Bayesian Modeling of Muscle Biopsy Contracture Testing for Malignant Hyperthermia Susceptibility 

(Table 1) summarizes sensitivity and specificity figures for the North American Malignant Hyperthermia Registry [38]and the EMHG. [40]For the North American Malignant Hyperthermia Registry CHCT, the sensitivity is 0.97 and specificity is 0.78. For the EMHG IVCT, the sensitivity is 0.99, and the specificity is 0.936.

Construction of a 2 x 2 contingency table using current estimates of sensitivities and specificities allowed the calculation of conditional probabilities associated with varying PTPs as the input variable. The positive predictive Value (PPV) is the calculated conditional probability of a true positive (TP), given a positive test result. The negative predictive value (NPV) is the conditional probability of a true negative (TN), given a negative test result. The PPV and NPV are calculated values that depend on fixed sensitivity and specificity and variable PTP. The efficiency of testing is calculated as the proportion of correctly assigned results (TP + TN) over all results, including false-positive (FP) and false-negative (FN) results (Table 2).

In the EMHG “clinical” IVCT, MHE results in the same treatment as MHS: Where a more “specific” IVCT result is required, such as for genetic linkage studies, MHE results are considered nondiagnostic. Accordingly, a 3 x 2 contingency table was constructed to model the “specific” IVCT. Equivocal predictive value is the calculated conditional probability of MH given an MHE result. In this case, efficiency is calculated as the proportion of correctly assigned results (TP + TN) over all results, which now also include equivocal positive (EP) and equivocal negative (EN) results (Table 3). The MHE rate was 0.14 in probands, and 0.05 in control patients. [35,40] 

All contingency tables were coded with computer spreadsheet software (Borland's Quattro Pro 5; Microsoft's [Redmond, WA] Excel, v. 7.0) and modeled with PTP values from 0 to 1. Selected values were checked by manual calculation. Results were plotted using Origin 3.73 (MicroCal, Northampton, MA).

(Figure 1) illustrates the effect of PTP on PPV, NPV, and efficiency of diagnostic contracture testing for MH. In all cases, for PTPs between 0 and 0.75, NPV remains near 1.00. A high NPV is required clinically so that the risk of a false-negative result is acceptably low. The PPV is a measure of the degree of certainty that can be associated with a positive test result. It is a function of PTP and specificity. When PPV is low, such as at low PTPs, a positive result is likely to be falsely positive.

In the case of the EMHG, the “specific” interpretation of the IVCT produces a higher PPV and NPV (Figure 1(B)). The graph of equivocal predictive value against PTP is close to the diagonal, confirming that MHE alone is a poor predictor of MH. The MHE classification implies that the likelihood of MH is unchanged by the test and remains at the PTP. The increased proportion of MHE patients who are left undiagnosed contributes to a reduction in efficiency by nearly 0.2 at high PTPs.

The PPV is likely to be affected by any imprecision, expressed as the 95% confidence interval, in estimating specificity (Table 1). However, even a major change in specificity from 0.82 to 0.92, within the 95% confidence, has a minor effect on the shape of the PPV curve, which retains an elbow at PTP between 0.125 and 0.25 (Figure 2), whereas NPV and efficiency are relatively unaffected. Conclusions about PPV are likely to be reliable for all PTPs.

In contrast, imprecision in estimating sensitivity has a profound effect on NPV at high PTP. When sensitivity is near 1, the NPV of the test will remain high at all PTPs (Figure 1(B)). However, as little as a 0.01 to 0.03 change in the estimate of sensitivity results in a dramatic change at high PTP from a nearly straight line (Figure 1(B)) to a curve (Figure 2(B)), which is similar to the NPV curve for the CHCT (Figure 1(A)), with little change in PPV and efficiency. Conclusions about NPV at high PTPs should account for the decrease in NPV.

The Bayesian model, used in this analysis, does not depend on the mechanism of the test procedure or the disease and can be applied where there is a discrete outcome (e.g., health and disease). There is no assumption about probability distributions, so the model is still valid if MH diagnostic tests do not have a bimodal frequency distribution [45]and even if strongly positive results occur in healthy persons for any reason unrelated to MH.

