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Related Concept Videos

Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Estimating Population Mean with Known Standard Deviation01:16

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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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...
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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Hazard Ratio01:12

Hazard Ratio

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The hazard ratio (HR) is a widely used measure in clinical trials to compare the risk of events, such as death or disease recurrence, between two groups over time. It reflects the ratio of hazard rates—the instantaneous risk of the event occurring—between a treatment group and a control group. This measure provides valuable insights into the relative effectiveness of a treatment by assessing how the risk of an event differs between the two groups.
For example, in a clinical trial...
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On Estimation of the Hazard Function from Population-based Case-Control Studies.

Li Hsu1, Malka Gorfine2, David M Zucker3

  • 1Biostatistics and Biomathematics, Fred Hutchinson Cancer Research Center.

Journal of the American Statistical Association
|March 26, 2019
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Summary
This summary is machine-generated.

This study introduces a novel method using family history data to estimate the baseline hazard function in case-control studies. This innovation aids in more accurate absolute risk assessment for chronic diseases.

Keywords:
Copula modelFamily historyMarginal hazard functionMultivariate survival analysis

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Area of Science:

  • Epidemiology
  • Biostatistics
  • Chronic Disease Etiology

Background:

  • Population-based case-control studies are vital for chronic disease etiology research.
  • Logistic regression models adapt Cox proportional hazards models for case-control data.
  • The baseline hazard function is crucial for absolute risk assessment but unidentifiable in standard case-control designs.

Purpose of the Study:

  • To propose a novel, simple approach for estimating the baseline hazard function in case-control studies.
  • To utilize routinely collected family history information for this estimation.
  • To enable more accurate absolute risk assessment in epidemiological research.

Main Methods:

  • Developed a new estimator for the baseline hazard function using family history data.
  • Applied the estimator within logistic regression models fitted to case-control risk factor data.
  • Assessed the estimator's consistency and asymptotic normality theoretically and via simulation.

Main Results:

  • The proposed baseline hazard function estimator is statistically consistent and asymptotically normal.
  • Simulation studies demonstrate good performance of the estimator in finite samples.
  • The method was successfully illustrated using a prostate cancer case-control study.

Conclusions:

  • Family history information can effectively be used to estimate the unidentifiable baseline hazard function.
  • This approach enhances absolute risk assessment capabilities in case-control studies.
  • The method offers a practical solution for improving epidemiological risk factor analysis.