what constant daily hire rate beginning in 2006 leads to an npv of $0?
Indian J Ophthalmol. 2008 Jan-Feb; 56(one): 45–50.
Agreement and using sensitivity, specificity and predictive values
Received 2007 Feb 23; Accepted 2007 Jul 31.
Abstract
In this article, we accept discussed the bones knowledge to calculate sensitivity, specificity, positive predictive value and negative predictive value. We have discussed the advantage and limitations of these measures and have provided how we should apply these measures in our day-to-mean solar day clinical practice. We also take illustrated how to calculate sensitivity and specificity while combining 2 tests and how to apply these results for our patients in solar day-to-day practice.
Keywords: Predictive values, sensitivity, specificity
Modernistic ophthalmology has experienced a dramatic increase in cognition and an exponential increase in engineering science. A lot of this ′hi-tech′ explosion involves diagnostic tests. Regrettably, there is sometimes a tendency to use tests just because they are bachelor; or considering they are howdy-tech. The basic thought of performing a diagnostic test is to increase (or decrease) our suspicion that a patient has a item disease, to the extent that we can make management decisions. In this commodity, nosotros have tried to explain the rationale backside tests and their ′scientific′ application in the practical management of a patient.
Diagnostic Tests
For this article, the term ′diagnostic tests′ will include everything physicians do to diagnose affliction. This includes assessing symptoms and signs, as well every bit what we conventionally refer to as tests: such as laboratory investigations, gonioscopy, Optical Coherence Tomography (Oct), etc.
Gold Standard
The gold standard is the best single test (or a combination of tests) that is considered the current preferred method of diagnosing a particular illness (Ten). All other methods of diagnosing X, including any new test, need to be compared confronting this ′gilt′ standard. The gilt standard is different for different diseases. If we are considering peripheral anterior chamber depth (van Herick examination 2) for the diagnosis of primary angle closure (PAC), the current gilt standard is gonioscopy. The gilt standard for demonstrating the functional defect in glaucoma is automatic perimetry. The gold standard for X may exist considered outdated or inadequate, only any new examination designed to replace the gold standard has to exist initially validated against the gold standard. If the new test is indeed better, there are ways to prove that; following which the new test may become the gilded standard.
Validity
It is the extent to which a exam measures what it is supposed to mensurate; in other words, it is the accuracy of the exam. Validity is measured by sensitivity and specificity. These terms, likewise every bit other jargon, are best illustrated using a conventional 2- by-ii (2 x ii) table.
The data obtained by comparing a new diagnostic examination with the gilt standard is conventionally summarized in a two-past-two tabular array [Tabular array 1].
Table 1
Shows ii × 2 (two-by-two) tabular array
In prison cell ′a,′ we enter those in whom the test in question correctly diagnosed the disease (as determined by the gold standard). In other words, the examination is positive, as is the gold standard. These are the true positives (TP).
In prison cell ′b,′ we enter those who have positive results for the test in question but do not have disease according to the ′gilt standard test.′ The newer test has wrongly diagnosed the disease: These are false positives (FP).
In cell ′c,′ we enter those who have disease on the ′gold standard test′ but have negative results with the test in question. The test has wrongly labeled a diseased person as ′normal.′ These are false negatives (FN).
In cell ′d,′ we enter those who have no disease as determined by the ′gilded standard test′ and are as well negative with the newer exam. These are truthful negatives (TN).
Sensitivity (positive in disease)
Sensitivity is the ability of a test to correctly classify an private every bit ′diseased′ [Table two].
Table two
Calculation of sensitivity and specificity
Sensitivity = a / a+c
= a (truthful positive) / a+c (truthful positive + false negative)
= Probability of being examination positive when disease nowadays.
Example: One hundred persons with primary bending closure glaucoma (PACG, diagnosed by ′gold standard′: gonioscopy) are examined by van Herick test. Seventy-v of them had narrow peripheral anterior chamber depth [Table 3]. The sensitivity of the peripheral inductive sleeping accommodation depth examination to PACG is therefore –
Tabular array 3
Shows example for the calculation of sensitivity and specificity
75 / 100 = 75%.
Specificity (negative in health)
The ability of a exam to correctly classify an individual as disease- free is called the examination′south specificity. [Tabular array 2]
Specificity = d / b+d
= d (true negative) / b+d (true negative + faux positive)
= Probability of being test negative when disease absent.
