a. Using the data from the table, for all death calculate: 1) The probability of death at the exact time when each death occurred Survival data for 20 participants of a hypothetical prospective Follow-up time (months) Event Total of participant ni Probability of death at exact time when death occurred qi = d/ni Probability of survival beyond time when death occurred Pi = 1-qi Conditional peobability of survival Cumulative probability of survival beyond time when death occurred Si Kaplan-Meier survival suntion 2 Death 20 1/20 = 0.050 19/20= .950 0.950 4 Censored 19 7 Censored 18 8 Death 17 1/17 =0.059 16/17=.0941 19/20 x 16/17 = 0.894 12 Censored 16 15 Death 15 1/15= 0.067 14/15=0.933 0.834102 17 Death 14 1/14= 0.071 13/14=0.929 0.774880 19 Death 13 1/13=0.077 12/13=0.923 0.715214 20 Censored 12 23 Death 11 1/11= 0.091 10/11=0.909 0.650130 b. What is the cumulative survival probability at the end of the follow -up period? C. Using arithmetic graph paper, plot the cumulative probability of survival d. What is the simple proportion of individual apparently surviving thought the end of the studys observation period? e. Why are the simple proportion surviving and the cumulative probability of survival are different? f. Using the same data, calculate the overall death rate per 100 person-years. (To facilitate your calculations, you may wish to calculate the number of person -months and then convert that in the number of person-years). g. Calculate the rates separately for the first and second years of follow-up. (For this calculation, assume that the individual who withdrew at month 12 withdrew just after midnight on the last day of the month). h. Assuming that there was no random variability, was it appropriate the calculate the rate per person per year for the 2-year duration of the follow-up? i. What is the most important assumption underlying the use of both survival analysis and the person-time period approach? j. Now, assume that the length of follow was the same for all individuals (except those who died). Calculate the proportion of deaths and the odds of death in this cohort. k. Why are these figures so different in the study? Survival data for 20 participants of a hypothetical prospective Follow-up time (months) Event Total of participant ni Probability of death at exact time when death occurred qi = d/ni Probability of survival beyond time when death occurred Pi = 1-qi Conditional peobability of survival Cumulative probability of survival beyond time when death occurred Si Kaplan-Meier survival suntion 2 Death 20 1/20 = 0.050 19/20= .950 0.950 4 Censored 19 7 Censored 18 8 Death 17 1/17 =0.059 16/17=.0941 19/20 x 16/17 = 0.894 12 Censored 16 15 Death 15 1/15= 0.067 14/15=0.933 0.834102 17 Death 14 1/14= 0.071 13/14=0.929 0.774880 19 Death 13 1/13=0.077 12/13=0.923 0.715214 20 Censored 12 23 Death 11 1/11= 0.091 10/11=0.909 0.650130.

1. a. Using the data from the table, for all death calculate: 1) The probability of death at the exact
time when each death occurred
Survival data for 20 participants of a hypothetical prospective
Follow-up time (months)
Event
Total of participant
ni
Probability of death at exact time when death occurred
qi = d/ni
Probability of survival beyond time when death occurred
Pi = 1-qi
Conditional peobability of survival
Cumulative probability of survival beyond time when death occurred
Si
Kaplan-Meier survival suntion
2
Death
20
1/20 = 0.050
19/20= .950
0.950
4
Censored
19

2. 7
Censored
18
8
Death
17
1/17 =0.059
16/17=.0941
19/20 x 16/17 = 0.894
12
Censored
16
15
Death
15
1/15= 0.067
14/15=0.933
0.834102
17
Death
14
1/14= 0.071
13/14=0.929
0.774880
19
Death
13

3. 1/13=0.077
12/13=0.923
0.715214
20
Censored
12
23
Death
11
1/11= 0.091
10/11=0.909
0.650130
b. What is the cumulative survival probability at the end of the follow -up period?
C. Using arithmetic graph paper, plot the cumulative probability of survival
d. What is the simple proportion of individual apparently surviving thought the end of the
studys observation period?
e. Why are the simple proportion surviving and the cumulative probability of survival are
different?
f. Using the same data, calculate the overall death rate per 100 person-years. (To facilitate your
calculations, you may wish to calculate the number of person -months and then convert that in
the number of person-years).
g. Calculate the rates separately for the first and second years of follow-up. (For this calculation,
assume that the individual who withdrew at month 12 withdrew just after midnight on the last
day of the month).
h. Assuming that there was no random variability, was it appropriate the calculate the rate per
person per year for the 2-year duration of the follow-up?
i. What is the most important assumption underlying the use of both survival analysis and the
person-time period approach?
j. Now, assume that the length of follow was the same for all individuals (except those who
died). Calculate the proportion of deaths and the odds of death in this cohort.
k. Why are these figures so different in the study?

4. Survival data for 20 participants of a hypothetical prospective
Follow-up time (months)
Event
Total of participant
ni
Probability of death at exact time when death occurred
qi = d/ni
Probability of survival beyond time when death occurred
Pi = 1-qi
Conditional peobability of survival
Cumulative probability of survival beyond time when death occurred
Si
Kaplan-Meier survival suntion
2
Death
20
1/20 = 0.050
19/20= .950
0.950
4
Censored
19

5. 7
Censored
18
8
Death
17
1/17 =0.059
16/17=.0941
19/20 x 16/17 = 0.894
12
Censored
16
15
Death
15
1/15= 0.067
14/15=0.933
0.834102
17
Death
14
1/14= 0.071
13/14=0.929
0.774880
19
Death
13
1/13=0.077
12/13=0.923
0.715214

6. 20
Censored
12
23
Death
11
1/11= 0.091
10/11=0.909
0.650130