Question

A mortality study is conducted on 12 individuals of age x initially You are given: (i)In addition to the 12 individuals of age x, one individual apiece enters the study at ages x0.4, x 0.8 and x1.0 (ii One individual leaves the study alive at age x +1.2 (ii One individual leaves the study alive at age x+1.4 (iv) One death apiece occurs at ages x+ 0.3, x+1.3, andx+ 1.6 (v) Two deaths occur at age x+ 0.5 The duration of the study is 2 years (a) Estimate the probability that a life age x would survive 2 years using (i Kaplan-Meier estimator; (ii) Nelson-Aalen estimator

Answer 1

SOLUTION: A:Sequence cwhen investization Ttme at ehich death Occurs OCCUUYS deaths at time t d:No of individeuals censored (net) betueen t and tjti Cie) No.of individeuals teaving the stedy beteveen t; and ti+ minus No.of irdivideuals entering the strudy betiw een ty and tit The giver information can be represented on the followin timeline: a508 10 12 Time (from x) 1-31 1-4 1-6 0-8 0.4 No-of deaths Net indi -Viduals censored 1 2 1 1 | 1-0 1 1-2-1

Nelson-Aalen Survival function rj Sunival function di nj 1-> 5x) xt -1 12 1 O.3 1 11 12 11/12 14 exp(-h2) 0-9200 2 O.5 -1 12 $16 3 1-3 1 1 0-4788 11 1544 epl-1uu) 25/36 1-6 1 =0-7111 lga ep-14/396) 50 0-6363

The Kap lan-meier estimate of the Suvival function is: t< n+O.3 1 ; nto.3< E < xto.5 D.9167 Sct)= 0.7639 ;+o-5 t< 2+1-3 0-6944 xt 1.3st <2t1.6 0-617 28; 71-6 ife aged years (usiog kaplanmeier estimator Thus : ProbabilTby that a would suvive & 20 is 0-61728 The Nelson- Aalen estimate of the Suovival function is: 1 ; t<x+o3 0.92 tD3 <t < xto.S O.FF88 to-5t6 XtI3 5CED = 0-7111 tI.3 SE< 2t1.6 0.6363 ; 7 1.6 Life aged % would bur vive 2 years (USing Nelson-Aalan esbimator Thus: Probabiuty that i's D.6363