====================================================================== ST 453 Final Project - Bootstrap Study Summary Trace Brown ====================================================================== BOOTSTRAP PARAMETERS ---------------------------------------------------------------------- Bootstrap method: Pairs/case resampling (resample (X, y) rows with replacement, n at a time) Number of bootstrap samples: N = 1000 Sample size per bootstrap: n = 299 (matches original) Number of parameters: p = 5 Convergence rate: 100 % Mean events per bootstrap sample: 96.13 (real data: 96 ) Random seeds: 1 through 1000 JUSTIFICATION OF N ---------------------------------------------------------------------- With N = 1000 bootstrap samples, the 2.5%/97.5% quantiles are estimated from order statistics near ranks 25 and 975 , giving stable percentile-CI boundaries. MC SE of quantile rank position: 0.004937 MC SE of bootstrap mean estimate (~SD / sqrt(N)): Intercept : 0.006883 Age : 0.005375 Ejection Fraction : 0.006780 Serum Creatinine : 0.008911 Time : 0.008287 BOOTSTRAP COEFFICIENT SUMMARY ---------------------------------------------------------------------- Coefficient Estimate BootMean BootMed BootSD Bias ---------------------------------------------------------------------- Intercept -1.2902 -1.3370 -1.3183 0.2177 -0.0468 Age 0.5154 0.5440 0.5367 0.1700 0.0287 Ejection Fraction -0.8853 -0.9306 -0.9156 0.2144 -0.0453 Serum Creatinine 0.7446 0.7856 0.7640 0.2818 0.0410 Time -1.5997 -1.6627 -1.6360 0.2621 -0.0630 STANDARD ERRORS: WALD (HESSIAN) vs BOOTSTRAP ---------------------------------------------------------------------- Coefficient Wald SE Boot SD Ratio ---------------------------------------------------------------------- Intercept 0.1953 0.2177 1.1145 Age 0.1769 0.1700 0.9608 Ejection Fraction 0.1841 0.2144 1.1647 Serum Creatinine 0.1806 0.2818 1.5601 Time 0.2237 0.2621 1.1717 95% CONFIDENCE INTERVALS (5 METHODS) ---------------------------------------------------------------------- Intercept Wald: [ -1.6730, -0.9074] width = 0.7656 Percentile: [ -1.8348, -0.9622] width = 0.8726 Basic: [ -1.6182, -0.7455] width = 0.8726 Normal: [ -1.7168, -0.8635] width = 0.8533 BCa: [ -1.7257, -0.8805] width = 0.8452 Age Wald: [ 0.1686, 0.8621] width = 0.6935 Percentile: [ 0.2361, 0.9002] width = 0.6642 Basic: [ 0.1305, 0.7946] width = 0.6642 Normal: [ 0.1822, 0.8485] width = 0.6663 BCa: [ 0.1881, 0.8263] width = 0.6382 Ejection Fraction Wald: [ -1.2461, -0.5245] width = 0.7217 Percentile: [ -1.3989, -0.5393] width = 0.8595 Basic: [ -1.2312, -0.3717] width = 0.8595 Normal: [ -1.3055, -0.4650] width = 0.8405 BCa: [ -1.2854, -0.4648] width = 0.8206 Serum Creatinine Wald: [ 0.3906, 1.0987] width = 0.7081 Percentile: [ 0.3310, 1.4493] width = 1.1183 Basic: [ 0.0400, 1.1583] width = 1.1183 Normal: [ 0.1923, 1.2969] width = 1.1046 BCa: [ 0.2980, 1.3432] width = 1.0452 Time Wald: [ -2.0381, -1.1613] width = 0.8768 Percentile: [ -2.2525, -1.2106] width = 1.0419 Basic: [ -1.9888, -0.9469] width = 1.0419 Normal: [ -2.1133, -1.0861] width = 1.0273 BCa: [ -2.1301, -1.1498] width = 0.9803 BCa BIAS-CORRECTION AND ACCELERATION CONSTANTS ---------------------------------------------------------------------- Coefficient z0 a ---------------------------------------------------------------------- Intercept 0.1484 0.0256 Age -0.1586 -0.0100 Ejection Fraction 0.1611 0.0236 Serum Creatinine -0.0577 -0.0011 Time 0.1611 0.0269 HYPOTHESIS TESTS (H0: beta_j = 0) ---------------------------------------------------------------------- Coefficient z-stat Wald p Boot p Wsig Bsig ---------------------------------------------------------------------- Intercept -6.6056 3.96e-11 1e-03 *** ** Age 2.9131 3.58e-03 4e-03 ** ** Ejection Fraction -4.8087 1.52e-06 1e-03 *** ** Serum Creatinine 4.1223 3.75e-05 1e-03 *** ** Time -7.1522 8.54e-13 1e-03 *** ** Significance codes: *** p<.001, ** p<.01, * p<.05 Note: Bootstrap p-values are floored at 1/N (resolution limit).