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Conditional bootstrap methods for censored data
Title
Conditional bootstrap methods for censored data.
Creator
Kim, Ji-Hyun., Florida State University
Abstract/Description
We first consider the random censorship model of survival analysis. The pairs of positive random variables ($X\sb{i},Y\sb{i}$), i = 1,$\...$,n, are independent and identically distributed, with distribution functions F(t) = P($X\sb{i} \leq\ t$) and G(t) = P($Y\sb{i} \leq\ t$) and the Y's are independent of the X's. We observe only ($T\sb{i},\delta\sb{i}$), i = 1,$\...$,n, where $T\sb{i}$ = min($X\sb{i},Y\sb{i}$) and $\delta\sb{i}$ = I($X\sb{i} \leq\ Y\sb{i}$). The X's represent survival times...
Show moreWe first consider the random censorship model of survival analysis. The pairs of positive random variables ($X\sb{i},Y\sb{i}$), i = 1,$\...$,n, are independent and identically distributed, with distribution functions F(t) = P($X\sb{i} \leq\ t$) and G(t) = P($Y\sb{i} \leq\ t$) and the Y's are independent of the X's. We observe only ($T\sb{i},\delta\sb{i}$), i = 1,$\...$,n, where $T\sb{i}$ = min($X\sb{i},Y\sb{i}$) and $\delta\sb{i}$ = I($X\sb{i} \leq\ Y\sb{i}$). The X's represent survival times, the Y's represent censoring times. Efron (1981) proposed two bootstrap methods for the random censorship model and showed that they are distributionally the same. Akritas (1986) established the weak convergence of the bootstrapped Kaplan-Meier estimator of F when bootstrapping is done by this method. Let us now consider bootstrapping more closely. Suppose that we wish to estimate the variance of F(t). If we knew the Y's then we would condition on them by the ancillarity principle, since the distribution of the Y's does not depend on F. That is, we would want to estimate Var$\{$F(t)$\vert Y\sb1,\...,Y\sb{n}\}$. Unfortunately, in the random censorship model we do not see all the Y's. If $\delta\sb{i}$ = 0 we see the exact value of $Y\sb{i}$, but if $\delta\sb{i}$ = 1 we know only that $Y\sb{i} > T\sb{i}$. Let us denote this information on the Y's by ${\cal C}$. Thus, what we want to estimate is Var$\{$F(t)$\vert{\cal C}\}$. Efron's scheme is appropriate for estimating the unconditional variance. We propose a new bootstrap method which provides an estimate of Var$\{$F(t)$\vert{\cal C}\}$., In this research we show that the Kaplan-Meier estimator of F formed by the new bootstrap method has the same limiting distribution as the one by Efron's approach. The results of simulation studies assessing the small sample performance of the two bootstrap methods are reported. We also consider the model in which the $X\sb{i}$'s are censored by the $Y\sb{i}$'s and also by known fixed constants, and propose an appropriate bootstrap method for that model. This bootstrap method is a readily modified version of the new bootstrap method above.
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Date Issued
1990, 1990
Identifier
AAI9113938, 3162201, FSDT3162201, fsu:78399
Format
Document (PDF)
Information and Culture
Title
Information and Culture: Cultural Differences in the Perception and Recall of Information from Advertisements.
Creator
Kim, Ji-Hyun, Gross, Melissa, Goldsmith, Ronald, Marty, Paul F., Lustria, Mia Liza A., School of Library and Information Studies, Florida State University
Abstract/Description
Information in general is congruent with cultural values because a culture consists of transmitted social knowledge. Cross-cultural research demonstrates that audiences who are fostered by different cultures may have different understandings of information. This research represents a comprehensive cross-cultural study using an experimental method, and contributes to multicultural studies in understanding individuals' perceptions of information, recalls of information, and attitudes based on...
Show moreInformation in general is congruent with cultural values because a culture consists of transmitted social knowledge. Cross-cultural research demonstrates that audiences who are fostered by different cultures may have different understandings of information. This research represents a comprehensive cross-cultural study using an experimental method, and contributes to multicultural studies in understanding individuals' perceptions of information, recalls of information, and attitudes based on cultures. This study investigates whether people in individual or collective cultures have different perceptions of information in advertisements, recall of information in advertisements, and attitudes toward advertisements providing information in high- or low- context conditions. The theoretical frameworks of interest in the study are two cultural theories: Hofstede's (1980) individualism vs. collectivism and Hall's (1976) high context vs. low context. The hypotheses were tested using a 2 × 2 factorial between-subject experimental design: individualism/collectivism and high context/low context. The low-context condition employed facts and direct information in a test advertisement, while the high-context condition included indirect messages (e.g. images, moods, and symbols) in a test advertisement. The responses of experimental groups were compared and analyzed after they were exposed to two different stimuli. The subjects consisted of 82 American students and 82 Korean students. To check the two subject groups' cultural differences, this research employs Oyserman et al.'s (2002) individualism and collectivism scale. The test results indicate that American subjects are classified as an individualistic culture, while the Korean subjects represent a collectivistic culture. The experiment results indicate that students in individualistic and collectivistic cultures respond differently to information in high- or low-context advertisements. Koreans tend to be more comfortable with high-context culture that uses indirect and ambiguous messages. The Korean subjects showed higher ratings for perceptions of information in a high-context advertisement than the American subjects. The American subjects perceived more information than Korean subjects in the low-context advertisement, but this result was not statistically significant. There is no statistically significant difference in recall of information from high- and low-context conditions between American and Korean subjects. The American subjects showed significantly more favorable attitudes toward the low-context advertisement than the Korean students. However, there was no statistically significant difference in attitudes toward the high-context advertisement between American and Korean students. This study partially supports the notion that cultural differences influence the perception of information in advertisements, recall of information in advertisements, and attitudes toward advertisements providing information in high- or low- context conditions. The findings obtained in this study suggest several exciting opportunities for future research.
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Date Issued
2012
Identifier
FSU_migr_etd-4950
Format
Thesis