Diagnostic accuracy of pattern differentiation algorithm based on Chinese medicine theory: a stochastic simulation study

Background Clinical practice of Chinese medicine requires little information for differentiation of Zang-fu patterns. This study is to test the impact of information amount on the diagnostic accuracy of pattern differentiation algorithm (PDA) using stochastic simulation of cases. Methods A dataset with 69 Zang-fu single patterns was used with manifestations according to the Four Examinations, namely inspection (Ip), auscultation and olfaction (AO), inquiry (Iq) and palpation (P). A variable quantity of available information (N%) was randomly sampled to generate 100 true positive and 100 true negative manifestation profiles per pattern to which PDA was applied. Four runs of simulations were used according to the Four Examinations: Ip, Ip+AO, Ip+AO+Iq and Ip+AO+Iq+P. The algorithm performed pattern differentiation by ranking a list of diagnostic hypotheses by the amount of explained information F%. Accuracy, sensitivity, specificity and negative and positive predictive values were calculated. Results Use the Four Examinations resulted in the best accuracy with the smallest cutoff value (N% = 28.5%), followed by Ip+AO+Iq (33.5%), Ip+AO (51.5%) and Ip (52.0%). All tested combinations provided concave-shaped curves for accuracy, indicating an optimal value subject to N%-cutoff. Use of N%-cutoff as a secondary criterion resulted in 94.7% (94.3; 95.1) accuracy, 89.8% (89.1; 90.6) sensitivity, and 99.5% (99.3; 99.7) specificity with the Four Examinations. Conclusion Pattern differentiation based on both explained and optimum available information (F% and N%-cutoff) is more accurate than using explained and available information without cutoff (F% and N%). Both F% and N%-cutoff should be used as PDA's objective criteria to perform Zang-fu single pattern differentiation.


Standard references for evaluating accuracy of pattern differentiation
Diagnosis established by expert Chinese medicine practitioners has been used as the standard for diagnostic accuracy tests of computational models [11][12][13]. However, the agreement in diagnosis among practitioners may be low (31.7%; 27.5-35%) [20], despite some improvement after training (73%; 64.3-85.7%) [21]. Standards for Reporting Interventions in Controlled Trials of Acupuncture (STRICTA) [22] recommend that the experience of Chinese medicine practitioners should be reported in clinical studies because such experience may influence diagnosis. As such, new diagnostic tests should not be used for comparison with diagnoses made by Chinese medicine practitioners but with methods that guarantee correct diagnosis.
Stochastic simulation models have been used for research in health sciences. A well-known simulation method is the Monte Carlo [23,24], in which the basic idea is to stochastically generate examples of a numerical variable and then evaluate the outcome of the model under evaluation. With stochastic methods, simulated patients can have their health status characterized by a computational model. For the determination of the accuracy of Chinese medicine diagnostic tests, a large number of patients with possible combinations of the manifestations for each pattern can be generated. The patterns must be differentiable; thus, it is virtually impossible to estimate the diagnostic accuracy without computer methods. However, some modifications based on Chinese medicine are needed to enable stochastic methods to process nominal variables.

Objective criteria for Chinese medicine pattern differentiation
Recognition of factors related to the performance of diagnostic methods is relevant to the development of reliable methods that can be implemented for clinical and research purposes. For instance, the amount of information necessary to accurately perform pattern differentiation seems to be a key factor for Chinese medicine diagnosis [9]. Although Maciocia [9] stated that little information (i.e. few manifestations) is necessary for successful differentiation of Zang-fu single patterns, no evidence was presented to support this claim. Accurate diagnosis with minimum information is required to be recognized as "superior" traditional Chinese medicine practitioners, who detect patterns in early stages "to treat who is not yet ill" [4][5][6]25]. This statement suggests that patterns must be differentiated in early stages so treatment of unaffected systems can be initiated (according to the transmission effect). None of the abovementioned works [1,3,18,19] estimated the impact of available information on the accuracy of pattern differentiation.
This study aims to evaluate the effect of information amount on the diagnostic accuracy. The method was tested with Zang-fu single patterns using combinations of the Four Examinations of examination. It was hypothesized that the quantity of available information can optimally describe patterns, providing enough information for an accurate single pattern differentiation. Stochastic simulations and receiver operating characteristic (ROC) curves [26][27][28] were used to estimate the cutoff point of available information.

