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#1
04-25-2013
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What is the true negative rate?

A test has just become available to detect a new strain of hepatitis virus. In early trials 1000 people were enrolled to undergo testing. Four hundred participants had a positive initial test, but confirmatory testing showed that only 200 people were truly infected. The remaining participants were negative by both experimental testing and confirmatory testing. What is the specificity of this new test?

The answer is 0.75. I want to understand how. Here's what I got this far. 1,000 people jumped in. 400 of those are tested positive. Okay. Next, they say that from 400, only 200 are truely infected. So that would be True Positive. And the other 200 from the same 400 is False Positive. Okay, this was clear.

200 = TP and 200 = FP

What about the negative? Well, from what I understand is this: 1,000 people jumped in. 400 of those are positive. The rest of 600 people are negative.

Now, my problem is what is TN and FN (I only care about TN since they are asking Specificity)? This is where I am finding trouble with. We broke 400 into TP and FP. How do we break 600 into TN and FN

#2
04-26-2013
 USMLE Forums Veteran Steps History: 1 + CS Posts: 209 Threads: 18 Thanked 111 Times in 74 Posts Reputation: 121

tn=450
fn=150
tp=200
fp=200
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#3
04-26-2013
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Quote:
 Originally Posted by neha_subh tn=450 fn=150 tp=200 fp=200
Pls explain. where did u get the 450 and 150?
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#4
04-26-2013
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hi..
well if u substitute the whole 600 as TN U get the ans .75
I don't think... well from the info given u can est wat TN &FN is exactly...
r u sure .75 is the ans...?
 The above post was thanked by: Doctor Ali (04-26-2013), neha_subh (04-26-2013)
#5
04-26-2013
 USMLE Forums Veteran Steps History: 1 + CS Posts: 209 Threads: 18 Thanked 111 Times in 74 Posts Reputation: 121

Quote:
 Originally Posted by nsesereso Pls explain.where did u get the 450 and 150?
sorry i did mistake...

but ya you are right if we solve it in this way:
600/800=0.75
then we can get the answr.

Doctor ali pls put here the other options..
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 The above post was thanked by: Doctor Ali (04-26-2013)
#6
04-26-2013
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 1,109 Threads: 31 Thanked 520 Times in 394 Posts Reputation: 539
This is the explanation to the answer!

Specificity is calculated from two formulae according to Kaplan.

1. TN/(TN+FP)
2. 1- specificity= FP rate

Therefore using the 2nd formular
FP rate is= FP/all negative results

So FP rate is 200/ 800= 0.25

Therefore specificity is 1-0.25 = 0.75

Hope this helps.
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#7
04-26-2013
 USMLE Forums Veteran Steps History: 1 + CS Posts: 209 Threads: 18 Thanked 111 Times in 74 Posts Reputation: 121

Quote:
 Originally Posted by nsesereso Specificity is calculated from two formulae according to Kaplan. 1. TN/(TN+FP) 2. 1- specificity= FP rate Therefore using the 2nd formular FP rate is= FP/all negative results So FP rate is 200/ 800= 0.25 Therefore specificity is 1-0.25 = 0.75 Hope this helps.
FP rate=FP/total negative
this equation
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#8
04-26-2013
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 1,109 Threads: 31 Thanked 520 Times in 394 Posts Reputation: 539

Quote:
 Originally Posted by neha_subh FP rate=FP/total negative this equation
Doctor any suggestions or corrections?
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#9
04-26-2013
 USMLE Forums Veteran Steps History: Step 1 Only Posts: 283 Threads: 35 Thanked 205 Times in 115 Posts Reputation: 215

A. 40%
B. 50%
C. 70%
D. 75% This is the correct answer.
E. 80%
F. 90%
G. 100%

This is from Usmlerx qbank. I know the formulas and etc. I am stuck with 600. Because they gave:

1000 people
400 from 1000 is positive tested
200 from 400 is True Positive. This makes other 200 False Positive.