Example: 1 hundred persons with normal angles (diagnosed by ′gold standard′: gonioscopy) are examined by peripheral angle bedchamber depth examination. Lxxx-v persons had normal peripheral angle bedchamber depth [Table 3]. The specificity of the peripheral angle chamber depth examination to PACG is therefore –
85 / 100 = 85%.
Sensitivity and specificity are inversely proportional, meaning that equally the sensitivity increases, the specificity decreases and vice versa. What do nosotros mean by this? Let us say that an intraocular pressure (IOP) of ≥25 mmHg is examination positive and <25 mmHg is test negative. Very few normal subjects would have IOP more 25 mmHg, and hence the specificity (NIH – negative in wellness) would be very high. But as a significant number of glaucoma subjects would have an IOP <25 mmHg (remember that shut to l% of glaucomas detected in population are normal-tension glaucomas), the sensitivity (PID – positive in disease) of IOP >25 mmHg in the detection of glaucoma would be depression. Suppose we accept the IOP cutoff for test positive to be 35 mmHg. Almost no normal field of study would take this high an IOP, and the specificity would be very high (>99%); and a highly specific examination if positive (for case an IOP >35 mmHg), rules in the disease. Remember this equally SpPIN: a highly Specific exam if Positive, rules IN disease. Similarly, if we take a cutoff of 12 mmHg, well-nigh no glaucoma bailiwick would have an IOP <12 mmHg (high sensitivity). An eye with an IOP <12 mmHg is extremely unlikely to have glaucoma. A highly sensitive test if negative, rules out the affliction. Remember this as SnNOUT: a highly Sensitive test if Negative, rules OUT affliction. (Near all normals would have an IOP >12 mmHg, a very depression specificity; but that is a unlike event). Another instance of SnNOUT would be the absence of venous pulsation in papilledema. The sensitivity of the sign ′absenteeism of venous pulsation′ in the diagnosis of papilledema is 99%, and specificity is 90%. So if venous pulsation is present, so we tin can apply SnNOUT and rule out papilledema. At that point in fourth dimension, papilledema may be evolving and may nonetheless develop a few days or a calendar week later; or patients may have papilledema, but the intracranial pressure at the time of exam is normal.
Positive Predictive Value (PPV)
Information technology is the percentage of patients with a positive exam who actually take the disease. In a 2 x 2 table [Table one], cell ′a′ is ′true positives′ and cell ′b′ is ′fake positives.′ In existent life state of affairs, we do the new test first and we do non have results of ′gold standard′ available. We want to know how this new test is doing. PPV tells usa about this – how many of exam positives are true positives; and if this number is higher (as close to 100 every bit possible), then it suggests that this new test is doing as good as ′golden standard.′
PPV: = a / a+b
= a (true positive) / a+b (true positive + false positive)
= Probability (patient having disease when test is positive)
Example: Nosotros will use sensitivity and specificity provided in Tabular array 3 to calculate positive predictive value.
PPV = a (true positive) / a+b (truthful positive + false positive)
= 75 / 75 + 15 = 75 / 90 = 83.3%
Negative Predictive Value (NPV)
It is the percentage of patients with a negative test who exercise not have the disease. In 2 x 2 table [Table 1], cell ′d′ is ′true negatives′ and cell ′c′ is ′imitation negatives.′ NPV tells u.s.a. how many of test negatives are true negatives; and if this number is college (should be shut to 100), then it suggests that this new test is doing as proficient every bit ′gilded standard.′
NPV: = d / c+d
= d (true negative) / c+d (simulated negative + truthful negative)
= Probability (patient not having disease when test is negative)
Example: We volition utilize sensitivity and specificity provided in Tabular array 3 to calculate negative predictive value.
NPV = a (true negatives) / c+d (fake negative + true negative)
= 85 / 85 + 25 = 85 / 110 = 77.3%
Positive and negative predictive values are direct related to the prevalence of the disease in the population [Fig. one]. Assuming all other factors remain constant, the PPV will increment with increasing prevalence; and NPV decreases with increase in prevalence. This is illustrated by the following example.