Methods
The study was performed in the following sequence. First, computational simulation from patterns in a dataset was performed to obtain manifestation profiles that were applied to ROC curve analysis and the estimation of cutoff values for the available information. Next, the cutoff value for this new criterion was incorporated into PDA (as a secondary criterion to the explained information criterion), and the respective impact on the diagnostic accuracy was obtained with confusion matrices. All algorithms were implemented in LabVIEW 8.0 (National Instruments, USA) and executed on an 1.73 GHz Dual Core Intel ® microprocessor with 2.00 GB RAM running Windows Vista (Microsoft Corporation, USA). This work followed the Standards for Reporting of Diagnostic Accuracy [29] where applicable to simulation studies.

Patterns dataset
The patterns dataset was developed in a previous work [14]. Sixty-nine Zang-fu single patterns (Additional file 1) [9] were listed, and all possible manifestations of each pattern K were listed separately according to the Four Examinations. The total quantity of manifestations describing pattern K in the dataset was represented by N T,K . Each entry in the dataset is separated by a comma and has case-insensitive letters. Manifestations were described as specifically as possible including onset ("palpitation in the morning," "palpitation in the evening"), duration ("acute headache," "chronic headache"), location ("occipital headache," "ocular headache") and severity ("dry tongue," "slight moist tongue," "moist tongue"), as well as any other characteristic that may be necessary to allow the pattern differentiation. Manifestations that cooccur in two or more patterns were assigned with the same term to increase the accuracy of string search algorithm. Patterns in the dataset have 16 (range 5-39) manifestations. A total of 504 manifestations were distributed among Ip (n = 108; 21%), AO (n = 36; 7%), Iq (n = 335; 66%), and P (n = 25; 6%).
Dataset consistency and quality were computationally tested before the simulation and diagnostic procedures. Internal (intrapattern) and external (interpattern) exploratory analyses were performed with string search algorithm. Intrapattern consistency was obtained by excluding repetitions of any manifestation in the same examination method, as well as among the Four Examinations describing the respective pattern. Interpattern consistency was obtained by ensuring that two patterns were not described with the same complete manifestation profile (both constitute the same pattern). Patterns in the dataset are mutually exclusive and collectively exhaustive, that is, for each manifestation there is at least one possible pattern, and there is no pattern without manifestations (considering the Four Examinations).

Manifestation profile simulation algorithm
Study population Cases (true positive) and controls (true negative) manifestation profiles were generated by the manifestation profile simulation algorithm (MPSA). The inclusion criterion was the simulation of cases representing a Zang-fu single pattern in the dataset. For both types of simulation, it was assumed that the probability of each manifestation in the general population is given and follows a uniform distribution.

Sample size
There is no formula specifying the exact number of simulations needed in stochastic simulation studies, but the number should increase with the complexity of the patterns to reduce simulation variability in the result [30]. Thus, the sample sizes were estimated based on the previous results of PDA [14] and equations (1) to (4), which were derived for detecting differences in accuracy tests using ROC curves [26]: Where AUC i is the area under the ROC curve calculated for each new criterion N % (i = 1) and N %-cutoff (i = 2).

Participant recruitment and sampling
Four runs of simulations were performed according to the following combination of examination methods: Ip, Ip+AO, Ip+AO+Iq and Ip+AO+Iq+P. Two hundred mani- festation profiles (100 true positive and 100 true negative cases) were prospectively generated for each of the 69 patterns, summing to 13,800 cases per examination method. Globally, 55,200 cases were simulated and tested.