An alternative approach, using pre-test odds and likelihood ratios, although more cumbersome, is also possible. It is less suitable, however, because contracture test results are reported as discrete outcomes (MHS and healthy) rather than as ranks of likelihood (e.g., a scale of 1 to 10). Because all current clinical testing protocols report discrete outcomes, Bayesian modeling is appropriate.

Sensitivity and specificity refer to the ability of diagnostic testing to discriminate between healthy persons and patients at risk for life-threatening reactions to anesthesia. There was no attempt in this model to characterize discrimination for less typical reactions, such as isolated masseter muscle rigidity, sudden hyperkalemic cardiac arrest, or events not related to anesthesia.

Our model is valid as long as estimates of sensitivity and specificity are accurate. Values from the North American Malignant Hyperthermia Registry and the EMHG (Table 1) indicate general agreement for sensitivity and specificity. In the event that more accurate estimates of sensitivity and specificity become available in the future, the models can be recalculated.

Any bias during measurement of sensitivity, such as unintentional selection or incomplete case finding would affect NPV at high PTPs. A potential source of bias lies in the selection of patients for study based on diagnostic test results. Strict inclusion and exclusion criteria that do not depend on diagnostic test results should be satisfied to avoid over or underestimates based on unintentional bias.

Clinical history was used to define control and proband groups for estimating sensitivity and specificity. [38,40]The validity of CGS, as applied to probands, relies heavily on laboratory measurements made during the management of an anesthetic reaction. It is considered valid because only those patients tested since current protocols were established can be included for analysis, and only those patients with severe reactions were included in the proband group.

The model can regard MH as a single disorder or as a group of disorders that share the features of a life-threatening anesthetic reaction, identifiable by the CGS and by contracture testing. Acute MH can progress so rapidly that any delay in treatment can result in severe morbidity and death despite valiant measures. [2]Aborting a reaction early with dantrolene treatment is lifesaving and also the standard of care. To determine whether MH might demonstrate a spectrum of severity if left untreated is highly unethical. For practical purposes, human MH is an all-or-none phenomenon.

Referral of patients for contracture testing occurs after they have survived an anesthetic reaction that suggests MH. After exclusion of differential diagnoses such as sepsis, thyroid storm, and pheochromocytoma, features of the anesthetic reaction may be reviewed and recognized as typical of MH (e.g., generalized rigidity, fever, family history, elevated creatine kinase) or atypical (e.g., lack of metabolic acidosis or absence of myoglobinuria). On this basis, a clinician can assign low, medium, and high PTP status of MH in a proband. This subjective process is a clinical skill. However, a similar process is used in the coding for the CGS. Therefore, we propose that the CGS can also be used as a guide to PTP assessment for probands, provided that the information used to score the CGS is complete and accurate.

The CGS was constructed so that D1 indicates a low likelihood that MH occurred (PTP close to 0), and D6 indicates that MH almost certainly occurred (PTP close to 1). [41]D3 and D4 fall on either side of 50% probability (MG Larach, verbal communication, October 1997) and represent medium PTP. Therefore, the CGS can guide estimation of PTP to within a range that is helpful for calculating PPV and NPV.

Separate conclusions can be drawn for conditions of low, medium and high PTP. Provided that sufficient data were collected to allow accurate CGS grading, patients with CGS D1 or D2 will have low PTP, between 0 and 0.25. An example of an anesthetic event ranking CGS D2 is unexplained sinus tachycardia in the absence of electrolyte abnormalities, muscle breakdown, hypercapnia, acidosis, or fever.

For low PTP patients, a negative test result would effectively rule out MH, since NPV approaches 1.00. The PPV, however, is only 0.50 or lower, so a false-positive result becomes as likely as, or more likely than, a true-positive result. Although a negative result would be useful, there would be no simple way to distinguish true positive results from false-positive results. Deciding whether to test remains a clinical decision that can only be determined in each individual case.

When a patient is referred for consultation after D3, D4, or D5 reactions, there is medium PTP, resulting in PPV in the range of 0.70–0.95, and NPV approaching 1.00. This is the situation in which the risk of observing a false-negative result is low, with an acceptable false-positive risk. Thus test results are useful, and testing is clinically indicated. Such a situation would occur, for instance, in a case of isolated masseter muscle rigidity (CGS D3).

