Readings

Delta method and bootstrap in linear mixed models to estimate a proportion when no event is observed: application to intralesional resection in bone tumor surgery

Francq, B. G., & Cartiaux, O. (2016). Delta method and bootstrap in linear mixed models to estimate a proportion when no event is observed: application to intralesional resection in bone tumor surgery. Statistics in Medicine. https://doi.org/10.1002/sim.6939

• Estimation of rare proportions
  • could be useful for my work
  • I wonder how many zeroes can be in the data for this method to work
    • that will be my main question at the moment
• Give the example of adverse events in clinical trials
  • here, many adverse events will have 0 counts
• Provide a toy example of estimating probabilities of height thresholds in small samples
  • expect different probabilities from different thresholds
  • clearly due to ordering of heights
• the problem with the existing methods is that they give the same interval for different thresholds
  • e.g. when when two observations fall below a threshold
    • here they have different values, but give a 0 value anyway
    • so they should have different intervals due to the different values
• first extension is the delta method on the z-score
  • using the observed values, calculate sample mean and sd, and z-score
  • find variance of the z-score using delta method
  • then confidence interval of z-score gets transformed for the probability confidence interval
• can also be used on the cdf of z
  • this has problems with intervals though
• standard nonparametric bootstrap doesn\’t work
  • if you have no events, none will be in the bootstrap resamples!