Data collection (simulation) of true positive cases
True positive cases of Zang-fu pattern K were simulated by selecting from the dataset a random quantity (N R, K ) in the interval (1;N T, K ), according to the selected methods of examination. Each sorted manifestation was excluded from the set of possible manifestations to prevent multiple occurrences of the same manifestation at the respective simulated case. This iterative process continued until the N R, K manifestations were sorted to generate the manifestation profile.

Data collection (simulation) of true negative cases
To obtain a true negative case for the same pattern K, this respective pattern was removed from the dataset and the same quantity N R, K (from the total of manifestations for the excluded counterpart true positive pattern, N T, K ) was selected from the entire dataset and respective examination methods. In other words, the MPSA sorted N R, K manifestations from the entire dataset after the exclusion of pattern K. This procedure allows a quantitative pair-wise comparison between true positive and true negative cases with respect to the available information for pattern K, N %, K . Although the true positive pattern was removed from the dataset, its manifestations that co-occur in other patterns are still present and could be selected to compose a true negative manifestation profile.

Missing cases
Because patterns may not present manifestations for some of the examination methods, empty manifestation profiles related to these examination methods represent missing cases and were excluded from analysis.

Reference standard
Because cases were simulated from all possible manifestations of each pattern in the dataset, the output of the diagnostic algorithm was compared to the actual name of the simulated pattern in the dataset. Thus, it was considered a gold-standard method. The result was treated as a binary variable for further classification according to the confusion matrix displayed in Table 1.
All simulated cases were evaluated by PDA. No user intervention was required during the entire process (simulation; identification with F % ; cutoff estimation for N % ; identification with F % , N % , and N %-cutoff ; and statistical analysis). Additionally, MPSA and PDA are composed of independent algorithmic codes (i.e., there is no code sharing), so the results of the identification were considered to be blinded to the simulation parameters.

Pattern differentiation algorithm (PDA) Strategy description
The first version of PDA was developed and validated previously for Zang-fu single patterns [14]. Its strategy was based on the reasoning that as more manifestations are explained by a single pattern, the higher the probability of this respective pattern to be the diagnosis. An implicit assumption is that the patients are capable of reporting their symptoms and that the Chinese medicine practitioners are able to correctly identify manifestations. Briefly, the algorithm performed pattern differentiation in a three-stage schema using the same pattern dataset used for simulation of true positive and true negative cases. Below is presented the pseudocodes of PDA algorithm: Step Step 3. Calculate explained (F %,K ) and available (N %,K ) information for pattern K on dataset. F %,K = N E,K /N P × 100%; N %,K = N E,K /N T,K × 100% Step 4. Populate vectors CP, F %,K , and N %,K Step 5. Populate diagnostic hypothesis (DH) from CP with patterns in which F % >0%. Filter F %,K and N %,K accordingly Step 6. Diagnosis and output else ⇒ display("Zang-fu single pattern differentiation was not possible with these manifestations").

Data entry and hypotheses generation
The first stage comprised data collection and a dataset search. During data entry of manifestations, PDA searched with a combinatorial procedure for quoted terms to increase the sensitivity of the method. Sequentially, a list of candidate patterns was generated with patterns that explain at least one manifestation collected at the exam. Patterns with no manifestations recognized were not used for further analysis.

Ranking hypotheses by the quantity of explained information
The candidate patterns were ranked by the amount of explained information, F % (equation 5): Where N E, K is the number of explained manifestations for pattern K in the diagnostic hypothesis list and N P is the number of presented manifestations either from simulated profiles or real patients.
Thus, F %, K represents the explained information of pattern K on the clinical history. Notice that for the simulated true positive and true negative profiles N R, K = N P . It is expected that the occurrence of a successful pattern differentiation increases with decreasing F %, K . Hence, the candidate patterns ranked in descending order of F % represent diagnostic hypotheses.

