1.       Introduction

The present article proposes inverse analysis of clinical test trial which was provided in order to assess the safety, tolerability and glucose-lowering effect of the Oshadi oral insulin - Oshadi Icp - in Type I diabetes patients. 

Inverse Analysis can find hidden phenomena that are not easily or may be impossible to observe.

The analysis of any test trial must take into account the existence of non-measured parameters, which cannot be included in the database or inaccuracy of the calculations of the measured values. 

Randomized Controlled Trials (RCTs) are considered the gold standard approach for estimating the effects of treatments, interventions, and exposures on outcomes. RCT allocation ensures that the treatment status will not be confounded with either measured or unmeasured values and will be only estimated by comparing outcomes directly to the baseline characteristic differences between treated and untreated subjects [1-3]. 

"There is a growing interest in using observational (or nonrandomized) studies to estimate the effects of treatments on outcomes. In observational studies, treatment selection is often influenced by subject characteristics. As a result, baseline characteristics of treated subjects often differ systematically from those of untreated subjects. Therefore, one must account for systematic differences in baseline characteristics between treated and untreated subjects when estimating the effect of treatment on outcomes. Historically, applied researchers have relied on the use of regression adjustment to account for differences in measured baseline characteristics between treated and untreated subjects. Recently, there has been increasing interest in methods based on the propensity score to reduce or eliminate the effects of confounding when using observational data. Examples of recent use of these methods include assessing the effects of kindergarten retention on children’s social-emotional development (Hong & Yu, 2008), the effectiveness of Alcoholics Anonymous (Ye & Kaskutas, 2009), the effects of small school size on mathematics achievement (Wyse, Keesler, & Schneider, 2008), and the effect of teenage alcohol use on education attainment (Staff, Patrick, Loken, & Maggs, 2008)"[3].

Such situations are well known for test trials of aggressive intervention; however Inverse Analysis is more useful for chronic diseases and the relatively soft “physiologically applicable” regime of treatment. The standard statistical analysis of the treatment may lead to errors of the first or second kind. The uncertainties and missing data create problems which cannot be solved by classic statistical methods with different regression models including neural networks [1,2,4,5]. Such problems may be solved by the use of modern inverse analysis only. 

There are uncertainties which are observed in physics (Heisenberg uncertainty), in mathematics (Goedel's theorem), in logics (Frege, Bertrand Russell, Whitehead A.N. [1,6]), in biology and in medicine [1,2,4] which cannot provide exact measurements.

All physiological measurement data are always inexact and incomplete. It is a truism, which always has to been taken into account in data analysis. It means that unstable or "ill-posed" problems are unavoidable. 

The standard deductive analysis method in such cases may cause a principal mistake due to algorithmic or "deterministic" direct problems. Inverse analysis or induction is more challenging, however more appropriate in such situations. 

Interaction and relationships between statistics, direct and inverse analysis may be easily explained by the following: 

 1. Forward Problem: 

- Predictions

 - Stimulations

 - Need: Mathematics and computing.

 2. Inverse Problem:

 - Parameter estimation

 - Need: Statistics 

The Inverse Analysis is more challenging for clinical test trials as a rule due to the following: 

·                     Possibility of the problem’s identification for complex mathematical models

·                     Usage of high-dimensional parameter space

·                     Capacity of the analysis at model structure uncertainty and identification

·                     Capacity of analysis at variability of some parameters

·                     Usage of the sparse data

·                     Possibility of the model evaluation and diagnostics 

We used inverse analysis for clinical test trials because it is single way to describe the quantitative and transitional biological processes [7-13]. Any organism is an open complex nonlinear system which demonstrates dynamic response to any change of the external conditions of treatment. Such analysis provides a more exact interpretation of the experimental data, which was produced by a small group of patients with natural limitations of checked parameters.

Inverse analysis allows for processing with a vast amount of complex data and provides a better prediction and targeting analysis for a drug than routine statistic deductive analysis [2, 4, 5, 7-13]. 

