Development of Prognostic Criteria of Kidney Transplantation Complications Based on Open-Circuit Potential Moniroting Using Probit Analysis
It has been previously shown that an electrochemical measurement of open-circuit potential (OCP) at the platinum electrode in blood plasma or blood serum is a reflection of the redox state of these biological media , and the final OCP value after 15 min of measurement, corresponding to near-equilibrium conditions, was used as the characteristic OCP value for further analysis, termed “redox potential” (RP) in relevant medical literature. Moreover, changes in the time dependence of the measured RP correlate with clinically diagnosed transplant dysfunction, with RP changes often preceding clinical symptoms by one or more days . Thus, in order to develop prognostic criteria to predict the probability of posttransplant complications, the above method of RP measurement was used, and statistical analysis of RP values was performed.
RP measurements were performed in blood plasma against a silver/silver chloride reference electrode using an IPC-Compact potentiostat (NPO “Volta”). The electrode was pre-treated prior to each measurement according to the previously developed method . A total of 59 kidney transplant patients took part in the study (42 male and 17 female) in the early postoperative recovery period (20-35 days). Statistical analysis was performed using the STATISTICA 6.0 (StatSoft), EViews 8.0 (IHS Global Inc.) and IDE Microsoft Visual Basic 6.0 software.
Patients who took part in the study can be categorized into two groups, according to their recovery dynamics: 35 patients had unremarkable recoveries, without any complications, while 24 patients experienced complications. A total of 967 analyses was performed.
Statistical analysis performed on the RP values and clinical/laboratory data has yielded average values of complication probability depending on RP, shown in Fig. 1: an RP more positive than +20 mV corresponds to a 50 percent probability of posttransplant complications, while an RP of +50 mV or higher, to a 75% probability.
Subsequently, an evaluation of the probability of postoperative complications depending on the time elapsed since transplantation was performed.
Since the presence or absence of complications is a qualitative characteristic, the method of probit analysis  was used for the evaluation of complication probability. This method is based on the interpretation of the standard normal distribution function (Ф) as the conditional probability of the event at the given value of its argument; the latter is derived from a linear transformation of the observed value (RP in this case). Then the probability (P) of incidence of a complication can be evaluated from the following equation:
P = Ф(α + β∙E)
where α, β are coefficients determined by the maximum-likelihood estimation (MLE) method and E is the RP value.
The correlation of the probit function curve with a sampling of data points was evaluated using the χ2 test.
The use of probit analysis allows for the evaluation of transplant complication probability depending on the measured RP for a specific day of patient postoperative recovery during the hospital stay (Fig. 2).
 Khubutiya M.Sh., Evseev A.K., Kolesnikov V.A., et al. Russ J Electrochem 2010 46(5): 537-541
 Khubutiya M.Sh., Goldin M.M., Evseev A.V., et al. ECS Trans. 2011 35(35): 45-50