Now, 1000 - 400 = 600. This 600 is negative. From here, where do we go?
#10
04-26-2013
 USMLE Forums Scout Steps History: Not yet Posts: 27 Threads: 1 Thanked 9 Times in 7 Posts Reputation: 19

Quote:
 Originally Posted by Doctor Ali The answer choices are: A. 40% B. 50% C. 70% D. 75% This is the correct answer. E. 80% F. 90% G. 100% This is from Usmlerx qbank. I know the formulas and etc. I am stuck with 600. Because they gave: 1000 people 400 from 1000 is positive tested 200 from 400 is True Positive. This makes other 200 False Positive. Now, 1000 - 400 = 600. This 600 is negative. From here, where do we go?

The specificity meanly deals with the people who are are not sick, so what we do is first we find the True negative which is 600 then we find the people who are False positive which is 200 now we can calculate it in the formula of specificity : TN/TN+FP AND here it is 600/600+200 = 0.75
 The above post was thanked by: Doctor Ali (04-26-2013)
#11
04-26-2013
 USMLE Forums Veteran Steps History: 1 + CS Posts: 209 Threads: 18 Thanked 111 Times in 74 Posts Reputation: 121

Quote:
 Originally Posted by nsesereso Specificity is calculated from two formulae according to Kaplan. 1. TN/(TN+FP) 2. 1- specificity= FP rate Therefore using the 2nd formular FP rate is= FP/all negative results So FP rate is 200/ 800= 0.25 Therefore specificity is 1-0.25 = 0.75 Hope this helps.
i know this equation:

TN/TN+FP

but
acording to above its FP/ TN+FP

as DR.mah said i have also solved in that way.i dont know exact way my biostatic concepts are not good enough so i cant coment more about it.i have just asked from you about that equation.
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#12
04-26-2013
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Quote:
 Originally Posted by mah2 The specificity meanly deals with the people who are are not sick, so what we do is first we find the True negative which is 600 then we find the people who are False positive which is 200 now we can calculate it in the formula of specificity : TN/TN+FP AND here it is 600/600+200 = 0.75

1 - FP

or
1-FN

how/when we can use this formula, stil i havnt solved any question with this formula
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Last edited by neha_subh; 04-26-2013 at 08:33 PM.
#13
04-26-2013
 USMLE Forums Veteran Steps History: Step 1 Only Posts: 283 Threads: 35 Thanked 205 Times in 115 Posts Reputation: 215

Thanks a ton for helping. I finally figured out.

A test has just become available to detect a new strain of hepatitis virus. In early trials 1000 people were enrolled to undergo testing. Four hundred participants had a positive initial test, but confirmatory testing showed that only 200 people were truly infected. The remaining participants were negative by both experimental testing and confirmatory testing. What is the specificity of this new test?

So if we use 2 x 2, we will get the following:

1,000 people walked in. 400 from 1,000 are tested positive. 200 from that 400 are truely infected. This gives us:

TP = 200 and FP = 200. TP + FP = 400. One concept done.

Next, 400 people from 1,000 are positive which leaves us 1,000 - 400 = 600 people. This 600 is negative and needs to be subdivide into TN and FN; since these are left behind. However, look at the last sentence before question. It states remaining participants were negative by both experimental testing and confirmatory testing. This means that 600 people are not infected. This concludes that FN = 0. And TN= 600. Never came in my head that 0 exists too.

Now we can solve this in peace of mind.

TP = 200
FP = 200
FN = 0
TN = 600

TP + FP = 400
FN + TN = 600

TP + FN = 200
FP + TN = 800

Spec. = TN/ (TN + FP)
= 600/800
= 75%
 The above post was thanked by: neha_subh (04-28-2013), nsesereso (04-26-2013)
#14
04-26-2013
 USMLE Forums Veteran Steps History: Step 1 Only Posts: 283 Threads: 35 Thanked 205 Times in 115 Posts Reputation: 215

Quote:
 Originally Posted by neha_subh dr.mah2 , doctor ali , dr.nsesereso , residency2015 pls tell me about this equation i always confused about this equation: 1 - FP or 1-FN how/when we can use this formula, stil i havnt solved any question with this formula