Patients with CGS D6 will have high PTP. An example of a D6 reaction is an anesthetic event with generalized muscle rigidity, muscle breakdown with a creatine kinase level > 20,000 U/l and myoglobinuria, inappropriately elevated end-tidal carbon dioxide, sinus tachycardia, rapid inappropriate increase in body temperature, severe metabolic acidosis, and rapid reversal of respiratory and metabolic acidosis with dantrolene. Based on the CGS, such an episode is “almost certainly MH.”

A positive test result in the setting of high PTP produces a high PPV but does not alter clinical management. In addition, in cases of high PTP (> 0.85), NPV decreases to < 0.80 for the CHCT (Figure 1), so the risk that a negative result is false increases to 0.20 or more. Similar behavior can be seen within the 95% confidence interval for sensitivity of the EMHG IVCT at high PTPs (Figure 2(B)). For these patients, a negative test result cannot rule out MH with acceptable certainty, defeating the clinical use of contracture testing. They should be offered contracture testing only to provide useful data about sensitivity.

Based on the assumption that MH is inherited as an autosomal dominant trait, [7,11–18,20,21]PTP is a function of the degree of certainty of MH in the proband and the degree of kinship to the closest related proband. Unless a relative has other clinical features (such as having suffered an anesthetic reaction suggestive of MH, elevated resting creatine kinase level, identical siblings, or consanguinity), PTP is fixed at a ratio of 0.5 for first-degree relatives, 0.25 for second-degree relatives, 0.125 for third-degree relatives, and so on. Any uncertainty in the diagnosis of MH in the proband, as indicated by the PPV for the proband, reduces the PTP for the relatives of that proband proportionately.

A Markov chain, a mathematical method of calculating dependent probabilities, [46]was constructed (described subsequently) to model the effect of different pedigree testing strategies. The calculations in the text below apply to the North American Malignant Hyperthermia Registry CHCT (Figure 3(A and B)), and calculations for the EMHG IVCT are depicted in Figure 3(C and D). The same conclusions were obtained for the two tests. For illustrative purposes, proband PTP is set at 1.

A “haphazard” testing strategy describes the situation in which a patient is tested without having first tested the intermediary relatives, leaving gaps in phenotyping of the pedigree (Figure 3(A and C)). For each patient, PTP must be assigned only on the basis of the degree of kinship to the proband. For first-, second-, and third-degree relatives, PTP is sufficiently high that PPV and NPV are informative. For more distant relatives, however, the PPV decreases to < 0.5 for the CHCT and the IVCT, although the NPV is high. A PPV of 0.5 indicates moderate risk of MH, and it is sufficiently high that triggering drugs should be avoided during anesthesia. However, the high likelihood of observing a false-positive reaction poses a significant problem for genetic linkage studies.

An alternative to the “haphazard” strategy would be to test close relatives of the proband first and then to offer testing to the nearest relatives of a person who tested positive. Our model confirms that such a “sequential” testing strategy can optimize the information that can be gained from contracture testing (Figure 3(B and D)) and that it does so by optimizing PTP.

For first-degree relatives of a proband, PTP is 0.5, producing a PPV of 0.82. First-degree relatives have a PTP of one half of 0.82; i.e., 0.41 (Figure 3(B)). If the initial first-degree relative had not been tested (as in the case of a “haphazard” testing strategy), the PTP for the second-degree relative would be only 0.25, with a PPV of only 0.60 (Figure 3(A)). By comparison, “sequential” testing of this second-degree relative results in a higher PPV of 0.75 (Figure 3(B)). This effect is even more pronounced for more distant relatives.

The sequential testing strategy maximizes PTPs, producing the best-case performance for PPV, whereas a haphazard strategy uses PTPs based solely on degree of kinship, resulting in worst-case performance. These represent the upper and lower limits of diagnostic performance. Diagnostic accuracy for real pedigrees will fall somewhere between these two limits because some relatives are dead, have refused testing, or have yet to be tested.

Even if the sequential testing strategy could be used to trace a pedigree to completion, there is an inevitable downward drift of PPV as the relationship to the pro-band becomes weaker (Figure 3(B)) because PTP depends on the PPV of the nearest tested relative. Although PPV drifts to a value that is sufficiently high (about 0.7 for CHCT, and 0.9 for IVCT) to warrant avoidance of MH-triggering drugs, the drift may pose a considerable problem for linkage studies, especially in large pedigrees with many distant relatives.