As the disease prevalence increases, the positive predictive value too increases
A new test has been developed to diagnose principal angle closure glaucoma (PACG). To clarify the terminology used in the instance, we volition repeat definitions of primary bending closure (PAC) and PACG. PAC is defined equally a person with an occludable angle (>180° of posterior trabecular meshwork not visible) with peripheral inductive synechiae with or without raised intraocular pressure (IOP). Optic disc and visual field do not show glaucomatous damage. PACG is defined as PAC with optic disc and visual field changes. PAC affects approximately 3 to 4% of population, while PACG affects approximately 1% of population.
This new test has been performed in i,000 patients that had documented PACG (disease positive) on gonioscopy (gilt standard) and 1,000 normal persons equally controls. The authors found that 900 were correctly classified as PACG by the ′new test,′ and 950 were correctly labeled as open angle [Tabular array 4a]. The authors would study the sensitivity and specificity of a test equally 90 and 95% respectively. With a sensitivity of 90% and a specificity of 95%, the new test appears to be an excellent test.
Table 4a
Showing example of calculation of predictive value at 50% prevalence
Let′due south apply this test to a one thousand thousand people where just i% is afflicted with PACG. Of the million people, 10,000 would exist affected with PACG. Since our new test is 90% sensitive, the test will detect 9,000 (TP) people who are actually affected with PACG and miss 1,000 (FN). Looking at those numbers, we would recollect that our test is very skillful considering nosotros have detected nine,000 out of 10,000 PACG-affected people. Notwithstanding, of the original i meg, 990,000 are not affected. If we look at the examination results on the normal population (recollect, the specificity of the test is 95%), we find that while 940,500 are found to be non affected past the new test (TN), we have 49,500 individuals who are establish to be positive by the new test (FP).
If nosotros get-go using this new examination without confirmatory testing on the aureate standard gonioscopy, we would diagnose 49,500 people, or approximately 5% of the population, equally PACG when in reality, they are non. The sensitivity and specificity of the test have not changed. The sensitivity and specificity were nonetheless determined with a 50% prevalence of PACG (1,000 PACG and ane,000 normals) with PPV of 95%. We are now applying it to a population with a prevalence of PACG of merely 1%. With a one% prevalence of PACG, the new test has a PPV of 15%. Although the sensitivity and specificity of the test have non changed, the PPV has inverse drastically. If the prevalence (also known as the pre-examination probability in this state of affairs) of the illness is low, such equally with glaucoma or sight-threatening diabetic retinopathy in the full general population, the number of false-positive results will be far higher than the number of true-positive results.3 This leads to a number of problems, including labeling of normal as aberrant resulting in unnecessary handling.
The NPV of the test likewise change depending on the prevalence of the disease and commonly in reverse direction to PPV. In the to a higher place example, in high-prevalence situation (50% prevalence) [Tabular array 4a], the NPV was ninety%. In low-prevalence situation [Tabular array 4b], the NPV increased to 99%. And so why not utilize a exam for the NPV value? If the prevalence is already so low, the NPV will certainly reduce it farther but nonetheless not to zero.
Tabular array 4b
Showing instance of adding of predictive values at 1% prevalence
The PPV can increment if we repeat the test in certain situations. For case, in HIV, if we repeat ELISA with unlike kit in the group that is already ELISA positive, the specificity and PPV will increase. However, if the same examination is repeated, then concordance will exist a problem.
Everything nosotros have discussed and so far has assumed that the sensitivity and specificity practice not change as one deals with dissimilar groups of people. Sensitivity and specificity, nonetheless, can change if the population tested is dramatically different from the population you serve, specially if the spectrum of the disease is dissimilar. In more severe disease, we are more probable to be able to make a diagnosis; and thus sensitivity goes up.
What if the new test is actually meliorate than the gold standard? There is no shortcut to the procedure of comparing it to the existing golden standard. The new (presumably better) test volition detect more disease than the ′gold standard.′ In the 2 x 2 table, the subjects labeled equally ′diseased′ by the new test (but nevertheless ′normal′ on the ′gold standard′) will go in cell ′b′ (false positives). If on follow-up, a meaning number of these patients really develop disease (golden standard positive), then the new test is in fact detecting illness before than, and is ameliorate than, the gilt standard. In some instances, there may be other strategies available to determine straight away whether the new test is in fact better.4
Clinical application
So far we have discussed how to summate sensitivity, specificity, positive and negative predictive values using 2 ten 2 table. Now we volition discuss the clinical application of these parameters.
The sensitivity, specificity of IOP, torch light examination, van Herick test are shown below [Table 5].
