REVIEW Chu ARTICLE et al
Current and Future Research in Diagnostic Criteria and Evaluation of Caries Detection Methods Chun Hung Chua/Alex M. H. Chaub/Edward C. M. Loc Abstract: The biochemical definition of dental caries is reasonably understood and generally agreed upon, but there is no consensus on a clinical definition among dentists. There are many proposed diagnostic criteria of dental caries in the dental literature. The recently developed International Caries Detection and Assessment System (ICDAS II) has been constructed to allow data comparison between studies. It can be used in epidemiological studies, public health research, clinical research, clinical practice and dental education. A good study evaluating a caries detection method should contain information on caries prevalence of the study sample and other measures, including sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV). It is noteworthy that measuring sensitivity and specificity provides no quantitative information on how likely a tested tooth is to be carious because the true caries status of the tooth is not known in a clinical situation. Moreover, the study design for caries detection should address the interpretation of predictive values because PPV and NPV are affected by the caries prevalence. The study design should also measure patient-oriented outcomes, address allocation concealment and avoid lead-time bias to generate valid and clinically relevant studies. Prudent evaluation of caries detection methods is the standard of care. This paper reviews current diagnostic criteria for caries detection and discusses proper ways to evaluate new diagnostic methods. Key words: assessment, caries, demineralisation, detection, diagnosis, research Oral Health Prev Dent 2013;11:181-189
Submitted for publication: 24.09.11; accepted for publication: 17.05.12
doi: 10.3290/j.ohpd.a29365
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ental caries can be defined as a localised acid attack of dental hard tissue as a result of the metabolism of bacterial plaque biofilm (Selwitz et al, 2007). It may also be understood as an imbalance towards demineralisation from remineralisation (Kidd, 2005). Untreated dental caries can cause pain, form dental abscesses or even result in severe infections (Chu, 2000; Chu et al, 2002). It is a multifactorial disease, in which frequent snacking habits, poor oral hygiene and inadequate fluoride exposure have been attributed to the pathogenesis of dental caries (Fejerskov et al, 1990). Early diagnosis with caries risk assessment is imperative in contemporary caries management. Dentists should develop appropriate protocols to help
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Clinical Associate Professor, Faculty of Dentistry, University of Hong Kong.
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Honorary Clinical Assistant Professor, Faculty of Dentistry, University of Hong Kong.
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Clinical Professor, Faculty of Dentistry, University of Hong Kong.
Correspondence: Dr. C.H. Chu, Faculty of Dentistry, The University of Hong Kong, 34 Hospital Road, Hong Kong SAR, China. Tel: +8522859-0422, Fax: +852 2858 7874. Email:
[email protected]
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in protecting their patients from dental caries and to avoid invasive restorative treatment through early intervention. Caries detection can be facilitated in several ways. For instance, intraoral radiographs are commonly used to aid clinical examination. Digital radiography allows immediate image preview and is convenient. It has special image processing techniques that enhance the overall display of the image. Radiographic assessment has consistently had a higher specificity but lower sensitivity than visual inspection and other diagnostic methods. One study found that by using bitewing radiographs, 105% more caries can be detected than by clinical examination alone (Chu et al, 2008). Caries detection can also be enhanced by the use of magnifying loupes. Furthermore, the sensitivity and specificity of caries detection can be improved by the use of laser-induced fluorescence (LIF) technology. For example, the DIAGNODent (KaVo Dental; Biberach/ Riss, Germany) is a small chairside battery-powered, LIF-based caries detection device that uses a quantitative optical method to detect mineral loss (Chu et al, 2010). Other caries detection methods include near-infrared light (NIR) and quantitative
