Please Check my work. Thank you in advanced

Chapter 21, Problem 7

In the table in the textbook on page 511 you will find survival times in months since diagnosis for 10 AIDS patients suffering from concomitant esophageal candidiasis, an infection due to Candida yeast, and cytomegalovirus, a herpes infection that can cause serious illness. Censored observations are denoted by a plus sign.

a. How many deaths were observed in this sample of patients?

5 deaths

b. Use the product-limit method to estimate the survival function S(t).

S(t)= = (1 - dj/nj) ^dj

where dj = 1 if observed, 0 if censored

nj = number of individuals at risk in the beginning of the jth month

dj = number of events in the jth month

c. What is S(1), the estimated probability of survival at one month? What is the estimated probability at 5 months? At 6 months?

S(t) = (1 - d_j/n_j) ^d_j

S(t) = 1* (1-3/9) = 2/3

t S(t) t S(t)

0.5 1 - (0/10) =1 0 t <1 1

1 1* (1- (3/9)) = 2/3 1 t <2 2/3

2 2/3 * (1-(1/6))= 5/9 2 t <9 5/9

5 5/9 * (1-(0/5))= 5/9 t 9 10/27

8 5/9 * (1-(0/4))= 5/9 - -

9 5/9 * (1-(1/3))= 10/27 - -

10 10/27 * (1-(0/2))= 10/27 - -

12 10/27 * (1-(0/1))= 10/27 - -

At the 5^th and 6^th month, S(t) = 5/9

d. Construct a survival curve (do not submit) based on the product-limit estimate.

used points above and intervals based on t

Chapter 21, Problem 9

In a study of bladder cancer, tumors were removed from the bladders of 86 patients. Subsequently, the individuals were assigned to be treated with either a placebo or the drug thiopeta. Time to recurrence of tumor in months is saved under the variable name time in the data set bladder. Treatment status is saved under the name group; the 1 value represents placebo. Indicators of censoring status; where 0 indicates a tumor did not occur and the observation was censored, is saved under the name censor.

a. Use the product-limit method to estimate the survival function in each treatment group.

b. Plot a survival curve--do not submit.

c. Does it appear that the individuals in one group have a longer time to first recurrence than in the other group?

it appears that those in group 2 who received the drug thiopeta had longer survival times to the first recurrence of bladder tumors.

d. Test the null hypothesis that the distributions of recurrence times are identical. What do you conclude?

it appears that all tests give the same result. There is no statistically significant difference between the distribution for recurrence of bladder tumors given all of the tests p-value.

e. The variable number is an indicator of tumors initially removed from the bladder. Test the null hypothesis that the one tumor group has the same distribution as the more than one tumor group. What do you conclude?

all the tests suggest that the null hypothesis are true and the distribution of recurrence time are identical for the two groups.