Sure I will help you out. You know that Sens. = TP / (TP + FN) and Spec. = TN / (TN + FP). Sometimes, they give Sens and/or Spec. and they ask you what is TP, TN, FP, and or FN. So, here is where you need to use the following:

1. TP = (SENS.) X (# PEOPLE WITH DISEASE)
2. FN = (1 - SENS.) X (#PEOPLE WITH DISEASE)
3. TN = (SPEC.) X (# PEOPLE WITHOUT DISEASE)
4. FP = (1 - SPEC.) X (# PEOPLE WITHOUT DISEASE)

This is all you need to know. 1 - FP or 1 - FN doesn't make sense.

I can give you an example problem.

Given:

Specificity = 80%
Sensitivity = 75%
Total paients with MI = 200
Total patients without MI = 400

Find:

1. TP
2. FN
3. FP
4. TN

1. TP = (SENS.) X (# PEOPLE WITH DISEASE)
TP = (0.75) X (200)
TP = 150

2. FN = (1 - SENS.) X (#PEOPLE WITH DISEASE)
FN = (1 - 0.75) X (200)
FN = (0.25) X (200)
FN = 50

3. TN = (SPEC.) X (# PEOPLE WITHOUT DISEASE)
TN = (0.80) X (400)
TN = 320

4. FP = (1 - SPEC.) X (# PEOPLE WITHOUT DISEASE)
FP = (1 - 0.80) X (400)
FP = (0.20) X (400)
FP = 80
 The above post was thanked by: ag2011n (11-05-2013), neha_subh (04-28-2013)
#15
04-26-2013
 USMLE Forums Veteran Steps History: Step 1 Only Posts: 283 Threads: 35 Thanked 205 Times in 115 Posts Reputation: 215

Quote:
 Originally Posted by nsesereso Specificity is calculated from two formulae according to Kaplan. 1. TN/(TN+FP) 2. 1- specificity= FP rate Therefore using the 2nd formular FP rate is= FP/all negative results So FP rate is 200/ 800= 0.25 Therefore specificity is 1-0.25 = 0.75 Hope this helps.

Now I understand here. This invloves two step process.

For SPEC:

1. You know FP and total non disease group. You divide FP by Total non disease which gives you FP RATE.
2. You take FP RATE and subtract by 1 and you get Spec.

Example:

1. FP / Total non disease = FP RATE
2. Spec. = 1 - FP RATE

Same applies to Sens.

You know FN and total disease group. You divide FN by Total disease which gives you FN RATE.
2. You take FN RATE and subtract by 1 and you get Sens.

Example:

1. FN / Total disease = FN RATE
2. Sens. = 1 - FN RATE

#16
04-26-2013
 USMLE Forums Veteran Steps History: Step 1 Only Posts: 283 Threads: 35 Thanked 205 Times in 115 Posts Reputation: 215

Quote:
 Originally Posted by nsesereso Specificity is calculated from two formulae according to Kaplan. 1. TN/(TN+FP) 2. 1- specificity= FP rate Therefore using the 2nd formular FP rate is= FP/all negative results So FP rate is 200/ 800= 0.25 Therefore specificity is 1-0.25 = 0.75 Hope this helps.

Now I understand here. This invloves two step process.

For SPEC:

1. You know FP and total non disease group. You divide FP by Total non disease which gives you FP RATE.
2. You take FP RATE and subtract by 1 and you get Spec.

Example:

Let's look at my previous post for calculations. We have FP = 80 and total patient without MI = 400. Find Spec.?

1. FP RATE = FP / Total non disease
FP RATE = 80/400
FP RATE = 0.2

2. Spec. = 1 - FP RATE
Spec. = 1 - 0.2
Spec = 0.8 = 80%

Same applies to Sens.

1. You know FN and total disease group. You divide FN by Total disease
which gives you FN RATE.
2. You take FN RATE and subtract by 1 and you get Sens.