Pattern differentiation
In this last stage, the differentiation was considered successful if PDA found a single pattern K among diagnostic hypotheses with the highest, unique F % . Otherwise, if at least two (or several) patterns were found among diagnostic hypotheses with high, equal values of F % , the procedure was unsuccessful because differentiation among single patterns was not possible with the explained information.

Calculation of the additional criterion: available information
Patterns maybe described by different quantities of manifestations. As such, the available information must be normalized to allow comparison among them. The normalized available information was calculated by equation 6: Where N E, K is the quantity of explained manifestations for pattern K. Note that for simulated true positive profiles N E, K = N R, K because all sorted manifestations will be explained by pattern K. It is expected that the occurrence of a successful pattern differentiation increases with increasing N %, K .

Statistical analysis Outputs from algorithms for statistical analysis
The MPSA output for each manifestation profile: binary classification of the simulated case as true positive (= 1) or true negative (= 0); the name of the simulated pattern K;N R, K ; N T, K and the manifestations as quoted terms, words separated by commas. PDA received the manifestation profile from MPSA and output for each tested profile: the name of the identified pattern (the diagnosis);F %, K N %, K and the quantity of candidate patterns N CP . The diagnosis of each manifestation profile was made according to the respective method used for the simulation of cases (e.g. profiles simulated with Ip were diagnosed using only Ip, and so on).

Estimation of cutoff for the available information
An algorithm for estimation of the optimum quantity of available information was implemented and integrated into MPSA and PDA. To determine the degree of available information that maximizes PDA's accuracy, its binary output to true positive cases was used as the reference method for evaluation of the new test. N % was used as the prediction variable to generate confusion matrices for each simulation run according to the examination methods. Cutoff values for N % were evaluated by maximizing both sensitivity and specificity obtained with ROC curves [26][27][28]. The smallest cutoff value was the minimum observed test value minus 1, and the largest cutoff value was the maximum observed test value plus 1. All the other tested cutoff values were the averages of two consecutive ordered observed test values.

Estimation of the diagnostic accuracy of PDA with both explained and available information criteria
The cutoff values of N % obtained for each combination of examination methods were incorporated as the second criterion for pattern differentiation. Because of the nature of ROC curve analysis [26], the accuracy of a diagnostic test is expected to decrease with either lower or higher cutoff values -producing a concave-shaped curve. Therefore, it is appropriate to subtract the cutoff values from N % to dislocate the accuracy curve to its optimum operating point (equation 7): Where cutoff represents the point of maximum accuracy obtained with each examination method. As such, the maximum accuracy is associated with the minimum N % . The identified pattern is then chosen by simultaneously arranging the diagnostic hypotheses by descending values of F % and by ascending values of N % or N %-cutoff .
Comparison between PDA with N % and N %-cutoff Both conditions (N % and N %-cutoff ) were tested to evaluate the effect of curve dislocation on diagnostic accuracy. All results were organized according to the examination methods. PDA was evaluated with estimations of accuracy (proportion of true results in the population, equation 8), sensitivity [31] (proportion of successful pattern differentiations that are correctly predicted by PDA, equation 9) and specificity [31] (proportion of unsuccessful pattern differentiations that are correctly predicted by PDA, equation 10) and negative and positive predictive values [32] (equations 11 and 12 respectively) ( Table 1).
Where TP and TN represent the number of true positive and true negative cases respectively; FP and FN represent the number of false positive and negative cases respectively.
The 95% confidence interval (95%CI) for the above binomial proportions p (equations 8-12) was calculated with Wilson's method (equation 13) [33]: Where p is the binomial proportion, Np is the sample size of the binomial proportion p, and Z α/2 is the two-sided significance value (α 5% = 1.96). As the tests (with both N % and N %-cutoff ) have been evaluated on the same samples of true positive and true negative cases, an adaptation of McNemar's test for correlated proportions is applied [24]. The true positive and the true negative subjects are divided into four parts according to their test responses (Table 2). Hence, for comparison of the results of the two tests with equal sample sizes (k = TP/TN = 1) the test statistic is (equation 14):  Where B is the number of true negative cases classified correctly by N %-cutoff and falsely by N % and conversely for C cases and analogously for the true positive group.
Estimations related to ROC (AUC and respective95%CI) were obtained with the nonparametric Wilcoxon statistic [26,27] (equations [15][16][17][18][19][20]: Where N %, S and N %, U stand for the quantity of cases with successful and unsuccessful procedures at N % respectively; n S and n U stand for the sample sizes of successful and unsuccessful procedures; Q 1 represents the probability that two randomly chosen unsuccessful procedures will both be ranked with greater suspicion than a randomly chosen successful procedure; and Q 2 represent the probability that one randomly chosen unsuccessful procedure will be ranked with greater suspicion than two randomly chosen successful procedures.