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light-induced fluorescence (QLF), which allow a quantification of hard-tissue demineralisation to help make critical decisions for treatment planning. A number of recent publications in caries assessment are summarised in Table 1. It is noteworthy that LIF and QLF are not suitable for detecting root caries. Clinical management of patients with caries is influenced by the number of teeth affected and the depth of the carious lesions in the affected teeth. Traditional caries diagnosis is targeted at cavitation level or caries extending into dentin. Caries is often referred to as ‘cavities,’ requiring restorative treatment, and its management is a surgical approach. Contemporary caries management focuses on prevention and early diagnosis and treatment. Caries now often refers to early white/brown lesions which can be ‘healed’ through remineralisation (Evans et al, 2008). The management is based on a diseasecentred philosophy that directs attention first to control and management of the disease that causes tooth decay and then to relief of the residual symptoms it has caused, which are the decayed teeth. A caries management protocol called ‘caries management by risk assessment’ (CAMBRA) has been proposed (Young et al, 2007) which emphasises the importance of recognising pathological and protective factors instead of focusing on caries removal and restoration. Initial or early enamel caries lesions without cavitation can be treated effectively by fluoride agents such as sodium fluoride varnish (Chu et al, 2010). In addition, dental cream or paste containing tri-calcium phosphate or casein phosphopeptide-amorphous calcium phosphate can be used to replace the calcium and phosphate ions lost due to demineralisation of enamel. The present authors find the term ‘minimal intervention dentistry’ (Tyas et al, 2000) misleading, as it may imply minimal treatment. On the contrary, early and vigorous intervention should be carried out to promote remineralisation of the detected demineralised dental lesions. Therefore, ‘minimally invasive dentistry’ is more suitable to illustrate its difference from the traditional surgical approach (Murdoch-Kinch et al, 2003). Remineralisation, however, is not without constraints. It was suggested that any cavitated carious lesions should be treated surgically with placement of a restoration, because it is too difficult to effectively remove plaque from the cavitation (Evans et al, 2008). Studies also show that caries extending into dentin can be arrested by topical application of silver diamine fluoride solution (Chu et al, 2002; Chu et
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al, 2010). Managing caries with the stepwise excavation technique (Hevinga et al, 2010), tunnel preparation (Markovic et al, 2008) and the use of composite resin have been shown to conserve more dental tissue if operative treatment is essential. In order to implement an adequate treatment plan for the best benefit of the patient, as well as to develop optimal preventive measures for dental caries, it is essential to detect caries accurately, objectively and promptly. This paper reviews current diagnostic criteria for caries detection and discusses proper ways to evaluate new diagnostic methods.
Caries detection versus caries diagnosis It is important to distinguish caries diagnosis from detection. Diagnosis is a complicated process performed by the clinician considering signs and symptoms (Wulff et al, 2000). It is a verdict which balances the need for treatment against consequences for the patient (Nyvad, 2004). In contrast, detection is an augmentation of the diagnosis in which earlier detection, more objective assessment or quantified outcomes become possible (Pretty, 2006). However, considering the fact that dental caries in early stages often exhibits no symptoms, some researchers have argued that there should not be a diagnosis of caries (Bader et al, 2002). Diagnosis can also act as a mental resting point before determining the treatment options to be taken (Baelum et al, 2008). In this way, the diagnostic criteria and recording system are critical in guiding the most appropriate treatment and monitoring disease progress.
What are the current diagnostic criteria for detecting caries? Ismail (2004) performed an extensive literature review on the diagnostic criteria for dental caries published between 1966 and 2001. A total of 29 diagnostic criteria systems were included in his review and there were several key findings. Firstly, there was variation in the use of dental explorers among the diagnostic criteria systems. Secondly, there was no consensus on whether the teeth should be cleaned or dried before examination. Thirdly, the diagnostic criteria systems developed in Europe focus mainly on the disease process, while those in the USA emphasise reliability and comparability. Furthermore, Ismail (2004) found that while new caries detection criteria measured different stages
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Table 1 Current publication of caries diagnostic methods Authors (year)
Aims
Main results/conclusion Radiographic assessment
Bottenberg et al (2011)
To compare CMOS and CCD sensors to detect enamel caries
AZ of CMOS was comparable to CCD at high exposure times
Diniz et al (2011)
To compare BW and ICDAS in vitro
ICDAS vs BW: Sp: 79% vs 94% (P < 0.05), Se: 83% vs 44% (P < 0.001)
Moreira et al (2011)
To study x-ray vertical incidence angles in caries detection with intra-oral radiographs.
