# A New, Vitamin D-Based, Multidimensional Nomogram for the Diagnosis of Primary Hyperparathyroidism

Adrian Harvey, MD; MengJun Hu, MS; Manjula Gupta, PhD; Robert Butler, MS; Jamie Mitchell, MD; Eren Berber, MD; Allan Siperstein, MD; Mira Milas, MD, FACS

Disclosures

Endocr Pract. 2012;18(2):124-131.

### Results

Multivariate analysis was used to determine those factors that were significantly correlated with PTH in the 222 healthy patients. Significant independent predictors of PTH were total serum calcium (P = .0002), 25(OH)D (P<.0001), and age (P = .015) (Table 1). Sex was not a significant, independent predictor of PTH. As shown in Figure 1, upper limits of normal PTH levels were evident for each gradation of 25(OH)D levels: insufficient (10 ng/mL), low-normal (30 ng/mL), and well-repleted (50 ng/mL).

Figure 1.

Upper limits of normal levels for intact parathyroid hormone (PTH) at 25-hydroxyvitamin D levels of varying adequacy: 10 ng/mL (insufficient), 30 ng/mL (low-normal), and 50 ng/mL (well-repleted). CI = confidence interval.

Mathematical modeling of the data set yielded the following predictive equation: PTH (pg/mL) = 90.73 - [6.07 × calcium (mg/dL)] - [0.52 × 25(OH)D (ng/mL)] + [0.26 × age (years)] (R 2 = 0.18; root mean square, 14.5). This equation calculates the expected PTH for a specific patient on the basis of his or her total serum calcium, 25(OH)D, and age measured on the same day. We then modified the equation to predict a patient-specific upper limit of normal PTH (with 95% confidence interval) and estimated this by adding 2 times the root mean square to the PTH value generated by the foregoing equation. Thus, the predictive equation for the upper limit of normal for PTH, or the PTH nomogram, becomes the following: PTH [upper limit of normal] (pg/mL) = 119.73 - [6.07 × calcium (mg/dL)] - [0.52 × 25(OH)D (ng/mL)] + [0.26 × age (years)]. As shown in Figure 2, this predictive equation is presented in a format that is easier to remember for clinical use, with numbers rounded to single digits (without affecting accuracy of the calculation). For example, this equation would predict that a 54-year-old man with a total serum calcium level of 9.5 mg/dL and a 25(OH)D value of 20 ng/mL should have a maximal PTH concentration of 66 pg/mL; a higher measured value would predict parathyroid disease.

Figure 2.

Predictive equation for expected normal parathyroid hormone (PTH) values. This equation provides a patient-specific upper limit of normal (ULN) PTH (R 2 = 0.18) based on clinical variables identified to affect PTH levels significantly in a cohort of healthy persons.

In applying this PTH nomogram to the entire series of patients with surgically confirmed 1°HPT, 331 of 351 surgical patients (94%) would have been correctly diagnosed on the basis of the initial preoperative laboratory results to indeed have 1°HPT (P<.001). All surgical patients with a classic laboratory presentation (total serum calcium >10.5 mg/dL and PTH >60 pg/mL) of 1°HPT were also clearly categorized as such by the nomogram (238 of 238 patients). In the original cohort of 222 patients deemed healthy by our screening criteria, 212 (95%) would also be classified as healthy by the nomogram. Ten individuals (5%) had an unexpectedly abnormal PTH measurement for which no cause was apparent in their clinical records. There are several potential explanations for this finding, including the following: (1) possible early, yet unrecognized 1°HPT; (2) an unrecognized or undocumented clinical condition affecting the calcium-PTH relationship that was not identified during screening for exclusion criteria; (3) false-positive findings within the nomogram; and (4) normal statistical variation, demonstrating the fact that "nomograms" such as the current one are designed to reflect the range of values that would encompass 95% of "normal" persons. Overall, the sensitivity, specificity, positive predictive value, and negative predictive value of the PTH nomogram to diagnose 1°HPT were 94%, 95%, 97%, and 92%, respectively.

Importantly, however, 76 of 351 patients presented with normocalcemic 1°HPT and 37 of 351 had normal PTH levels, demonstrating that 113 patients (32%) in our surgical cohort did not fulfill the classic criteria of 1°HPT and, by definition, had a more challenging diagnostic profile. Although these patients had atypical biochemical profiles before surgical intervention, they did have clinical symptoms and metabolic consequences consistent with 1°HPT that eventually led to surgical exploration. None of these patients underwent an operation in vain because they all had histologic confirmation of abnormal parathyroid glands, although the preoperative informed consent discussion with them quoted a higher risk for a potentially negative exploration. Thus, it was instructive to analyze how the PTH nomogram performed in these circumstances and whether it might have mitigated the surgical risks quoted to patients. In the subgroup with normocalcemic 1°HPT, the nomogram successfully identified 64 of 76 patients (84%). In addition, the model correctly classified 20 of 37 patients (54%) with "inappropriately" normal PTH values as having 1°HPT. Thus, the model reliably predicted normocalcemic 1°HPT and would have clarified a diagnosis for at least half of the remaining atypical patients. The multidimensional nature of the PTH nomogram (Fig. 3) in graph format clearly depicts its ability to separate normal ranges from those of various disease states or phenotypes of hyperparathyroidism.

Figure 3.

Multidimensional representation of the normal range of parathyroid hormone (PTH) levels in healthy normal individuals and disease subtypes of primary hyperparathyroidism (1°HPT) in a surgical cohort with confirmed parathyroid disease.