HAZARD INCREMENT ESTIMATE FROM NESTED CASE CONTROL DATA f case control set R wj More specialized weight than for rate ratio estimator b P e R 1 b w j j e j R 1 SIMPLE RANDOM SAMPLING OF m 1 CONTROLS Case control set estimator of increment wj n m n number in risk set b z0 e R 1 P e j R exp Zj z0 b log n m Include log n m as an offset in the model 2 SIMPLE RANDOM SAMPLING OF m 1 CONTROLS MATCHED ON C Case control set estimator of increment wj n m n number in unstratified risk set b z0 e R 1 P e j R exp Zj z0 b log n m Include log n m as an offset in the model 3 COUNTER MATCHED SAMPLING ON YEARS MINING 13 13 years Case control set estimator of increment wj nCj mCj nl number in risk set with C l b z0 e R 1 P e j R exp Zj z0 b log nCj mCj Include log nCj mCj as an offset in the model 4 PROPERTIES OF THE CASE CONTROL ESTIMATORS b z at Unbiased for full cohort 0 R 0 Variance estimated using the weights are valid Can use same software for estimation of risk as for the full cohort risk sets 5 Miners SRS 3 nested case control analysis data set actual data setno rsentry rstime record cc timeint offset cr500 1 1 1 34 4999 34 4999 34 4999 34 500 34 500 34 500 1790 2907 1379 1 0 0 1 1 1 6 31536 6 31536 6 31536 1 1 0 2 2 2 36 4199 36 4199 36 4199 36 420 36 420 36 420 2856 2608 809 1 0 0 1 1 1 6 40413 6 40413 6 40413 1 0 1 3 3 3 38 1699 38 1699 38 1699 38 170 38 170 38 170 1338 2682 324 1 0 0 1 1 1 6 47028 6 47028 6 47028 1 0 0 4 4 4 39 9199 39 9199 39 9199 39 920 39 920 39 920 185 1731 1174 1 0 0 1 1 1 6 53233 6 53233 6 53233 1 0 1 5 5 5 39 9999 39 9999 39 9999 40 000 40 000 40 000 258 3231 521 1 0 0 1 1 1 6 53233 6 53233 6 53233 1 0 1 6 6 6 40 0799 40 0799 40 0799 40 080 40 080 40 080 3242 3152 2650 1 0 0 1 1 1 6 53766 6 53766 6 53766 0 1 1 offset log weight log n m 6 CM 2 2 DATA FOR RISK ESTIMATION setno rsentry rstime record cc mine13 C i m C i n C i offset cr500 Z 1 1 1 1 34 4999 34 4999 34 4999 34 4999 34 500 34 500 34 500 34 500 316 2114 1790 2127 0 0 1 0 0 0 1 1 2 2 2 2 1498 1498 161 161 6 61874 6 61874 4 38826 4 38826 0 1 1 1 2 2 2 2 36 4199 36 4199 36 4199 36 4199 36 420 36 420 36 420 36 420 2445 2715 2856 1618 0 0 1 0 0 0 1 1 2 2 2 2 1612 1612 201 201 6 69208 6 69208 4 61016 4 61016 0 1 1 1 3 3 3 3 38 1699 38 1699 38 1699 38 1699 38 170 38 170 38 170 38 170 1283 761 1338 1256 0 0 1 0 0 0 1 1 2 2 2 2 1679 1679 258 258 6 73281 6 73281 4 85981 4 85981 1 0 1 1 4 4 4 4 39 9199 39 9199 39 9199 39 9199 39 920 39 920 39 920 39 920 1240 640 185 1700 0 0 1 0 0 0 1 1 2 2 2 2 1767 1767 294 294 6 78389 6 78389 4 99043 4 99043 1 0 1 1 5 5 5 5 39 9999 39 9999 39 9999 39 9999 40 000 40 000 40 000 40 000 258 1330 2160 2991 1 0 0 0 0 0 1 1 2 2 2 2 1768 1768 293 293 6 78446 6 78446 4 98703 4 98703 1 1 0 1 offset nCi mCi 7 RISK ESTIMATION FOR 500 WLM AND 500 WLM MINERS COX REGRESSION MODEL With z the 500 WLM variable t z 0 t exp z 0 t for 500 WLM 0 t exp for 500 WLM Standard Cox regression software to estimate risk Entry time rsentry Exit time rstime Failure indicator cc Covariate cr500 risk for 500 WLM and cr500 1 risk for 500 WLM offset log sampling weight For time interval risk estimates Strata timeint Ask for baseline cumulative hazard 8 SAS CODE FOR MINERS NESTED CASE CONTROL DATA NON PARAMETRIC title4 Non parametric data covs input offset datalines 0 run proc phreg data cm cm2 2 nosummary model rstime cc 0 entry rsentry offset offset rl baseline out ch rs covariates covs cumhaz cumhaz lowercumhaz lci uppercumhaz uci nomean strata cr500 rstime 50 70 run Only difference compared to full cohort is inclusion of the log weight as an offset in the model and in cov file 9 Estimated risk of lung cancer death between ages 50 69 from case control data WLM 500 500 WLM 500 500 Proportional hazard model Full cohort SRS 3 6 2 4 7 8 2 6 3 4 7 8 4 26 3 22 1 31 2 28 1 22 8 34 7 Non parametric Nelson Aalen Full cohort SRS 3 7 3 5 3 10 2 6 8 4 6 10 1 24 9 20 8 29 9 22 7 18 6 27 7 10 Estimated risk of lung cancer death between ages 50 69 from case control data continued WLM 500 500 WLM 500 500 Proportional hazard model SRS 3 Matched CM 2 2 6 4 4 8 8 5 5 8 4 3 7 7 27 4 22 0 34 2 29 8 24 3 36 6 Non parametric Nelson Aalen SRS 3 Matched CM 2 2 6 9 4 8 9 9 7 0 4 9 10 1 22 0 18 0 26 8 27 8 22 4 35 4 11 RISK ESTIMATION FROM NESTED CASE CONTROL DATA Analysis is completely analogous to full cohort just need to include sampling weights Need to include weights to connect casecontrol set size to risk set size Might need different weights than needed for rate ratio estimation but rate ratio estimate will not change 12