steps for simulation sample size

1. Write the statistical model mathematically.
2. Generate the sample according to the model with sample size N.
3. Fit the model, perform the test, and record the rejection or acceptance of hull hypothesis.
4. Repeat step 2 and 3 n (generally I used 5000) times.
5. Calculate the power by (# of rejections)/n.

6 If power is too higher, decrease sample size N, repeat 2 - 5. If power is too lower, increase sample size N, repeat 2 - 5.

number of basis fuction for spline regression

The number of basis function is n+d+1, where n is the number of (internal) knots, where d is the degree of the basis function.

R datasets

https://vincentarelbundock.github.io/Rdatasets/datasets.html

NOTES ON ACCURACY OF POINT PREDICTIONS IN SURVIVAL ANALYSIS

Producing graphs of the survival and baseline hazard function after Cox regression

• When only plots=survival is specified on the proc phreg statement, SAS will produce one graph, a “reference curve” of the survival function at the reference level of all categorical predictors and at the mean of all continuous predictors.

https://stats.idre.ucla.edu/sas/seminars/sas-survival/

Heine–Borel theorem

https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Heine%E2%80%93Borel_theorem.html

Math scripts