence of a relationship between specialization and couple time together among couples with young children.     

On Comparing Alternative Advertising Policies of Pulsation*

In this paper, five alternative advertising policies that belong to the advertising pulsation class are compared analytically for linear and concave response functions using a modified version of the Vidale-Wolfe model. The results of the research show that (1) For both linear and concave response functions, advertising pulsing/maintenance policy dominates advertising pulsing policy but is dominated by the Uniform Advertising Policy. For convex response functions, the order of dominance is reversed. (2) For linear response functions, uniform advertising policy dominates the impulse advertising policy but is dominated by the chattering advertising policy. (3) For concave response functions, uniform advertising policy dominates both the impulse advertising policy and the chattering advertising policy. (4) For convex response functions, chattering advertising policy dominates both the advertising pulsing policy and the impulse advertising policy. The Vidale-Wolfe model is estimated using the well-known Lydia Pinkham data. Optimality analysis shows that the company was overadvertising about half of the time studied. Overadvertising seems to have produced appreciable gain in sales and created significant barriers to competitive entry at a little cost in terms of foregone profits.     

Faculty Performance Evaluation: Modeling to Improve Personnel Decisions*

Based on likely future changes in faculty evaluation practices, this paper examines how institutions of higher education might operationalize performance evaluation as related to research, teaching, and service. A model is developed that allows coupling performance evaluation and relevant market considerations with merit pay, tenure, and promotion decisions. The approach is specifically applicable to tenure-track faculty members in colleges and universities.     

A new aging concept derived from the increasing convex ordering

In this paper, a comparison between the life distribution of a new unit with that of a used unit in the increasing convex order is made leading to a new class of life distributions which we call “new better than used in convex ordering of second order”. This class includes as subclasses the NBU and the NBUC and is a subclass of the NBUCA class. Preservation properties under convolution, random maxima, mixing and formation of coherent structures are established. Stochastic comparisons of the excess lifetime when the inter-arrival times belong to the NBUC(2) class are developed. Some applications of Poisson shock models and a test of exponentiality against NBUC(2) alternative are presented.     

The effect of small sample on optimal designs for logistic regression models

Asymptotic methods are commonly used in statistical inference for unknown parameters in binary data models. These methods are based on large sample theory, a condition which may be in conflict with small sample size and hence leads to poor results in the optimal designs theory. In this paper, we apply the second order expansions of the maximum likelihood estimator and derive a matrix formula for the mean square error (MSE) to obtain more precise optimal designs based on the MSE. Numerical results indicate the new optimal designs are more efficient than the optimal designs based on the information matrix.     

“Here One Moment… and Gone the Next?” Remittance as a Social Visibility Tool

Human labor is as much an export as any good. Remittances are a critical source of income for left‐behind families and communities. Transnational labor migrants often describe themselves as ‘invisible’: neither present in the lives of left‐behind families nor members of the receiving community. Building on social remittances literature, we argue that remittances serve as a remedy for this ‘invisibility.’ Through analysis of interviews with 26 temporary labor migrants from 11 countries resident in Israel, we find remittances can render migrants visible to transnational families and provide identity benefits to labor migrants. If visibility benefits decline because of familial role changes, reduced value as a remitter, cost exceeding benefits or because contracting partners change, remittance practices will change. Contrary to previous literature, our findings show that remittances decisions are dynamic, revealing why remittances practices change and even cease. Findings have implications for understanding the multibillion‐dollar remittances industry and immigrant incorporation.     

ON MODELING ADVERTISING PULSING DECISIONS

Based on empirical findings in the literature, sales response to advertising pulsing policy (APP) is modeled mathematically. The implications for APP are discussed. This policy is compared with an alternative policy of uniform expenditures (UAP), a commonly used strategy. The results of the research indicate that substantial savings in advertising budget or an increase in sales revenues may be achieved for a firm using APP.     

The matched pair sign test using bivariate ranked set sampling for different ranking based schemes

Bivariate rank set sample (BVRSS) matched pair sign test is introduced and investigated for different ranking based schemes. We show that this test is asymptotically more efficient and more powerful than its counterpart sign test based on a bivariate simple random sample (BVSRS) for different ranking schemes. The asymptotic null distribution and the efficiency of the test are derived. Pitman’s asymptotic relative efficiency is used to compare the asymptotic performance of the matched pair sign test using BVRSS versus using BVSRS in all ranking cases. For small sample sizes, the bootstrap method is used to estimate P-values. Numerical comparisons are used to gain insight about the efficiency of the BVRSS sign test compared to the BVSRS sign test. Our numerical and theoretical results indicate that using any ranking scheme of BVRSS for the matched pair sign test is more efficient than using BVSRS.     

Revenue Mobilisation in Sub‐Saharan Africa: Challenges from Globalisation I – Trade Reform

This is the first of two articles evaluating the nature and extent of, and possible responses to, two of the central challenges that globalisation poses for revenue mobilisation in sub‐Saharan Africa: trade liberalisation, and corporate tax competition. Both articles use a new dataset with the features needed to address these issues meaningfully: a disentangling of tariff from commodity tax revenue, and a distinction between resource‐related and other revenues. This first article describes that dataset, and provides a broad picture of revenue developments in the region between 1980 and 2005. Countries’ experiences have varied, but the overall picture is of non‐resource revenues having been essentially stagnant. Within this, however, and with exceptions, reductions in trade tax revenue have been largely offset by increased revenue from domestic sources.