Example:

Let's look at my previous post for calculations. We have FN = 50 and total patient with MI = 200. Find Sens.?

1. FN RATE = FN / Total disease
FN RATE = 50/200
FN RATE = 0.25

2. Sens. = 1 - FN RATE
Sens. = 1 - 0.25
Sens. = 0.75 = 75%

Basically its other way of calculating Sens.and Spec. But I prefer original way. Sorry for repeat.
#17
04-26-2013
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 1,109 Threads: 31 Thanked 520 Times in 394 Posts Reputation: 539

Quote:
 Originally Posted by Doctor Ali Sure I will help you out. You know that Sens. = TP / (TP + FN) and Spec. = TN / (TN + FP). Sometimes, they give Sens and/or Spec. and they ask you what is TP, TN, FP, and or FN. So, here is where you need to use the following: 1. TP = (SENS.) X (# PEOPLE WITH DISEASE) 2. FN = (1 - SENS.) X (#PEOPLE WITH DISEASE) 3. TN = (SPEC.) X (# PEOPLE WITHOUT DISEASE) 4. FP = (1 - SPEC.) X (# PEOPLE WITHOUT DISEASE) This is all you need to know. 1 - FP or 1 - FN doesn't make sense. I can give you an example problem. Given: Specificity = 80% Sensitivity = 75% Total paients with MI = 200 Total patients without MI = 400 Find: 1. TP 2. FN 3. FP 4. TN 1. TP = (SENS.) X (# PEOPLE WITH DISEASE) TP = (0.75) X (200) TP = 150 2. FN = (1 - SENS.) X (#PEOPLE WITH DISEASE) FN = (1 - 0.75) X (200) FN = (0.25) X (200) FN = 50 3. TN = (SPEC.) X (# PEOPLE WITHOUT DISEASE) TN = (0.80) X (400) TN = 320 4. FP = (1 - SPEC.) X (# PEOPLE WITHOUT DISEASE) FP = (1 - 0.80) X (400) FP = (0.20) X (400) FP = 80
The four equations above are really helpful. I have comfirm them from simple change of subject calculations.Let me add another deduction I made. Remember 1-fp and 1-fn are far fetched in themselves however
The second Kaplan formula 1-specificity= fp rate is still correct.
Note that it is not 1-specificity =fp but fp rate.

Like I said earlier on Fp rate = fp/ # number of people without the disease
Ie fp rate = fp/( fp+fn). This could simply be deducted or confirmed from dr. Ali's formula 4.
Fp rate becomes very important when one is asked to calculate eg the probability at which individuals tested are truelly negative or are false positive.
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#18
04-26-2013
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 1,109 Threads: 31 Thanked 520 Times in 394 Posts Reputation: 539

[QUOTE=Doctor Ali;187720]Now I understand here. This invloves two step process.

For SPEC:

1. You know FP and total non disease group. You divide FP by Total non disease which gives you FP RATE.
2. You take FP RATE and subtract by 1 and you get Spec.

Example:

Let's look at my previous post for calculations. We have FP = 80 and total patient without MI = 400. Find Spec.?

1. FP RATE = FP / Total non disease
FP RATE = 80/400
FP RATE = 0.2

2. Spec. = 1 - FP RATE
Spec. = 1 - 0.2
Spec = 0.8 = 80%

Same applies to Sens.

1. You know FN and total disease group. You divide FN by Total disease
which gives you FN RATE.
2. You take FN RATE and subtract by 1 and you get Sens.

Example:

Let's look at my previous post for calculations. We have FN = 50 and total patient with MI = 200. Find Sens.?

1. FN RATE = FN / Total disease
FN RATE = 50/200
FN RATE = 0.25

2. Sens. = 1 - FN RATE
Sens. = 1 - 0.25
Sens. = 0.75 = 75%

Basically its other way of calculating Sens.and Spec. But I prefer original way. Sorry for repeat.[/QUOTE
Yes u are right but when asked to calculate the probability that an individual who tested would really be true negative etc u would not have any choice than use the later equation. Hahahhahaha a.
I love mathematics.
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