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.     

“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.     

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.     

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.     

On the efficiency of monte carlo methods using steady state ranked simulated samples

Samawi (1999) showed that the efficiency of Monte Carlo methods of integrals estimation can be substantially improved by using ranked simulated samples (RSIS) in place of uniform simulated samples (USIS). However, in this paper it is shown that substantial improvement of efficiency can be achieved further by using the steady state ranked simulated sample (SRSIS). It appears that the modified Monte Carlo methods using SRSIS provide unbiased and more efficient estimators for the integrals. Some theoretical properties of SRSIS are given. A simulation study is conducted to compare the performance of the methods using SRSIS with respect to USIS, for some examples.     

Notes on two sample tests for partially correlated (paired) data

We provide several methods to compare two Gaussian distributed means in the two sample location problems under the assumption of partially dependent observations. Simulation studies indicate that our test procedure is frequently more powerful than other methods depending on the ratio of the unpaired data and the strength and direction of the correlation between the two variables. The tests used in our comparative study are illustrated with an example based on data from a small gynecological study.     

On quantiles estimation based on different stratified sampling with optimal allocation

This work considers the problem of estimating a quantile function based on different stratified sampling mechanism. First, we develop an estimate for population quantiles based on stratified simple random sampling (SSRS) and extend the discussion for stratified ranked set sampling (SRSS). Furthermore, the asymptotic behavior of the proposed estimators are presented. In addition, we derive an analytical expression for the optimal allocation under both sampling schemes. Simulation studies are designed to examine the performance of the proposed estimators under varying distributional assumptions. The efficiency of the proposed estimates is further illustrated by analyzing a real data set from CHNS.     

Methods improving the estimate of diagnostic odds ratio

Diagnostic odds ratio is defined as the ratio of the odds of the positivity of a diagnostic test results in the diseased population relative to that in the non-diseased population. It is a function of sensitivity and specificity, which can be seen as an indicator of the diagnostic accuracy for the evaluation of a biomarker/test. The naïve estimator of diagnostic odds ratio fails when either sensitivity or specificity is close to one, which leads the denominator of diagnostic odds ratio equal to zero. We propose several methods to adjust for such situation. Agresti and Coull’s adjustment is a common and straightforward way for extreme binomial proportions. Alternatively, estimation methods based on a more advanced sampling design can be applied, which systematically selects samples from underlying population based on judgment ranks. Under such design, the odds can be estimated by the sum of indicator functions and thus avoid the situation of dividing by zero and provide a valid estimation. The asymptotic mean and variance of the proposed estimators are derived. All methods are readily applied for the confidence interval estimation and hypothesis testing for diagnostic odds ratio. A simulation study is conducted to compare the efficiency of the proposed methods. Finally, the proposed methods are illustrated using a real dataset.     

WEIGHING THE MILITARY OPTION: THE EFFECTS OF WARTIME CONDITIONS ON INVESTMENTS IN HUMAN CAPITAL

Serving in the military is an important vehicle through which young Americans invest in their human capital. As such, changes in the desirability of military service may affect the attainment of enlistment requirements, such as a high school degree or equivalent. Using American Community Survey data, we find that exposure to home‐state combat fatalities during the Iraq and Afghanistan Wars decreased the probability of high school completion, and increased the probability of general equivalency diploma completion. Using military data, we confirm that exposure to home‐state fatalities selectively deterred some individuals from enlisting. The results suggest military service and educational investments are complements. (JEL I20, I26, J24)