Positive predictive values drift even assuming an optimal testing strategy, absolute certainty of proband diagnosis, and near-perfect sensitivity, as in the IVCT (Figure 3(D)). The PPV drift effect is exaggerated under suboptimal conditions and should be recognized as an important cause of uncertainty in phenotyping pedigrees for linkage studies.

A Markov chain also can be constructed for the alternative “specific” interpretation of the EMHG IVCT, in which the MHE classification is ignored. In Figure 1(C), the graph of the predictive value of an MHE result (shown as EPV) has a slope close to 1. After an MHE result, the likelihood of disease has not changed significantly from PTP, confirming that MHE is truly nondiagnostic.

The NPV for the “specific” IVCT is similar to the clinical protocols (Figure 1(A and B)), but there is higher PPV than the clinical protocols for all PTP (Figure 1(C)), thereby producing more certain phenotypic information for genetic linkage studies. However, the price paid for this is lower efficiency because a nondiagnostic MHE is likely to be observed, especially at moderate-to-high PTP (Figure 1(C)). If a MHE results, the PTP remains unchanged, just as if testing had not occurred. When using the “specific” IVCT, any MHE patients leave a gap in phenotyping a pedigree, producing dips and drift in PPV (Figure 3(F)).

There is difficulty in interpreting test results for parents of a child suspected to have MH, [47]particularly when causal genes might originate from both parents (MHS x MHS). We examined a hypothetical family using calculations from Bayesian modeling. In determining whether two different genes from two parents are causal for MH in a family, hypotheses can be stated as, “Only one gene from one parent is causal of MH in this family” or “Two genes from two parents are causal of MH in this family.”

The calculations that follow assume autosomal dominant inheritance, [7,11–18,20,21]that one and only one parent is MHS, and that there is no dispute about paternity or maternity. The PTP for a parent is set at 0.5. Even under such conditions, we show that it is not possible to use CHCT or IVCT to distinguish between MHS x MHS and MHS x MHN.

When one parent of an MHS patient has a positive contracture test and the other parent is untested, the probability that the result is a true positive is given by PPV, which is 0.94 for the IVCT and 0.82 for the CHCT (Figure 1). The remaining probability is accounted for entirely by false-positive results (Figure 4(A)). Thus, the probability of a false-positive result is calculated as 1 - PPV, which is 0.06 for the IVCT and 0.18 for the CHCT (Table 4). A false-positive result implies that the tested parent was healthy, so the untested parent must be MHS. The automatic assumption that the untested parent is negative will be wrong with this same probability (0.06 IVCT, 0.18 CHCT). “Incomplete” testing, therefore, poses an unacceptable risk of incorrectly identifying the untested half of the pedigree in 1 in every 6–16 such families (Table 4). Further, if these incompletely tested pedigrees were subjected to genetic analysis, the risk of genotype-phenotype discordance is high as a result of misclassification. [47] 

If the second parent is tested (Figure 4(B)), the risk of a false-negative diagnosis for that parent is calculated as (1 - PPV)(1 - sensitivity), which is 0.0006 for the IVCT and 0.0054 for the CHCT (Table 4). Based on this, a complete testing strategy, in which testing is offered to both parents, is far safer clinically than an incomplete strategy (Table 4).

Given the condition that one and only one parent is MHS, the probability that both parents will test positive by chance alone is calculated as sensitivity x (1 - specificity), or 0.063 for IVCT and 0.21 for CHCT (see Table 4). This probability, 1 in every 5–15 such families so tested, is sufficiently high to account for reported cases of apparent MHS x MHS without having to invoke the possibility that both parents are MHS, a spontaneous mutation rate, alternate modes of inheritance, or the existence of alternate genetic loci for MHS. [47] 

There is no simple way to determine whether both parents are truly MHS or whether only one parent is MHS and the other has a false-positive diagnosis. This does not pose any significant clinical problem, because in either case, both sides of the family are treated clinically as though they are MHS. This can be modified in the face of other clinical evidence, such as anesthetic reaction in one branch of the pedigree or a biopsy result from an identical sibling. However, subjecting families to genetic linkage studies in which both parents test positive holds little prospect for finding correct linkages.

