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Related Concept Videos

Bias01:22

Bias

Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected or encouraged over others in sampling or testing. Bias can occur during any research phase, including study design, data collection, analysis, and publication.
In statistics, a sampling bias is created when a sample is collected from a population, and some members of the population are not as likely to be chosen as others (remember, each member...
One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
Choosing Between z and t Distribution01:25

Choosing Between z and t Distribution

The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution to use for a calculation, one needs to determine the sample size, the nature of the distribution, and whether the population standard deviation is known. If the population standard deviation is known and the population is normally distributed, or if the sample size is greater than 30, the z distribution is preferred. The Student t distribution is...
Random Sampling Method01:09

Random Sampling Method

Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data01:16

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance, comparing...

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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
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Likelihood approaches for the invariant density ratio model with biased-sampling data.

Yu Shen1, Jing Ning, Jing Qin

  • 1Department of Biostatistics, MD Anderson Cancer Center, The University of Texas, Houston, Texas 77030, U.S.A. , yshen@mdanderson.org.

Biometrika
|July 12, 2013
PubMed
Summary

This study introduces efficient statistical methods for analyzing complex length-biased failure time data. The proposed full likelihood approaches improve estimation and inference for survival distributions, outperforming conditional methods.

Keywords:
Conditional likelihoodDensity ratio modelLength-biased samplingMaximum likelihood approachem algorithm

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Area of Science:

  • Statistics
  • Survival Analysis
  • Biostatistics

Background:

  • Full likelihood methods are optimal for statistical estimation and inference.
  • Complex length-biased failure time data present computational and theoretical challenges, particularly with infinite-dimensional parameters.
  • Existing methods for length-biased data are limited.

Purpose of the Study:

  • To develop and assess two likelihood-based approaches for estimating and comparing survival distributions with length-biased data.
  • To provide efficient estimators for complex survival data.
  • To enable consistent estimation of population failure times from censored length-biased data.

Main Methods:

  • Utilized the invariance property of length-biased data under the semiparametric density ratio model.
  • Developed maximum likelihood estimators using the EM algorithm and profile likelihood.
  • Introduced a conditional likelihood method for estimation and inference, generalizable to k-arm settings.
  • Proposed a test statistic based on the area between survival distributions to validate the model assumption.

Main Results:

  • The EM algorithm and profile likelihood yield the most efficient maximum likelihood estimators.
  • A conditional likelihood method offers a simpler estimation and inference approach.
  • The mean of population failure times can be consistently estimated from right-censored length-biased data.
  • Simulation studies demonstrated the superior efficiency of full likelihood estimators over conditional likelihood estimators.

Conclusions:

  • The proposed full likelihood approaches provide efficient statistical tools for analyzing length-biased failure time data.
  • These methods enhance the estimation and assessment of differences between survival distributions.
  • The study successfully applied these novel methods to an epidemiological dataset, validating their practical utility.