No significant difference detected in caries diagnosis
Mitropoulos et al (2010)
To study diagnostic accuracy of ICDAS, conventional (CR) and digital radiography (DR)
Se and Sp for ICDAS, CR and DR were (57%, 94%), (97%, 48%), (68%, 48%), respectively
Akarslan et al (2008)
To compare the diagnostic accuracy on posterior proximal caries in BW, periapical, PAN unfiltered, PAN sharpened, PAN smooth and PAN emboss
AZ: 0.95, 0.94, 0.74, 0.75, 0.74, 0.79
Laser-induced fluorescence (LIF) Thomas et al (2010)
To determine discriminatory accuracy of LIF in: Enamel caries vs sound teeth Dentinal caries vs sound teeth Enamel caries vs dentinal caries
Se and Sp for distinguishing enamel caries from sound teeth, dentinal caries from sound teeth and enamel caries from dentinal caries were (85%, 90%), (100%, 100%) and (88%, 77%), respectively
Chu et al (2010)
To assess in vivo validity of diagnosing dentinal fissure caries by VI, BW, DIAGNODent and BW + DIAGNODent
Se and Sp for VI, BW, DIAGNODent and BW+DIAGNODent were (89%, 44%), (13%, 100%), (70%, 84%) and (67%, 94%), respectively
Karlsson et al (2009)
To assess validity of LIF, VI and surface texture on root caries in vitro
LIF was not suitable as a diagnostic tool for root caries
Near-infrared light (NIR) Fried et al (2011)
A case report using NIR and PS-OCT for planning a restoration of an occlusal caries
Combining OCT and NIR provided valuable information on severity of caries
Zakian et al (2009)
An in vitro study on accuracy of NIR for detecting enamel caries and dentinal caries
Se and Sp for enamel and dentinal caries were (>99%, 88%) and (80%, >99%), respectively. NIR could map lesion distribution and was non-invasive and stain insensitive
Fried et al (2005)
A review on optical properties and potential use of PS-OCT for producing caries images
NIR could be useful in imaging early caries lesions. PS-OCT was useful for quantifying and monitoring caries lesions over time
Quantitative light-induced fluorescence (QLF) Ferreira Zandona et al (2010)
A longitudinal study to combine ICDAS and QLF in monitoring caries in children
Clinical potential for earlier caries detection especially on occlusal surfaces
Kuhnisch et al (2007)
To compare diagnostic accuracy of QLF and VI in non-cavitated occlusal caries
QLF detected more non-cavitated occlusal lesions than VI, but was more time consuming
Heinrich-Weltzien et al (2005)
To compare diagnostic accuracy of QLF and VI on smooth surfaces
QLF is sensitive in detecting visually undetected initial caries, but it is difficult near gingival margin
CCD – charge-coupled device; CMOS – complementary metal oxide semiconductor; BW – bitewing radiographs; ICDAS – International Caries Detection and Assessment System; PAN – panoramic radiographs; VI – visual inspection; PS-OCT – polarisation-sensitive optical coherence tomography; Sp – specificity; Se – sensitivity; AZ – area under receiver operating characteristic curve.
of the caries process, there were inconsistencies in how the caries process was measured. An interesting debate on the use of an explorer in the diagnosis of caries has been initiated. The
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proponents of using an explorer claimed that its use is time efficient, well accepted by dentists and patients, and has an excellent sensitivity in in vivo studies, while there is inadequate in vitro evidence
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opposing the use of this caries detection aid (Hamilton, 2005). The opponents argue that probing with an explorer cannot improve accuracy of diagnosis (Stookey, 2005). It can cause iatrogenic damage on initial carious lesions and thus its use should be limited to plaque removal. In general, many researchers are in favor of not using dental probes, in particular a sharp probe, for caries detection. However, it is not uncommon to find a clinician using quite forceful probing in detecting caries in the dental practice. Perhaps the most common diagnostic criterion in caries research, particularly in community-based epidemiological surveys, is the one recommended by the World Health Organisation (WHO) (1997). As part of ‘tooth status’ assessment, caries on the crown or root was defined as an unmistakeable cavity or undermined enamel seen clinically without any doubt. Although this method is simple, quick, cost efficient and does not requiring any explorers, it may not be appropriate for clinical trials (Pitts et al, 2004). As it does not include early white/brown lesions in the criteria, it is not a sensitive method for caries detection and adequate early prevention management cannot be justified. Moreover, exclusion of arrested caries may pose a further complication in recording caries status and disease monitoring.
