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Related Concept Videos

Odds Ratio01:09

Odds Ratio

The odds ratio (OR) is a statistical measure used extensively in epidemiology and research to quantify the strength of association between exposure and outcome across different groups. Unlike relative risk, which compares the probabilities of an event occurring, the odds ratio compares the odds of an event occurring in the exposed group to the odds of it occurring in the unexposed group. The odds, in this context, are calculated as the probability of the event happening divided by the...
Variance01:15

Variance

The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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...
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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.
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Variability: Analysis01:11

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Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
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Estimating Population Mean with Unknown Standard Deviation01:22

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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 Guinness...

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An R-Based Landscape Validation of a Competing Risk Model
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Published on: September 16, 2022

Accurate variance estimation for prevalence ratios.

M Wolkewitz1, T Bruckner, M Schumacher

  • 1Institute of Medical Biometry and Medical Informatics, University Medical Center Freiburg, Stefan-Meier-Str. 26, 79104 Freiburg, and Department of Clinical and Social Medicine, University Hospital Heidelberg, Germany. wolke@fdm.uni-freiburg.de

Methods of Information in Medicine
|October 17, 2007
PubMed
Summary

For calculating prevalence ratios in cross-sectional studies, the log-binomial model can be unstable. If it fails, the Poisson model with a robust variance is recommended for reliable results.

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Area of Science:

  • Epidemiology
  • Biostatistics

Background:

  • The log-binomial model is standard for prevalence ratio estimation in cross-sectional studies with binary outcomes.
  • Numerical instability can cause convergence issues with the log-binomial model.
  • Alternative methods are needed when the log-binomial model fails.

Purpose of the Study:

  • To compare different adjustments for the Poisson model when the log-binomial model fails.
  • To evaluate the performance of adjusted Poisson models against the log-binomial model for prevalence ratio calculation.

Main Methods:

  • Simulated data were used to assess Poisson models with robust variance, Pearson's chi-square adjustment, and deviance adjustment.
  • Model performance was evaluated based on hypothesis testing, considering confounding and effect modification.
  • Comparison was made against the log-binomial model.

Main Results:

  • All tested Poisson model adjustments improved variance estimation compared to unadjusted models.
  • The Poisson model with a robust variance demonstrated the best performance.
  • The log-binomial model provided acceptable power and Type I error rates even when unstable.
  • The Poisson model with Pearson's chi-square adjustment also yielded favorable results.

Conclusions:

  • The Poisson model with a robust variance estimate is recommended when the log-binomial model fails to converge for prevalence ratio estimation.
  • This approach offers a reliable alternative for analyzing binary outcomes in cross-sectional studies.