## 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

- e.g. when when two observations fall below a threshold
- 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!