International caries detection and assessment system A clinical scoring system known as the International Caries Detection and Assessment System (ICDAS) has been recently developed for use in epidemiological studies, public health research, clinical research, clinical practice and dental education (Pitts, 2004). Air drying and plaque removal are necessary in the current ICDAS II system (Topping et al, 2009). A ball-ended explorer is often used to aid visual assessment by removing any remaining plaque and debris and to check for surface contour, minor cavitation or sealants. Two digits are needed to represent the status of a tooth; the first digit is for restoration or sealant, and the second is for caries severity. A detailed description of this system has been published (Pitts, 2004). This system was constructed to present an international system for caries detection that would allow for data comparison between studies. The ICDAS committee suggested that future research should be directed toward detection of caries adjacent to restorations
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and sealants as well as on tooth root surfaces (Topping et al, 2009). Studies have been conducted to evaluate the validity and reproducibility of ICDAS in caries detection. An in vitro study on extracted permanent molars using histological assessment showed that ICDAS had good reproducibility and accuracy in detecting occlusal caries, especially if the caries was confined to enamel (Diniz et al, 2009). Another study showed that examining multiple teeth had no effect on the assessment of occlusal caries using ICDAS when compared with examining a single tooth (Jablonski-Momeni et al, 2009). For proximal caries in both primary and permanent dentition, it was shown that tooth separation could help to improve the classification in ICDAS when compared to radiograph (Ekstrand et al, 2011). Validity and reproducibility of caries assessment on primary molars were also found acceptable using ICDAS II and thus was recommended for use in the assessment of primary teeth (Shoaib et al, 2009). ICDAS can be valuable in the detection of early enamel lesions. This is advantageous for contemporary caries management, which emphasises early intervention and prevention. One study used ICDAS to detect enamel demineralisation confined to the outer 50% area, and it demonstrated satisfactory specificity and sensitivity (Ekstrand et al, 1997). However, another study reported that ICDAS could overestimate the caries activity of cavitated lesions (Braga et al, 2010) when compared to Nyvad criteria (Nyvad et al, 1999). When socioeconomic factors of the subjects are considered, it has been suggested that no additional discriminatory power can be obtained over the WHO criteria, even though the ICDAS has a more detailed classification (Mendes et al, 2010). The practicality in terms of cost effectiveness of using ICDAS in public health studies is another concern, because on average, at least 15 minutes is required to examine an adult having more than 30% of teeth with codes higher than zero in ICDAS (Bonner et al, 2011). The advantages of the WHO criteria are time efficiency, acceptable accuracy in field studies, popular use in the literature for interstudy comparison, high specificity of caries detection and generally high interand intra-examiner agreement. The advantage of ICDAS is that it is a more detailed classification system for early lesion detection and caries monitoring.
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Bringing diagnostic criteria into action – How to evaluate a screening test Numerous methods of caries detection with techniques based on visual, optical, radiographic and some emerging technologies such as auto-fluorescence and electrical resistance of teeth have been reviewed (Maupomé and Pretty, 2004; Pretty and Maupomé, 2004a,b,c,d; Pretty, 2006). However, it is important to understand how to correctly evaluate a test. Sensitivity and specificity are two of the most common measures in evaluating a test (Pretty and Maupomé, 2004a). By assuming that the true status of the test tooth is known, sensitivity and specificity are the measures of correct positive and negative results, respectively. Statistically, sensitivity is defined as the probability of obtaining positive test results when the tested tooth is truly diseased, while specificity is defined as the probability of obtaining negative test results when the tested tooth truly lacks the disease. Therefore, to interpret sensitivity and specificity, it is assumed that the true status of the tooth is already known, while in clinical situations, tests are performed because the true status of the tooth has yet to be determined. These parameters provide no quantitative information on how likely the tested tooth has or does not have a carious lesion. If a positive result is obtained from a new diagnostic method with a sensitivity of 99%, there is not enough information to make any conclusion on the accuracy of the test result. The clinical value of a test should be represented by the positive predictive value (PPV) and the negative predictive value (NPV). In caries detection, PPV is defined as the probability of the tooth being truly carious when the test result is positive, while NPV is defined as the probability of the tooth being caries free when the test result is negative. However, unlike sensitivity and specificity, PPV and NPV should be interpreted with caution, as prevalence can affect the values of PPV and NPV. Applying the Bayes’ Theorem (Slawson et al, 2002), sensitivity may be expressed as true positive rate divided by disease prevalence. Any change in disease prevalence is balanced by the same proportional change in true positive rate, keeping a constant sensitivity (the same applies to specificity). This is different from predictive values. PPV, for example, may be expressed as true positive rate divided by total probability of obtaining positive test results. If the disease prevalence in the operator’s clinic is different from that in the validation study, the true posi-
