Coefficient of failure: a methodology for examining longitudinal beta-cell function in Type 2 diabetes

Diabet Med. 2002 Jun;19(6):465-9. doi: 10.1046/j.1464-5491.2002.00718.x.


Aims: We describe a new method, the determination of the coefficient of failure, which allows the assessment of beta-cell failure from any index of glycaemia. Previous methods using glycaemic thresholds and calculating time-to-failure have systematic deficiencies relating to bias, reproducibility and statistical power. Analyses using threshold methodologies and conventional survival analysis have an intrinsic disadvantage in that they use categorical data and thus make no allowance for near-failure, or progression towards failure. In contrast, the coefficient of failure includes all data in the analysis and takes into account improvement of glycaemia as well as deterioration of glycaemia.

Methods: We describe the use of a 'coefficient of failure' defined as the slope of the least-squares regression line of a glycaemic index vs. time calculated for each individual patient on constant monotherapy. We exemplify the method using HbA1c levels from data from patients on chlorpropamide (n = 64) or glibenclamide (n = 65) monotherapy in the Oxford cohort of the UKPDS.

Results: Chlorpropamide-treated patients showed a mean coefficient of failure of 0.34 HbA(1c)%/year (0.44%/year sd) and glibenclamide-treated patients 0.50 HbA(1c)%/year (0.50%/year sd) (P = 0.046; unpaired two-tailed t-test). Kolmogorov-Smirnov testing demonstrated that the coefficients did not differ significantly from a normal distribution (chlorpropamide P = 0.12; glibenclamide P = 0.13).

Conclusions: The coefficient of failure gives an estimate of beta-cell failure using any index of glycaemia. The coefficient is not constrained by predetermined glycaemic thresholds for failure and it allows the rate of decline in beta-cell function to be determined on any therapy or combination of therapies.

MeSH terms

  • Chlorpropamide / therapeutic use
  • Diabetes Mellitus, Type 2 / drug therapy*
  • Diabetes Mellitus, Type 2 / physiopathology*
  • Female
  • Glyburide / therapeutic use
  • Glycated Hemoglobin A / metabolism
  • Humans
  • Hypoglycemic Agents / therapeutic use
  • Islets of Langerhans / metabolism*
  • Least-Squares Analysis
  • Longitudinal Studies
  • Male
  • Middle Aged
  • Predictive Value of Tests
  • Regression Analysis
  • Time Factors
  • Treatment Failure
  • Treatment Outcome


  • Glycated Hemoglobin A
  • Hypoglycemic Agents
  • Glyburide
  • Chlorpropamide