Epidemiologic Methods (Epi 203)Answer key for problem set: “Disease Occurrence I”Due 10/16/01 at 1 pm section1. (a) Point prevalence of asthma. Even though the survey took 18 months to complete, it is not period prevalence because each participant was asked about backache at a single point in time, not whether he or she had had a backache at any time during a 18-month period.(b) Incidence rate of HIV infection. The information given allows calculation of a person-time denominator. The numerator will be 85 infections and the denominator 600 persons x 6.5 years to give 3900 person-years (the rate would be 2.3 per 100 person-years). Although cumulative incidence with the Kaplan-Meier method could be calculated in the cohort, you would need the time of each HIV infection for that calculation. It is possible to construct a life-table from the information by making some strong assumptions. For example, you could assume an equal number of infections each year and an equal number of drop outs each year and calculate an average population at risk each year that would add up to the 3900 person-years, but this would be a dubious application of the life-table method because of the lack of information about drop outs. (c) 10-year cumulative incidence of myocardial infarction. Because the estimate is a probability, a proportion, it is based on persons at risk. It is not a person-time rate. 2. (a) Kaplan-Meier TableTime Individuals Number Conditional prob Conditional prob Cumulative prob(mos) at risk of events of death of survival of survival 2 8 1 1/8 (0.125) 7/8 (0.875) 0.875 6 6 1 1/6 (0.166) 5/6 (0.833) 0.729 8 4 1 1/4 (0.25) 3/4 (0.75) 0.547 (b) Cumulative probability of death at 8 months = (1 – 0.547) = 0.453(c) 95% confidence interval cumulative survival = Cum surv + 1.96 x SE (Cum surv) SE (cum surv) = 0.547 x  1/8(8-1) + 1/6(6-1) + 1/4(4-1) = 0.547 x 0.0179 + 0.0333 + 0.0833 = 0.547 x 0.367 = 0.201 95% CI = 0.547 + (1.96 x 0.201) = 0.547 + 0.394 = 0.153 to 0.941 To get 95% CI for cumulative incidence, (1 – 0.153) and (1 – 0.941) = 0.059 to 0.847(note: if you try to calculate SE for death directly by using 0.453  7/8(8-1) + 5/6(6-1) + 3/4(4-1) in the formula above and then obtaining 95% CI by 0.453 + 1.96 x SE, CI exceeds 1.0, not possible for a proportion).(d) see next pageK a p l a n - M e i e r s u r v i v a l e s t i m a t e a n a l y s i s t i m e0 1 2 3 4 5 6 7 8 9 1 00 . 0 00 . 2 50 . 5 00 . 7 51 . 0 03. 10-year cumulative incidence of death = 1 – 0.3877 = 0.6123 Net Survivor Std. Time Total Beg. Fail Lost Function Error [95% Conf. Int.] .3836 394 1 0 0.9975 0.0025 0.9821 0.9996 .4795 393 0 1 0.9975 0.0025 0.9821 0.9996 .5671 392 0 1 0.9975 0.0025 0.9821 0.9996 .7534 391 1 0 0.9949 0.0036 0.9798 0.9987 .7699 390 1 0 0.9924 0.0044 0.9765 0.9975 1.23 389 1 0 0.9898 0.0051 0.9731 0.9962 1.266 388 1 0 0.9873 0.0057 0.9697 0.9947 1.29 387 2 0 0.9822 0.0067 0.9629 0.9915 1.318 385 1 0 0.9796 0.0071 0.9596 0.9897 1.337 384 1 0 0.9771 0.0076 0.9564 0.9880 1.356 383 1 0 0.9745 0.0080 0.9531 0.9862 1.441 382 1 0 0.9720 0.0083 0.9499 0.9844 1.46 381 1 0 0.9694 0.0087 0.9467 0.9825 1.477 380 1 0 0.9668 0.0090 0.9436 0.9806 1.499 379 1 0 0.9643 0.0094 0.9405 0.9787 1.523 378 1 0 0.9617 0.0097 0.9373 0.9768 1.529 377 1 0 0.9592 0.0100 0.9343 0.9748 1.537 376 1 0 0.9566 0.0103 0.9312 0.9728 1.625 375 1 0 0.9541 0.0106 0.9281 0.9708 1.638 374 1 0 0.9515 0.0108 0.9251 0.9688 1.811 373 1 0 0.9490 0.0111 0.9221 0.9668 1.819 372 1 0 0.9464 0.0114 0.9190 0.9647 1.871 371 1 0 0.9439 0.0116 0.9160 0.9627 1.915 370 1 0 0.9413 0.0119 0.9130 0.9606 1.953 369 1 0 0.9388 0.0121 0.9101 0.9585 1.973 368 1 0 0.9362 0.0123 0.9071 0.9565 1.984 367 1 0 0.9337 0.0126 0.9041 0.9544 2.036 366 1 0 0.9311 0.0128 0.9012 0.9523 2.082 365 1 0 0.9286 0.0130 0.8982 0.9501 2.137 364 1 0 0.9260 0.0132 0.8953 0.9480 2.148 363 0 1 0.9260 0.0132 0.8953 0.9480 2.17 362 1 0 0.9235 0.0134 0.8924 0.9459 2.181 361 1 0 0.9209 0.0136 0.8894 0.9437 2.26 360 1 0 0.9184 0.0138 0.8865 0.9416 2.348 359 1 0 0.9158 0.0140 0.8836 0.9394 2.479 358 1 0 0.9132 0.0142 0.8807 0.9372 2.482 357 1 0 0.9107 0.0144 0.8778 0.9350 2.521 356 1 0 0.9081 0.0146 0.8749 0.9329 2.534 355 1 0 0.9056 0.0148 0.8720 0.9307 2.537 354 1 0 0.9030 0.0150 0.8692 0.9285 2.592