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tive rate and total test positive rate will be affected differently, causing a change in PPV (see example below). Therefore, if a certain research method is planned to be implemented in a clinical situation and the PPV and NPV are to be adopted, the disease prevalence described in the study should be similar to that in the clinic, otherwise either PPV or NPV can be overestimated and endanger the patients (Slawson et al, 2002). A good study evaluating a caries detection method should contain information on at least the sensitivity, specificity, PPV, NPV and prevalence of dental caries in the study sample, apart from other measures such as validity and reproducibility (Pretty and Maupomé, 2004a). An example to illustrate the importance of PPV, NPV and prevalence of dental caries is given below. The latest population survey in Hong Kong revealed that the mean number of untreated decayed and missing teeth, shown by mean DT and MT score, of the elderly (65- to 74-year-old) group were 1.3 and 15.1, respectively (Hong Kong Department of Health, 2002). Therefore, on average, each elderly patient had 16.9 (32 minus 15.1) teeth remaining in their mouth. The pre-test probability of untreated caries on a tooth in this patient group was therefore 1.3 / 16.9 = 0.077 or 7.7%, and the proportion of teeth which had no caries was 92.3%. Let us consider a scenario in which a dentist uses a commercial laser-induced fluorescence detection device such as DIAGNOdent to aid caries detection by visual examination on every tooth in this patient group. According to the results of a Hong Kong study, this caries detection method has a sensitivity of 0.67 and specificity of 0.94 (Chu et al, 2010). Using the results of this caries detection method, the mathematical calculation would result in a PPV of 0.48 and a NPV of 0.97 (Appendix 1). This can be interpreted as 48% of the positive test and 97% of the negative test results being correct. In other words, 52% of the positive test results and 3% of the negative test results are wrong. Therefore, the dentist may end up performing many inappropriate treatments in teeth that are wrongly classified as ‘carious’ according to the test result. Let us look at a different scenario in which the dentist changes the examination protocol and now uses DIAGNODent only on teeth with doubtful caries status in a clinical examination. Since only teeth in doubt are tested, the pre-test probability of a tooth being carious will increase, for example to 50%. According to the same calculation method, the PPV and NPV obtained change dramatically to 92% and 74%, respectively (Appendix 1). This illus-
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tration shows that in the routine use of DIAGNODent on every tooth (the pre-test probability of caries is low), the positive test results are likely to be full of errors and are not useful, although the negative results are reliable. However, judiciously using the test on teeth with doubtful diagnosis of caries (the pre-test probability of caries is high) or when caries is very common among patients in a dental practice, the positive test results are more reliable, but a rather significant proportion of the negative test results are wrong (i.e. truly carious teeth are missed). Because in vitro and in vivo conditions are very different, it can be argued that the validity and effectiveness of laboratory studies should not be applied directly to clinical situations (Hamilton, 2005). Researchers can carry out randomised clinical trials for a higher level of evidence to confirm the validity of the dental caries assessment method. In the research design, it is important to take the patient-oriented outcome, allocation concealment and lead-time bias of the study into account. Patient-oriented outcome is crucial in research design because studies that measure patient-oriented outcomes, such as quality of life, should lead to change in practice if the reported results are valid (Ebell et al, 1999). Patient-oriented outcomes include quality of life, development of complications and tooth loss, instead of disease-oriented evidence, such as number of teeth with white lesions or any other surrogate endpoints. Articles or summaries on these studies are called Patient-Oriented Evidence that Matters (POEMs) (Ebell et al, 1999). POEMs have to meet three criteria. Firstly, they address a question that is common in the dentist’s daily practice. Secondly, they measure outcomes that dentists and their patients care about, such as development of complications. Thirdly, they take the potential to change dental practices into consideration. More and more studies have been published giving information that may be significant but do not matter to patients. Studies that provide evidence that matters to patients are few in the literature. POEMs sum up well-founded studies that are important to dentists and to their patients, and the evaluation of caries detection methods is a typical use of POEMs. Allocation concealment appears to be a very significant issue when thinking about how blinding can be achieved when evaluating the tests. Allocation concealment can be defined as the process that keeps clinicians and participants unaware of upcoming assignments (Schulz et al, 2002). While
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randomisation can be done correctly by using block randomisation or any random number table, the investigators may enroll the subjects selectively so that the effect is biased towards the desired direction. Chalmers et al (1987) suggested that up to 40% of the effect could be exaggerated through unconcealed allocation. Allocation concealment can be done by using sequentially numbered, opaque, sealed envelopes (SNOSE), central randomisation, etc. (Schulz et al, 2002) and should be explicitly stated in the published study. Lead-time bias should be discussed in any study evaluating screening tests if survival analysis is to be adopted (Black et al, 1990). Suppose a diagnostic test can successfully detect a significant number of subclinical carious lesions; it appears that time is ‘earned’ when compared to those teeth without the test. If a survival analysis is to be carried out in two groups of teeth (a test group and a control group), the investigator may place the starting time point at the time when positive screening is obtained or early intervention is applied in the test group. This design or arrangement has a leadtime bias, favouring the test group in which the survival rate appears naturally higher. For example, assuming that there is a screening test that can detect subclinical dental caries lesions and that these lesions will progress to clinically detectable lesions after 2 years, it is hypothesised that, on average, after carrying out the traditional screening method, a tooth can survive for 10 more years with proper intervention. Accordingly, a tooth having a positive result from the screening test will have a mean natural survival time of 12 years instead of 10 years. To eliminate this bias, the time frame of natural progression of dental caries should be investigated. However, this is not commonly mentioned in survival studies in dentistry.