Test reproducibility
Calculations of reference standard reproducibility were not performed because both true positive and true negative cases were always generated from the dataset.

Results
The flowchart describing this simulation study is presented in Figure 1. Regarding the simulation process, 200 of 13,800 (1.4%) cases were excluded from both Ip and Ip+AO examination methods due to the absence of manifestations in those respective examination methods in the dataset.

ROC curves and cutoff values for N %
ROC curves obtained for N % grouped by the examination methods are shown in Figure 3. The respective values of cutoff, accuracy, AUC, sensitivity and specificity are presented in Table 3. The combination of Examinations methods yielded distinct cutoff points to be used by PDA. The use of the Four Examinations resulted in the best overall statistical performance with the minimum cutoff value of available information (N % = 28.5%), followed by three (Ip+AO+Iq, N % = 33.5%), two (Ip+AO, N % = 51.5%) and single examination methods (Ip, N % = 52.0%).
The average accuracy of PDA as a function of N % is shown in Figure 4. All tested combinations provided concaveshaped curves, indicating that there is an optimum quantity of available information to accurately perform pattern differentiation. Also, inspection (Ip) or its combination with auscultation-olfaction (Ip+AO) provided lower average accuracies than the addition of inquiry (Ip+AO+Iq) and palpation (Ip+AO+Iq+P) to the examination procedure, as indicated by the relative position of the concavity (maximum value).
The N CP as a function of N % is shown in Figure 5. N CP was normalized to the quantity of patterns in dataset. The average normalized N CP increased as more information was available to perform pattern differentiation.

Comparison of diagnostic accuracy of PDA with both explained and available information (N % and N %-cutoff )
The diagnostic accuracy of PDA as a function of examination methods and criteria for diagnostic hypotheses sorting is presented in Table 4. The use of the Four Examinations of examination yielded the best diagnostic accuracy and associated statistical performance, followed by three (Ip+AO+Iq), two (Ip+AO) and one method (Ip), despite the use of N % or N %-cutoff as the secondary ranking criterion.
Among all combinations of examination methods tested, there was a statistically significant difference between N % and N %-cutoff (P < 0.001), indicating a better performance of N %-cutoff as a criterion. Higher values of accuracy, sensitivity, specificity (only for Ip), negative predictive value and positive predictive value (only for Ip) were observed when diagnostic hypotheses were ranked by N %-cutoff compared to N % . However, specificity and positive predictive values were significantly higher (P < 0.001) when diagnostic hypotheses were ranked by N % for the combinations Ip+AO, Ip+AO+Iq and Ip+AO+Iq+P.