Table 5
Shows sensitivity, specificity of intraocular pressure, torch light examination and van Herick examination
Which test should we utilize to screen the population for bending closure glaucoma? The prevalence and PPV discussed in a higher place (and other reasons provided in the reference) should accept convinced you that this is a bad idea.iii Then permit′due south take an case in a clinic. Table 5 shows the sensitivity and specificity of various tests we can use for detecting PACG. Gonioscopy is the ′gilded standard′ for diagnosis of angle closure, and that′s why nosotros should do gonioscopy in all patients we see in clinics. All other tests (IOP, torch lite test and van Herick test) have poor specificity.2,5,half-dozen Even with specificity as loftier as 90%, the PPV volition be poor. The prevalence of angle closure (equally opposed to angle closure glaucoma) is approximately 3%. With this prevalence, PPV of IOP would exist fifteen%; torch light test, 7.6%; and for van Herick test, 15%. These results mean that if we use IOP or van Herick examination to diagnose bending closure, simply 15% of suspected angle closure patients will really have disease, and the other 85% would be FP. The sensitivity of these tests is moderate and will miss nigh of the illness.
In twenty-four hours-to-day clinical practice, nosotros can still combine results of 2 independent tests to be more than confident of the diagnosis – for example, combining IOP and optic disc changes for chief open angle glaucoma (POAG), IOP and peripheral angle chamber depth for diagnosis of PACG, history of diabetes and frequency doubling engineering (FDT) defect for diabetic retinopathy.3
Case 1
A 54-year-sometime male person patient was diagnosed to have POAG. He did non have whatever ocular or systemic complaints. The vision was 20/20, N6 in each eye. The IOPs were 25 mmHg in both eyes on several occasions. Corneal pachymetry was normal and the bending was reported to be open up. The optic discs showed changes suggestive of glaucoma, and there were corresponding early on visual defects. The patient was started on a unilateral trial of timolol 0.five% twice daily.
The van Herick test when the patient was examined 2 weeks later on is shown in Fig 2. The peripheral anterior chamber depth was less than 1-quaternary the peripheral corneal thickness in both eyes.
Van Herick test showing shallow peripheral anterior chamber depth (< one-fourth the peripheral corneal thickness)
With this IOP and van Herick examination, a diagnosis of POAG becomes unlikely. Let u.s.a. examine the rationale backside this statement. The specificity of IOP for glaucoma is ninety%. That in itself is not enough for a SpPIN, or ′dominion in,′ and doesn′t help besides much. The specificity of the van Herick test for angle closure is 85%, which once again, on its ain is not of much help either. Yet, the 2 tests can be combined to increase the specificity and mayhap apply SpPIN and ′rule in′ diagnosis. The specificity of the two tests can be combined in the following manner6:
Specificity of combined test = 1 - (1 - specificity of test one) × (1 – specificity of examination 2)
Plugging in the values for our patient,
1 - (1 - 0.ix) × (one - 0.85) = 1 - 0.1 × 0.15 = i - 0.015
= 0.985, or 98.5%
This combined specificity of 98.5% definitely allows us to invoke SpPIN and dominion in a diagnosis: until proved otherwise, this patient has angle closure. (We assume that the IOP specificity of xc% holds for angle closure glaucoma too.)
The ′open angle′ described before is shown in Fig. 3.. The angles on repeat gonioscopy (indentation) are shown in Fig. 4.
'Open angle' in an inappropriate testing status
Gonioscopy in an appropriate condition showing closed bending (white arrow) and presence of a peripheral inductive synechia on indentation (black arrow)
One valid objection to combining tests in this mode is that the resultant sensitivity becomes the product of the sensitivities of the two tests – that is, the product of the sensitivity of an IOP >21 mmHg (fifty%) and the sensitivity of the van Herick test (69%) = 0.50 × 0.69 = 34.v%. While 35 is a low sensitivity equally far every bit tests in general are concerned, it doesn′t actually matter here as we are utilizing the ′rule in′ specifically to make the diagnosis in an individual patient.
Allow′s take another instance: a patient has repeatable IOP measurements of 24 mmHg with normal pachymetry, and the angles this time are really open. The specificity of the IOP measurement is 90%. And, while not also useful a measure, the loving cup disc ratio is 0.7 (specificity of CDR >0.55 is 73%). The combined specificity of IOP and disc at present becomes 1 - (1 - specificity of IOP) × (1 - specificity of Disc) = 1 - (1 - 0.90)×(1 - 0.73) = 1- (0.ane)×(0.27) = ane - 0.027 = 97.iii%.