CONCLUSION Caries research is an extremely broad topic, from pathogenesis to prognostic factors for undergoing certain treatments. The biological process of caries is reasonably well known and thus, caries should be preventable. However, caries is still prevalent, particularly in disadvantaged groups and children. Current management is focused on early diagnosis and preventive treatment. There are many diagnostic criteria in the dental literature. ICDAS is one of the recently developed indices that is scientifically based and internation-
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ally recognised; further research to validate its application is essential. Studies on diagnostic tools are also abundant. However, issues in evaluating the diagnostic criteria and tools should be addressed to produce relevant and valid studies. For instance, predictive values should be interpreted carefully before adoption of the test, and the use of patient-oriented outcomes and allocation concealment, together with avoidance of lead-time bias can help to generate more valid and clinically relevant studies in the future.
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Oral Health & Preventive Dentistry
Chu et al
APPENDIX 1 – CALCULATION OF PPV AND NPV OF CARIES ASSESSMENT Scenario 1 – Examining all teeth Pre-test probability of caries from survey [Department of Health, 2001] is 7.7%, hence, P(D+)=0.077, and P(D-) =1-0.077 = 0.923. Sensitivity, defined as P(T+ given D+), from study [Chu et al, 2010] is 0.67. From Bayes’ Theorem, P(T+ given D+) = P(T+ and D+) / P(D+). Therefore, P(T+ and D+) = 0.67 x 0.077 = 0.0516; P(D+ and T-) = 0.077 - 0.0516 = 0.0254 Specificity, defined as P(T- given D-), from study [Chu et al, 2010] is 0.94. From Bayes’ Theorem, P(T- given D-) = P(T- and D-) / P(D-). Therefore, P (T- and D-) = 0.94 x 0.9230 = 0.8676; P(T- and D+) = 0.9230-0.8676 = 0.0554. Carious (D+)
Caries-free (D-)
Total
Positive test result (T+)
0.0516
0.0554
0.1070
Negative test result (T-)
0.0254
0.8676
0.8930
Total
0.0770
0.9230
1
By completing the table above, the total values of P(T+) = 0.0516+0.0554=0.1070, and P(T-)=0.0254+0.8676=0.8930 PPV, defined as P(D+ given T+) = P(D+ and T+) / P(T+) = 0.0516 / 0.1070 = 0.48 or 48%. NPV, defined as P(D- given T-) = P(D- and T-) / P(T-) = 0.8676 / 0.8930 = 0.97 or 97%.
Scenario 2 – Examining teeth in doubt Pre-test probability of caries is assumed to be 50%, hence P(D+)=0.5 and P(D-) =1-0.5 = 0.5. Sensitivity, defined as P(T+ given D+), from study [Chu et al, 2010] is 0.67. From Bayes’ Theorem, P(T+ given D+) = P(T+ and D+) / P(D+). Therefore, P(T+ and D+) = 0.67 x 0.5 = 0.335; P(T+ and D-) = 0.5 - 0.335 = 0.165. Specificity, defined as P(T- given D-), from study [Chu et al, 2010] is 0.94. From Bayes’ Theorem, P(T- given D-) = P(T- and D-) / P(D-). Therefore, P(T- and D-) = 0.94 x 0.5 = 0.47; P(T- and D+) = 0.5-0.47 = 0.03. Carious (D+)
Caries-free (D-)
Total
Positive test result (T+)
0.335
0.03
0.365
Negative test result (T-)
0.165
0.47
0.635
Total
0.5
0.5
1
By completing the table above, P(T+) = 0.335+0.03=0.365 and P(T-) = 0.165+0.47=0.635. PPV, defined as P(D+ given T+) = P(D+ and T+) / P(T+) = 0.335 / 0.365 = 0.92 or 92%. NPV, defined as P(D- given T-) = P(D- and T-) / P(T-) = 0.47 / 0.635 = 0.74 or 74%.
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