Discussion
This study evaluated the diagnostic accuracy of PDA with the associated method for estimation of cutoff values for optimization of its accuracy. The findings indicate that early, unbalanced health status may be accurately assessed through pattern differentiation even if little information about the pattern itself is available. The computational Flowchart describing the simulation study Figure 1 Flowchart describing the simulation study. Departing from Zang-fu single patterns dataset, manifestation profiles were simulated according to the combination of traditional examination methods. Cases (true positive) and controls (true negative) profiles were tested with criteria F % and N % and with F % and N %-cutoff for comparison of diagnostic tests. PD+: successful pattern differentiation; PD-: unsuccessful pattern differentiation.
strategies implemented provided statistical data related to the Chinese medicine therapeutic principle of treating who is not yet ill.

Assessment of early unbalanced health status
The concave shape (Figure 4) of accuracy curves can be explained by the following reasons. As N % tends toward zero, the low average diagnostic accuracy resulted from the selection of manifestations that collectively did not represent a unique description of any pattern on the dataset. Likewise, as N % tends toward 100%, the low average diagnostic accuracy resulted from the selection of too many manifestations that generate several unique subgroups, including more candidate patterns (observed increase in the number of candidate patterns in Figure 5).
Regarding Zang-fu single patterns, those results suggest that PDA is more likely to perform successful pattern differentiation if about 28.5% of the information of the actual pattern is available using the Four Examinations. It is still possible to obtain an accurate diagnosis with lower or higher values of available information (Figure 3), but at lower expected frequencies. Moreover, the results do not indicate that any subset with 28.5% of the manifestations allow an accurate Zang-fu pattern differentiation because all manifestations were chosen at random. The discovery of which subsets lead to a more accurate diagnosis needs further evaluation. Methods such as latent tree models [34] may be used to identify such subsets. Finally, the concomitant increase in statistical performance and decrease in N % as a function of combined exam methods reinforces the Four Examinations as the best practice for Zang-fu single pattern differentiation when little information is available.
PDA was implemented to differentiate the correct pattern among possible ones rather than to identify the healthy/ sickness outcome [14]. In the current version of PDA, it is not possible to obtain the healthy status. However, a possible outcome is that no pattern satisfactorily explains the manifestations presented by the patient (non-unique, higher F % and non-unique, lower N % ). Such a case may need further exploration by the Chinese medicine practitioner to determine if the patient is actually sick. For PDA to obtain the "healthy pattern," it must be described in the same manner as the patterns already in the dataset. For instance, the "liver-blood deficiency" Zang-fu pattern should have the mutually exclusive counterpart "liverblood health" pattern. The description of such healthrelated patterns is possible because Chinese medicine is not limited to assessing presence/absence of manifestations (e.g. asymptomatic individuals may be also diagnosed). Constitutional and behavioral aspects are also considered relevant to establish the true pattern [9]. A completely healthy person will present all healthy patterns simultaneously. However, in clinical practice it is Percent time interval for execution of the simulation (MPSA) and identification (PDA) algorithms difficult to find a patient that is completely healthy and thus the pattern differentiation process must be applied. Future works should incorporate these aspects to improve PDA's validity and clinical use as a screening test between health and disease.