The problem was being written as:

Where:

 g is measurable BGL

 A is injected or oral insulin

 is body response function 

Determination of the body response function may be written as:

It allows estimate drug bioavailability and efficacy which cannot be observed and estimated by standard deductive procedure due to complexity and variability of the physiological subjects. All data was described and analyzed by this function

2.       Research Design and Methods 

This study employed a single center, double blind, randomized, placebo-controlled, crossover design. The study included two sessions of three consecutive days of a multiple-dose administration of a fixed dose of Oshadi Icp or placebo, with a washout period of 12 days. During those days’ patients were administered a reduced dose (half insulin dose compared to their routine use) of injected long and rapid acting insulin during both sessions. Patients were provided with rescue insulin when blood glucose exceeded a pre-defined level. Subjects were provided with identical low carb diets and maintained the same physical activity level during both sessions. Ten type I diabetic patients were recruited to the study. Glucose level was monitored by a Continue Glucose Monitoring System in addition to finger prick capillary glucose concentrations test. Mean glucose levels and Area Under the Curve (AUC) in both sessions were analyzed and compared. In addition, the injected insulin doses, in matching days of each session, were compared. 

3.       Results 

Safety: No adverse events and no clinically relevant changes in vital signs, electrocardiograms, or in standard safety laboratory parameters were observed throughout the study.

Episodes of low glucose: Although patients were administrated with a half routine dose of injected insulin, 4 cases of low glucose concentration (<80mg/dL, measured by meter, 2 in the hypoglycemic range ≤70mg/dL) were detected during the study. All cases occurred during the Oshadi Icp administration sessions. 

Efficacy: Mean rapid acting insulin dose, on the third day of the session, was significantly lower during the Oshadi administration session, compared to the placebo. Patients were administrated with 25% lower doses of rapid acting insulin during the third day of the Oshadi session, compared to the placebo. 

By the third administration day, study results demonstrated that the Oshadi Icp session exhibits significantly lower Glucose Concentration (GC) values at all parameters that were analyzed (mean GC and AUC values) compared to the placebo. This lower glucose concentration was statistically significant although patients were administrated with 25% lower doses of rapid acting insulin during the day, and glucose concentrations adjusted to insulin amounts.

4.       Conclusions of the Study 

This study demonstrated the safety and the glucose lowering effect of the Oshadi Icp formulation. This study further elucidates the clinical potential and beneficial effect of the Oshadi Icp formulation for type I diabetic patients. 

The inverse analysis of the test trial results was performed for a more detailed analysis of the results and for examination of the efficacy of inverse analysis in interpretation and understanding clinical test trial results.

The first experiment includes comparative estimation of the reliability and accuracy of Blood Glucose Level (BGL) measurement by sensor and standard invasive finger capillary blood strips. This experiment demonstrated the equivalent quality of these measurements. This method used three days of automatic sensor data for the inverse analysis of injected and oral insulin effect on BGL. 

The correspondence of the calculated and observed data and reliability of prediction may be used for checking the drug effect.

 The forward problem may be written as: 

Where:

 g is measurable BGL

 A is injected or oral insulin

 f is body response function 

The inverse problem is a determination of the body response function and may be written in the common case as: 

We used this specific method of analysis, which was developed by Mavrodiev and successfully used for prediction, discovery, and description of 4 quarks, characteristics of nuclear particles interactions [14-18], problems of ecology [19], earthquakes [20-23].

The essence of such analysis may be described by the following: Expt(X) = Th(A,X); where X is a vector of experiment’s variables, Th(A,X) is the unknown function (model), which describes the experimental data with some errors and A is the solution vector of the over-determinate algebraic system. 

Graphical results of the inverse analysis are shown in the Appendix, which contains the BGL - time function and relative impact of the injected and oral insulin for each patient during both sessions (placebo and oral insulin). 

5.       Conclusion 

1. The inverse analysis of the ICP clinical test trial allowed the detection and estimation of the relative effect of the injected and oral drug in spite of very limited data.
2. This analysis demonstrates the observed BGL curve “peaks” resulting from the treatment regime including oral formulations.
3. This analysis demonstrates the transition process (adaptation) of patients to decreased insulin dosage (placebo) as well as to the OSHADI insulin uptake.
4. Careful solution allows BGL prediction during for next 24 hours at a minimum.
5. The inverse analysis provides significant refining of physiology, of the disease and treatment understanding, which is necessary for treatment improvement. 

Figure 1: represents the mean glucose level (±STDEV) over daytime (7:00-24:00) during the Oshadi and Placebo administration on the third administration day.

Figure 2: Mean glucose level (±STDEV) over daytime (7:00-24:00) during Oshadi and Placebo administration on the third administration day. The black dotted line indicates GC of 180mg/dL.

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