Coefficient of failure to assess therapy success

Original article:
Coefficient of failure: a methodology for examining longitudinal b-cell function in Type 2 diabetes. Wallace TM, Matthews DR. Diabetic Med 2002; 19: 465–9.

Summary
It is well known that sulfonylureas lose their effectiveness with time. This loss of effect can be individually ascertained by monitoring the progressive increase in blood glucose (and/or HbA1c) levels. The gradual blood glucose increase reflects the progressive failure of the b-cells to provide enough insulin to maintain euglycemia. As shown in this paper by Wallace and Matthews, there are important differences among subjects. In some (around 3%) type 2 diabetic patients, the decline in b-cell function accounts for a rapid increase in HbA1c levels (1.5% per year). At the other extreme, some patients (around 15–20%) have very little loss of b-cell function, as evidenced by their long-term stable HbA1c levels. Interestingly, the progressive increase in blood glucose (i.e. decline in b-cell function) differs with different sulfonylurea compounds. In chlorpropamide-treated patients, HbA1c increases at a mean rate of 0.34% per year (95% CI 0.23–0.44%), while for glibenclamide the mean rate of increase is 0.50% per year (95% CI 0.38–0.62%). The difference between the treatments is statistically significant. By contrast, when the long-term efficacy of both compounds is compared using other mathematical methods (for instance Kaplan-Meier estimates for failure rates), no statistically significant differences are observed.
Based on this, Wallace and Matthews propose a simple and practical method to assess loss of functionality with time, provided that there is a measurable parameter that changes as function declines. In this case, the functionality assessed is b-cell function and the measured parameter is blood glucose (or its integrated measure: HbA1c level). The pathophysiological basis of this approach is clear. In steady-state conditions (i.e. basal state), blood glucose levels increase as insulin concentration at the site of action decreases, provided that tissue response to insulin (insulin resistance) remains unchanged. The insulin concentration at the site of action depends on circulating levels of the hormone, which reflect the changes in insulin secretion and therefore b-cell function. Even in cases of moderate or severe insulin resistance, blood glucose rises significantly only if there is a concomitant ‘relative’ b-cell failure. Consequently, in steady-state conditions (basal state), the progressive blood glucose increase is a clear expression of the gradual decline in b-cell function. In other words, the rate of blood glucose increase occurring with time in type 2 diabetic patients (or even in non-diabetic subjects) can be considered an index, or coefficient, of b-cell failure: the higher the rate of increase in blood glucose (in mg/dl per year) or HbA1c (in % per year), the faster the relative decline of b-cell function. For each individual patient, the coefficient of failure is calculated as the slope of the least-square regression line of a glycemic index vs. time. This method presents several advantages: any index of glycemia can be used for calculation; it is not constrained by predetermined glycemic thresholds; it allows an update of information as new glycemic readings are incorporated in the regression; and it changes as b-cell function changes.

Comment
Physicians treating diabetic patients wish to know which treatment is going to be the most effective and for how long. Their choice is based on the available scientific evidence and on personal experience. Clearly not all treatments are equally effective, and even those that are, may differ in terms of persistence of effect. In addition, the specific response may vary from patient to patient and even between different time periods within the same patient. This is the case with sulfonylureas. Not all the sulfonylurea compounds are equally effective for the same time in each patient. Furthermore, their effects in terms of preservation of b-cell function may differ between patients and between compounds. The key is to make the best choice in terms of therapeutic efficacy, persistence of action and preservation of physiological function. In this article, the authors provide important clues of clinical interest.
Let us consider, for example, an initially healthy subject whose blood glucose levels, measured every 10 years from the age of 25 to 55 years, were 70, 94, 118 and 142 mg/dl. If, at the time of each measurement, the subject was free of intercurrent disease or physical stress, we may think that his ‘insulin action’ is deteriorating at a rate of 2.4 mg/dl basal blood glucose increase per year. This value may well correspond to a coefficient of failure of ‘insulin action’, practically expressed as an increase in glycemia per year. Instead of using basal blood glucose, we can also use an integrated value such as HbA1c. When the subject’s blood glucose reaches 142 mg/dl, treatment is given that effectively decreases basal blood glucose but thereafter it gradually begins to increase again. After several basal measurements, performed in similar physiological conditions, we can recalculate a new coefficient of failure, this time with regard to a specific treatment. We may even compare the coefficient of failure in different subjects or in the same subject with different treatments, provided that we have a sufficient number of reliable and comparable measurements over a sufficiently long period of time. The coefficient of failure is therefore a useful tool of clinical interest, for instance to assess long-term therapeutic success.
We have referred to ‘insulin action’, but it is known that ‘insulin action’ depends on both the insulin concentration at the site of action and the tissue response to insulin. As previously stated, a decrease in insulin concentration at the site of action in the presence of hyperglycemia indicates an absolute b-cell failure. Similarly, any decrease in tissue response to insulin (i.e. increase in insulin resistance) should be readily compensated by an increase in insulin concentration (i.e. secretion) unless the b-cell fails to produce this increase. In that case we have relative b-cell failure. Consequently, a coefficient of failure of ‘insulin action’ corresponds to a coefficient of failure of b-cell function, either absolute or relative.
Ideally, the blood glucose values considered for estimation of the coefficient of failure should be obtained in similar physiological and/or pathological conditions and measured using the same analytical method. In spite of these precautions, we cannot expect a linear increase in blood glucose: first, because the decline in b-cell function is not linear; second, because of the multiple physiological and pathological variables influencing b-cell function and blood glucose levels; and third, because of the unavoidable imprecision of the assay method. In these circumstances, the better fit for each individual can be obtained from the least-squares regression of glycemic index (basal blood glucose or HbA1c) vs. time, the slope of the line being the coefficient of failure described by Wallace and Matthews: the greater the slope, the greater the decline in b-cell function.
Most physiological functions (if not all) follow the theoretical pattern of change represented in Figure 1.

Fig. 1: Simplified theoretical pattern of change for most physiological functions with time.

Functional capacity initially increases until it attains a maximum and then it gradually declines. This functional loss is imperceptible until the so-called functional reserve is exhausted. At that moment, clinical manifestations of failure appear. In reality, the functional decline is not a regular process and it also differs among individuals and functions. In addition, many different pathological and physiological processes influence this functional decline. On the other hand, maximal functional capacity is a relative term and important differences may exist among individuals. Consequently, the pattern of change of most physiological functions, including b-cell function, is represented by a non-linear (and variable) declining line (Figure 2).

Fig. 2: Functional decline is a variable phenomenon intra- and inter-subjects.