To treat who is not yet ill
The proposed computational strategies are based on the explained (F % ) and available (N %-cutoff ) information. Both strategies preserve the traditional concepts of patterns. The quantity of explained information, F % , allows the interpretation of manifestations collectively, that is, diagnostic hypotheses are ranked by the strength of the simultaneous occurrence of manifestations rather than individual manifestations. Additionally, N %-cutoff is based on the hypothesis of optimum information for diagnosis, which was confirmed in this study at least for Zang-fu single patterns. Thus, when F % is identical among diagnostic hypotheses, the optimized available information (meas-ured with N %-cutoff ) can be used to rank patterns to better identify the diagnosis.
The significant increase in diagnostic performance (accuracy, sensitivity, and negative predictive value) using N %cutoff compared to N % reflect the recognition of more true positive cases with this secondary criterion. The significant decrease in performance (specificity and positive predictive value) occurred because PDA identified an incorrect diagnosis in true negative cases using N %-cutoff as the decision criterion when two or more patterns presented the same F % (when no diagnosis would be identified by F % alone).
In the theoretical field, this study provides statistical data related to one of the most important Chinese medicine principles, namely "treat who is not yet ill" [4][5][6]25]. Patterns may be transmitted among Zang-fu by fixed or not fixed laws [9,25], adding manifestations or changing their severity and location. However, Zang-fu patterns in early Receiver operating characteristic curves with respect to the available information for diagnosis Figure 3 Receiver operating characteristic curves with respect to the available information for diagnosis. The combination of methods yielded distinct cutoff points. The Four Examinations (Ip+AO+Iq+P) resulted in the best overall statistical performance with the minimum cutoff value of available information, followed by three (Ip+AO+Iq), two (Ip+AO) and single (Ip) examination methods.
stages may be well explained by a single pattern, as it represents the first stage of progression through the Zang-fu system [9]. Thus, patterns must be recognized in early stages so treatment of unaffected systems can be initiated. As such, the ability to detect single patterns is of extreme relevance if the treatment is intended to be immediately started. PDA correctly identified 94.7% of the cases as true positive or true negative and can be used to help Chinese medicine practitioners in the pattern identification process of Zang-fu single patterns.

Simulated manifestation profiles versus real cases
Studies on the evaluation of accuracy of Chinese medicine diagnostic methods [1,3,12] relied on real cases instead of simulated cases. Those studies used the diagnoses given by Chinese medicine practitioners as the gold-standard, which may not be reliable because of the low agreement among practitioners [34]. Simulation of manifestation profiles is more appropriate for diagnostic accuracy studies because it guarantees that the diagnosis is known. Moreover, the implemented stochastic method allows a focus on the properties of manifestation profiles instead of individual manifestations [23]. This procedure is to generate a large number of examples of any given pattern (stochastic process) and then examines the relative proportion of successes of the diagnostic test (deterministic process) [24]. The proposed MPSA is suitable for diagnostic studies because it tests several cases found in clinical practice. The main advantage of the simulation method is that the actual diagnosis is known from the dataset, which means that no gold-standard method is necessary.
Epidemiological information for manifestations describing Zang-fu (or any other theory-based) patterns is insufficient in the current literature [35]. Studies with small sample sizes [36][37][38][39] described the frequencies of manifestations among patterns but were not designed to obtain these data in the general population. Moreover, there is no description of mathematical models to simulate frequency distributions of the Zang-fu manifestations. Any assumed distribution may introduce selection bias (by increasing the frequency of low-probability manifestations and/or decreasing the frequency of high-probability ones). Future clinical research should focus on determining the distribution of manifestations in each pattern (and patterns in the dataset) to further improve the MPSA.
Another possible influence is the dataset which comprises the core of the process. Different datasets may result in better or worse diagnostic accuracies (as well as cutoff values) depending on characteristics such as the quantity of patterns and manifestations, use of specific or general terms to describe the manifestations and co-occurrence of manifestations among single patterns. Those datasets should be arranged by the Four Examinations so that the same evaluation can be made and comparisons performed. Such comparisons would evaluate the use of PDA for clinical and research purposes. This aspect stresses the need for internationally available Web-based datasets [3].
MPSA and PDA are related to single patterns, which is the simplest case found in clinical practice. In fact, a patient may present several patterns simultaneously that are not mutually exclusive (i.e. lung-qi deficiency and spleen-qi deficiency), which may explain the decrease of accuracy when more information was made available. Additionally, common etiologies and pattern transmissions among Zang-fu -which is also implied in the determination of the Root-Manifestation relationship -are factors that must be incorporated into MPSA and PDA to extend (only real or simulated cases). Although it is possible to apply a "reverse model" and recreate the dataset from these presented cases (by grouping all cases from the same classification pattern and removing repetitive data), the attributes distributed with this procedure would not cover the Four Examinations. Finally, if the dataset were constructed and the cases from this repository were tested regardless of the issues stated above, they do not present the variable of amount of information and thus no cutoff value for this variable could be obtained to test its influence on the PDA's accuracy.