When one parent of an MHS patient has a negative contracture test result and the result for the other parent is unknown, the certainty of the negative diagnosis is equal to NPV. This value is 0.99 for the IVCT and 0.96 for the CHCT. If this result is a true negative one, then the untested parent must be positive, with the same degree of certainty. This value (0.99 IVCT, 0.96 CHCT) is the PTP for the untested parent. In this case, as in the case for high PTP probands, if testing is performed, PPV is unchanged, and NPV decreases to a dangerously low value.

Given our assumptions, testing the second parent provides little extra clinical information and exposes the parent to an unacceptable risk of a false-negative result. A “rational” testing strategy implies that the partner of a negative parent should not be tested, a conclusion that may appear to be counterintuitive. This conclusion may not apply if the assumptions are violated, such as nonpaternity or nonmaternity, spontaneous MH mutation, or alternate genetic modes of inheritance.

The estimates of sensitivity and specificity used in our Bayesian model were made by examining diagnostic test performance in two populations, one with “severe” MH (D6 probands) and the other with an extremely low prevalence of MHS (control patients). Using such extreme populations, “the sickest of the sick” and the “wellest of the well,” may overestimate sensitivity and specificity for populations with intermediate prevalence of MHS. This effect is called “spectrum bias.”[26]If MHS is truly unequivocal, then spectrum bias may be minimal. If contracture testing for MHS shows a graded spectrum of responses, [48–50]then sensitivity and specificity will be lower in a population with intermediate prevalence than in the extreme populations.

In the absence of an independent “gold-standard” for MHS, there is no simple way to verify true sensitivity and specificity. Any spectrum bias, however, would result in lower PPV and NPV values, but unless true sensitivity and specificity are known, it is not possible to estimate the magnitude of this effect. Even given the highest possible estimates of sensitivity and specificity, limitations in PPV and NPV are inevitable so long as sensitivity and specificity are not both 1.0. By recognizing these limitations, it is possible to make effective use of diagnostic testing information for clinical and research purposes.

The use of Bayesian modeling based on the estimated sensitivity and specificity of diagnostic contracture testing for MH can allow an understanding of the strengths and limitations of muscle biopsy contracture testing. Bayesian modeling of PTP, PPV, NPV, and efficiency can aid in deciding whom to test, when to test, and how best to interpret the test result, both for clinicians and for researchers.

A clinician relies on the excellent NPV, which accounts for the clinical utility of this test. For any person other than a D6 proband, a negative contracture test effectively rules out MH for them and their descendants. To achieve this, there is an acceptably low false-positive rate, measured by high, but imperfect, PPV. In the absence of a better alternative, contracture testing is a useful clinical tool when properly applied with sequential and complete testing strategies.

For genetic analysis, a much higher PPV is required to be certain that a person who had a positive test result is truly MHS. One approach is to alter the test to achieve higher specificity. This is the EMHG “specific” IVCT interpretation. However, the PTP for a relative is fixed by distance in kinship, especially when there are gaps or MHE diagnoses in the pedigree. Even with a highly specific test, an optimal testing strategy, certain proband identification, and perfect sensitivity, a downward drift in PPV is unavoidable.

A more accurate approach is to accept the limitations of contracture testing and to work within them. Previous linkage models have been used to find association with a positive contracture test result, which has a small, but quantifiable, inherent error in predicting MHS. An alternate linkage model that incorporates the estimated errors in phenotyping contained in this article would be less prone to identifying discordance where discordance does not exist.

The current estimate that only 50% of MH families [20]are linked to chromosome 19q13.1 is almost certainly a large underestimate, once allowance is made for phenotypic uncertainty. The frequent finding of about one discordant individual for each six to eight subjected to the CHCT or IVCT [18,21,51,52]would be expected from the modeling presented here. Where such discordance is observed, it is possible that the linkage exists, but it is obscured by phenotypic uncertainty.

The authors thank Drs. M. Larach, G. Allen, and H. Ording for sharing their data on sensitivity and specificity of the CHCT and IVCT as they developed the model, and for their critical reading of the manuscript. The authors also thank Dr. B. A. Britt for her insight into malignant hyperthermia and Dr. A. Logan for his assistance in clinical epidemiology.