To Yeabiruh... Biostat... NBME 4 Block 2 Q 17 - drock

[ArchivalUser]

The table reports survival of patients who had an operation for a particular form of cancer.

..Number of Patients Number of Patients Percent of Patients
..at the Beginning who Died .....Surviving
Interval .of the Interval During the Interval ....This Interval
0-1 year 300. 115 .62
1-2 year.185 37 80
2-3 years .148 24 84
3-4 years..124 18 85
4-5 years..106 25 76
If a patient survives 2 years after the operation, which of the following is the probability of surviving at least 4 years?
A) .80
B) .85
C) .84 x .85
D) .62 x .80 x .84 x .85
E) .85 - .80

So as this normal surviving period is two years we have to calculate the extended survival time for another 2 years? that™s make 2+2 = 4 years?
So we have start calculating after two years of survival after operation and his normal survival length? So that will make the answer choice C as correct???

Because normally 4 years survival will have to count from zero day (first day after operation) to upto 4 years. That makes the correct answer as D.

Will you please clear my doubts and misconception if any? Thank you so much.

[ArchivalUser]

hi drock...this is about conditional probablity....i got the concept from Sarim...

here is my understanding

U explained we have to calculate the 4 years survival from the Zero day ....this could be true if this is not a conditional probablity ...What do I mean by that ....

---Let us say the probablity of surviving two years is = B
---Let us say the probablity of surviving at least 4 years is =A

--Now the probablity of surviving at least 4 years (A) GIVEN that the patient survives 2

years (B) IS = number of times A and B occur jointly /number of times B occurs

--to elaborate in conditional probablity ...the denominator is changed from the whole set into

part of a set...like in this example instead of taking the denominator from the Zero day

(number of patients at the beginning ,which is 300) ...we will take the denominator from the

2 year(number of patients at the beginning of 2-3 years interval =148)

--Hence we have our denominator (the lower part of the fraction) = 148 (reduced from the starting 300 ...explained by the death of the patient)....

---so what is our numerator ...the numerator in this case is the number of patients that survived at least 4 years ...and from the data it is 106 (only count those survived ...excluding the dead ones)...

---then the probablity of surviving for at least 4 years GIVEN the patient survived 2 years after operation is = 106/148=0.716216

---or Simply the estimated survival to each interval is computed as the PRODUCT of PROBABLITIES OF surviving each preceding interval (1- probablity of DYING)

using the above principle

probablity of surviving at least 4 years given the patient survives 2 years = u take the PRODUCT of the probablities between the second row and the 5 th row ...which is 0.85 * 0.84 =0.714

[ArchivalUser]

for example if they ask what is the probablity of surviving at least 4 years with out saying after the patient survived 2 years of the operation ...ur method of calculating is the right one..which is D

number of patients that survived at least 4 years =106
number of patients at the beginning of the operation= 300

probablity of patients surviving at least 4 years = 106/300=0.35(which is the same as D )

[ArchivalUser]

Hi Yeabiruh thank you so much from my heart. Awesome explanation. Now it make sense to me. Thanks again.

[ArchivalUser]

guys answer is DDD..

this is a epidemiology question in my MPH program..

[ArchivalUser]

@ anonyme can you please give your explanation of your answer? thank you

[ArchivalUser]

have anyone guys read the practice q in kaplan biostats? here it is:

If the chance of surviving for 1 year after being diagnosed with prostate cancer is 80%, and the chance of surviving for 2 years is 60%, what is the chance of surviving for 2 years after the diagnosis, given that the patient is alive at the end of the first year?
A) 20%
B) 48%
C) 60%
D) 75%
E) 80%

the last statement: given that the pt is alive at the end of the first year, isnt the same as saying: what is the chance of surviging for 2 yrs given the the pt survived the first year??

the answer that is give for the q is: 60/80 = 75%

[ArchivalUser]

Conditional Probability:....Freaking biostates

lets try this... If given that the pt survived say like 1 yr( or 2 yrs etc.) and asking for probability of surviving certain # of yrs (e.g 2 yrs or 3 yrs etc.).

and the data is given in one of these two ways:

.....STRAIGHT SURVIVAL.

0--1 yr = 80 %
0--2 yr = 60 %
0--3 yr = 40 %
0--4 yr = 20 %

say like if pt survived 1 yr what would be the probability--?(in this case u DIVIDE probabi)

(prob.of yr u want to know) DIVIDE by (prob.of # yr pt already survived e.g. 1 yr)

probability of surviving 2 yrs.......60/80 =75%
probability of surviving 3 yrs.......40/80 =50%
probability of surviving 4 yrs.......20/80 =25%

if the pt survived say like 2 yrs and probability of surviving 4 yrs?
20/60 =33 %

.......SURVIVING THIS INTERVALE.

0--1 yr = 80%
1--2 yr = 60%
2--3 yr = 40%
3--4 yr = 20%

say like if pt survived 1 yr ,what would be the probability? (in this case MULTIPLY probabil.)
Note: Multiply probabilities in between(SKIPPING the survived yr probability in this case 80%)

probability of surviving 3 yrs = 60 times 40
probability of surviving 4 yrs = 60 times 40 times 20

If asked probability of surviving straight say like 4 yrs(from the day one without condition of already survived certain # of yr) = multiply all probabilities 80 times 60 times 40 times 20

NOw in NBME 3 bloc 2, 16 answer is D
0.875 times 0.9 times 0.9

B- would have been the answer if asked straight 4 yr survival
C- is the probability of surviving 3 yrs once the pt already survived for 1 yr

IN NBME 4 bloc 2, 17 answer is C .Pt already survive 2 yrs so skip the 62 and 80 and now asking survival for AT LEAST 4 yrs(not the 5 yrs) so multiply the probabilities in between
0.84 times 0.85

D- straight survival for 4 yrs (without any condition of already survived # of yr)

[ArchivalUser]

hmm... interesting... thx sarim...