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A frailty model is a random effects model for time variables, where the random effect (the frailty) has a multiplicative effect on the hazard. It can be used for univariate (independent) failure times, i.e. to describe the influence of unobserved covariates in a proportional hazards model. More interesting, however, is to consider multivariate (dependent) failure times generated as conditionally independent times given the frailty. This approach can be used both for survival times for individuals, like twins or family members, and for repeated events for the same individual. The standard assumption is to use a gamma distribution for the frailty, but this is a restriction that implies that the dependence is most important for late events. More generally, the distribution can be stable, inverse Gaussian, or follow a power variance function exponential family. Theoretically, large differences are seen between the choices. In practice, using the largest model makes it possible to allow for more general dependence structures, without making the formulas too complicated.

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In the participating centers with a multidisciplinary team, only one third of the patients had an HbA1c level of < 8%.

OBJECTIVETo find a simple definition of partial remission in type 1 diabetes that reflects both residual β-cell function and efficacy of insulin treatment.RESEARCH DESIGN AND METHODSA total of 275 patients aged <16 years were followed from onset of type 1 diabetes. After 1, 6, and 12 months, stimulated C-peptide during a challenge was used as a measure of residual β-cell function.RESULTSBy multiple regression analysis, a negative association between stimulated C-peptide and A1C (regression coefficient −0.21, P < 0.001) and insulin dose (−0.94, P < 0.001) was shown. These results suggested the definition of an insulin dose–adjusted A1C (IDAA1C) as A1C (percent) + [4 × insulin dose (units per kilogram per 24 h)]. A calculated IDAA1C ≤9 corresponding to a predicted stimulated C-peptide >300 pmol/l was used to define partial remission. The IDAA1C ≤9 had a significantly higher agreement (P < 0.001) with residual β-cell function than use of a definition of A1C ≤7.5%. Between 6 and 12 months after diagnosis, for IDAA1C ≤9 only 1 patient entered partial remission and 61 patients ended partial remission, for A1C ≤7.5% 15 patients entered partial remission and 53 ended, for a definition of insulin dose ≤0.5 units · kg−1 · 24 h−1 5 patients entered partial remission and 66 ended, and for stimulated C-peptide (>300 pmol/l) 9 patients entered partial remission and 49 ended. IDAA1C at 6 months has good predictive power for stimulated C-peptide concentrations after both 6 and 12 months.CONCLUSIONSA new definition of partial remission is proposed, including both glycemic control and insulin dose. It reflects residual β-cell function and has better stability compared with the conventional definitions.