Implications for research and clinical use
Despite the lack of comparison with other methods, some inferences can be made by comparing PDA with other diagnostic methods. PDA has the several major advantages over the conventional learning algorithms. There is no need to train PDA, which is a mathematical process Average normalized accuracy as a function of the available information for diagnosis Figure 4 Average normalized accuracy as a function of the available information for diagnosis. All tested combinations provided concave-shaped curves, indicating that there is an optimum quantity of available information to accurately perform pattern differentiation. Also, inspection (Ip) or its combination with auscultation-olfaction (Ip+AO) provided lower average normalized accuracies than addition of inquiry (Ip+AO+Iq) and palpation (Ip+AO+Iq +P; Four Examinations) to the examination, as indicated by the relative position of the concavity (maximum value).
already subject to bias. PDA's method is simple, and both criteria (F % and N % ) can be calculated even manually by a Chinese medicine practitioner (for a low number of candidate patterns). Its reasoning is entirely based on the actual process executed by Chinese medicine experts [4][5][6][7][8] and thus reduces the error in data collection and analysis. The practitioner can add, change or delete manifestations in the dataset based on other Chinese medicine publications and then retest the impact of those changes in terms of diagnostic accuracy with the methods describe in this work. Finally, PDA is more stable than other learning algorithms because the final diagnosis does not depend on the initial guess (or sequence of manifestations) used during the learning phase (i.e. given the same manifestations PDA will always provide the same diagnosis, no matter the sequence in which the manifestations are collected).
Recent studies on Chinese medicine have focused on computer aids to diagnose patients [1,3,12,40,41], pre-scribe treatment [2] and statistical methods [13,14] for validation of Chinese medicine theories. It is believed that the combination of traditional theories and modern techniques may improve the scientific approach of Chinese medicine interventions by means of computerization and standardization of diagnosis and treatment based on traditional rules. Practitioners may implement algorithms to become "superior doctors." In this direction, PDA can be used by Chinese medicine practitioners and researchers as a software tool for real-time assessment of patients with actual information about its statistical performance.

Conclusion
This study suggests that pattern differentiation based on both explained and optimum available information (F % and N %-cutoff ) is more accurate than using explained and available information without a cutoff (F % and N % ). Both F % and N %-cutoff should be used as PDA's objective criteria to perform Zang-fu single pattern differentiation.
Average number of candidate patterns as a function of available information for diagnosis Figure 5 Average number of candidate patterns as a function of available information for diagnosis. The average normalized number of candidate patterns increased as more information was available to perform pattern differentiation.

Abbreviations
Ip: inspection; AO: auscultation and olfaction; Iq: inquiry; P: palpation; PDA: pattern differentiation algorithm; ROC: receiver operating characteristic;K: single pattern from dataset; MPSA: manifestation profile simulation algorithm; N T, K : quantity of manifestations describing pattern K in dataset; AUC: area under the curve; N R, K : quantity of randomly selected manifestations of pattern K; N %, K : proportion of available information of pattern K in dataset; F %, K : proportion of explained information of pattern K from clinical history; N %-cutoff : proportion of optimized available information of pattern K in dataset; N E, K : quantity of explained manifestations of pattern K; N P : quantity of presented manifestations on the clinical history; N CP : quantity of candidate patterns; 95%CI: 95% confidence interval; p: binomial proportions; N %, S : quantity of cases at N % with successful procedure; N %, U : quantity of cases at N % with unsuccessful procedure; n S : sample size with successful procedure; n U : sample size with unsuccessful procedure; Q 1 : probability that two randomly chosen unsuccessful procedures will both be ranked with greater suspicion than a randomly chosen successful procedure; Q 2 : probability that one randomly chosen unsuccessful procedure will be ranked with greater suspicion than two randomly chosen successful procedures