This specificity is high plenty to ″rule in″ the diagnosis of POAG, without further testing. Any farther testing is probably required for monitoring. Of course, whether we treat or non is a different affair.
Some of us desire even more evidence than this. The approach we describe allows incorporation of further testing (including optimal and effective apply of mod imaging techniques) likewise. The GDX ′number (NFI)′ in the above patient is more than 32 (specificity of nigh 85%). If we combine this with just the IOP, can yous calculate the combined specificity?
ane - (1 - specificity of IOP)) × (1 - specificity of ′number′ >30)
You should get 98.five%.
This should be confirmatory; but if you are still non satisfied and desire to take it further, you can use the IOP, Disc and the GDX. 1 - (1 - specificity of IOP) × (1 - specificity of Disc)×(1 - specificity of ′number′ >30).
Did y'all get 99.v%? Every bit a ′rule in,′ this is (most) as good every bit it gets. Regrettably, there is no accented certainty. According to our clinical Bible, absolute certainty is limited to theologians and like-minded clinicians.1 And as the tests are ′independent,′ our estimate of specificity should work. If the tests were not contained, in that location would be some ′convergence,′ every bit information technology is technically called. When we use three tests, such convergence would have minimal clinical significance.
Case 2
A forty-year-erstwhile male is suspected to have sarcoidosis. It is an idiopathic multi-system granulomatous affliction, where the diagnosis is made past a combination of clinical, radiological and laboratory findings. The gilded standard is a tissue biopsy showing noncaseating granuloma. Ocular sarcoidosis could present equally inductive, intermediate, posterior or panuveitis; but none of these are pathognomonic. Therefore, ane has to rely on ancillary testing to ostend the diagnosis.
Angiotensin-converting enzyme (ACE) has a sensitivity of 73% and a specificity of 83% to diagnose sarcoidosis. Abnormal gallium scan has a sensitivity of 91% and a specificity of 84%.vii Though individually the specificity of either exam is not impressive, when we combine both the tests, the specificity becomes –
1 - (1 - 0.84) × (i - 0.83) = 1 - (0.16 × 0.17)
= 1 - 0.03 = 0.97 = 97%
The combination sensitivity becomes = 0.73×0.91 = 0.66 = 66%.
Sensitivities tin be used in the aforementioned manner to dominion out diagnoses. Let us assume that the loving cup disc ratio (usually useless without a mention of the disc size, but having a sensitivity of fifty% for a cutoff of >0.55) is 0.six; and the IOP is 21 mmHg (GHT, sensitivity of simply 50%). Just you feel the disc is suspicious or the patient has a family history or has been referred or whatsoever. Based on the above information, could the patient still have glaucoma? The combined sensitivity is calculated equally:
1 - (i - sensitivity of IOP)×(one - sensitivity of CDR >0.55).
Did yous effort to summate that? You lot should become 75%. That′s certainly non proficient plenty to rule out a disease similar glaucoma. The visual fields, specifically the glaucoma hemifield test (sensitivity 95%), are normal. The combined specificity now becomes 1 - (0.25)×(1 - 0.95) = 98.75. Y'all should be able to rule out ′functional′ glaucoma at present. Actually a normal field with a normal GHT with a sensitivity of 95% is on its own a adept enough ′dominion out,′ only we know that the field may be normal with a lot of disc damage. So y'all can use the GDX to combine data near the nerve fiber layer. The ′number′ on GDX is 31, the sensitivity of which is 74%. What is the combined sensitivity at present? 98.8%. Can we transport the patient home at present?
In summary, we accept provided the bones knowledge to calculate sensitivity, specificity, PPV and NPV. More importantly, we take discussed the advantage and limitations of these measures and provided how we should use these measures in our day-to-solar day clinical practice. We also take illustrated how to calculate sensitivity and specificity while combining 2 tests and how to use the results for our patients in day-to-day practice.
Footnotes
Source of Back up: Nil
Conflict of Involvement: None
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Articles from Indian Periodical of Ophthalmology are provided here courtesy of Wolters Kluwer -- Medknow Publications
Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2636062/
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