For the total pool of CKD patients in this study, analysis of the claims data revealed that 435 patients had at least one HCH (i.e., HCH = 1) month. The remaining 453 patients had no HCH during the 13 study-months (HCH = 0).

The average annual payment per patient for the group designated non-HCH (outcome 0) was $3,167 with a range of $264 to $17,197. The average monthly payment per patient in this group was $313.

In contrast, the HCH (outcome 1) group had average annual payments of $35,892 with a range of $4,276 to $314,533. Their average monthly per patient payment was $3,136.

Figure 1 is a stacked histogram demonstrating the average yearly payments per patient. Payments for hospital only services are shown in light gray, and payments for other medical services shown in black for both the HCH and non-HCH groups. In the HCH group, payments for hospital only services averaged $31,242 per patient with a range of $3,068 to $307,906. Other medical services for those same patients had average annual payments per patient of $4,671 with a range of $55 to $25,153.

On the other hand in the non-HCH (outcome 0) group, payments for hospital only services averaged $830 per patient with a range of $0 to $5,865. For other medical services, that average total payment per patient was $2,652 with a range of $264 to $16,572.

For the 267 patients with repeated PTH and serum phosphate testing, logistic regression analysis demonstrated a significant association between increasing PTH levels and HCH at p < 0.005. The Hosmer-Lemeshow Goodness-of-Fit test p-value was calculated at 0.06 with 66.5% concordant pairs between the response variable and the predicted probabilities.

For those variables associated in the literature with mineral metabolism disorders (age, PTH, phosphorus, bicarbonate, albumin, potassium, calcium, sodium, alkaline phosphatase, eGFR) their overall p-value for correlation with HCH was significant at p < 0.005, nonetheless, a number of variables had p-values that were not significant. After a step-wise elimination of the least significant variable, the regression calculation for the most parsimonious model demonstrated that PTH, phosphorus and albumin had significance at p < 0.005 with a Chi-Square Goodness of Fit test that was not significant (p = 0.83). In addition, there was an association of 74.3% concordant pairs between the response variables and predicted probabilities.

Using the calculated regression coefficients for the linear predictor's constant and PTH, phosphate, and albumin coefficients, we calculated a probability curve for HCH as a function of the linear predictor, using the following formula for probability of HCH given e^{lp}/(1+e^{lp}), where

\mathsf{\text{lp}}=-\mathsf{\text{1}}.\mathsf{\text{21}}+0.0\mathsf{\text{3}}*\mathsf{\text{PTHz}}-\mathsf{\text{score}}+0.\mathsf{\text{36}}*\mathsf{\text{PO4z}}-\mathsf{\text{score}}-0.\mathsf{\text{54}}*\mathsf{\text{albuminz}}-\mathsf{\text{score}}.

By calculating e^{lp}/(1+e^{lp}) for each patient and plotting versus the linear predictor (lp) we produced the curve shown in Figure 2.

The probability for HCH increased sharply to 50% as the linear predictor for serum PTH, phosphorous and albumin increased from 0.0 to 1.0. With an increase of the linear predictor to 2.0, the probability for HCH rose to 65%. As the linear predictor increased to 4.0, the probability for HCH reached 80%. And as the linear predictor doubled from 4.0 to 8.0, the probability of HCH increased to 90%.

In order to tabulate the impact of individual variables on the outcome of HCH, we calculated individual probability curves for PTH, phosphorus and albumin. By holding each of the non-selected variables at Z-score = 0, we recalculated logistic regression values and subsequent probability values. For Z-scores of PTH at 20, 40 and 70, the probability of HCH was 34%, 50% and 72% respectfully. For Z-scores of phosphorus at 2, 4, 6, the probability of HCH was 36%, 55%, and 70% respectively. For Z-scores of albumin at -2.0, -3.0 and -4.0, the probability of HCH was 42%, 55%, and 69% respectively.

Since the reference range for normal can vary in different laboratories, practicing clinicians can calculate the Z-scores for their patient's test values and substitute those values within the above formulas in order to calculate patient specific probabilities.

Since the data pool for renal patients with serum testing other than PTH and phosphorous was considerable larger (792), we calculated logistic regression coefficients for the variables of age, glucose, hemoglobin, bicarbonate, albumin, creatinine, BUN, potassium, calcium, sodium, alkaline phosphatase, ALT, leukocytes, eGFR and to achieve the most parsimonious model each variable with the least significant value was eliminated in a step wise fashion and the logistic regression recalculated. The final list consisted of age, hemoglobin, albumin, creatinine, ALT, and eGFR.

This calculation had p < 0.005 and a Chi-Square Goodness of Fit test by the Hosmer-Lemeshow method that was not significant at the 0.40 level. In addition, the association between the response variable and the predicted probabilities had 69.9% concordant pairs.

Calculation of a probability curve for the outcome of HCH over the study period versus the linear predictor for those variables is displayed in Figure 3.

Figure 3 illustrates the steep rise in probability for HCH to 67% as the linear predictor increased from 0.0 to 2.5. As the curve begins to plateau at a predictor value of 3.0 to 5.0, the probability of HCH increased from 67% to 82%. With an increase in predictor values from 10.0 to 17.0, the probability for HCH rose from 90% to 97%.

Figure 4 is the ROC area curve based on a sequence of cut-points on the linear predictor defined by the weighted Z scores of PTH, PO4, and albumin.

The Area under the Curve (AUC) shown in Figure 4 was calculated at 0.68. This value was compared to the AUC for a model based on the sum of the non-weighted Z scores for PTH, PO4 and albumin. The AUC for that curve was 0.64. Significance of the difference between these two curves revealed, as expected, a p-value > .05. In a similar manner, the AUC derived from the Z score of PTH alone, as well as for stages of CKD, both had areas of 0.64.

For the cohort of 792 patients, the AUC derived from the linear combination of predictor values for age, serum hemoglobin, albumin, creatinine, ALT and eGFR compared to the true positive occurrence for HCH had an area of 0.699.

In contrast, Figure 5 demonstrates the ROC curve comparing CKD stage to the true positive occurrence of HCH. That AUC was calculated at 0.585. The significance of the difference between the AUC shown in Figures #4 and #5 demonstrated significance at p < 0.005.

In a similar manner, The ROC area curves based on the sum of the non-weighted Z scores for hemoglobin, creatinine, albumin and ALT was calculated at 0.472, and when compared to AUC for Figure #4 demonstrated significance at p < 0.0005. Similarly, the AUC derived from comparison of the average eGFR to the true positive and true negative occurrence of HCH was calculated at 0.414 and when compared to Figure #4 demonstrated a significance at p < 0.0005.

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