Competing risks analysis of the Finnish diabetes prevention study
Moustafa M. A. Ibrahim (1,2,3), Vanessa D. de Mello (4), Matti Uusitupa (4), Jaakko Tuomilehto (5), Jaana Lindstr÷m (5), Maria C. Kjellsson (1), Mats O. Karlsson (1)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Sweden (2) Department of Pharmacy Practice, Helwan University, Cairo, Egypt (3) Pharmetheus, Uppsala, Sweden (4) Institute of Public Health and Clinical Nutrition, School of Medicine, University of Eastern Finland, Kuopio, Finland (5) Department of Chronic Disease Prevention, National Institute for Health and Welfare, Helsinki, Finland
Clinical studies are often performed to assess a certain primary endpoint or event (e.g. manifestation of diabetes), in the presence of other competing risk events , i.e. the occurrence of an event that prevents the primary event from being observed, e.g. dropout. If these competing risk events are dependent on the primary event e.g. if dropout of a patient reflects a greater risk of diabetes manifestation, then predicting the primary event in a patient with the competing risk event is impossible. Marginal survival functions, when risks are dependent, are inestimable from the data and Kaplan-Meier estimators or standard survival models in such case result in profoundly biased estimates of the cumulative probabilities of the competing risks. When treatment groups are compared, the relative differences between treatment groups may be biased [2,3]. These are consequences of the underlying assumption that censoring is independent of the primary event and that the survival probability is constant over the occurrence of competing events. Also, if subjects are observed only at finite clinical visits, i.e. interval-censored data, there is an additional uncertainty of whether the patients experienced one or more of the competing events between the last event-free visit and the diagnostic visit. In this work, we considered model-based analysis of competing and semi-competing risks to describe data from the Finnish diabetes prevention study (FDPS) . Afterward, we explored potential covariates on the different risks and investigated the predictiveness of various assessment methods of insulin sensitivity (SI) for the onset of development of type 2 diabetes (T2D).
The FDPS is a randomized controlled study carried out in Finland 1993-2001 with follow-up until 2010. Data was collected from 522 overweight middle-aged subjects with impaired glucose tolerance, randomly assigned to control and lifestyle intervention. The aim of the FDPS was to investigate the effect of lifestyle changes among subjects with impaired glucose tolerance on the development of T2D. Oral glucose tolerance test (OGTT) for all subjects was performed yearly for assessment of subjects’ clinical status, and subjects with 2 hr postprandial glucose concentrations > 200 mg/dL were diagnosed with T2D and excluded from the study. From the yearly OGTT, SI could be measured by nine surrogate methods .
During the FDPS, subjects failed by one of the three possible and mutually exclusive events: developing T2D, dropping out (DO), or death. Here, DO refer to stopping treatment, and does not mean lost to follow up as all subjects were followed until 2010. Once the subject had failed, his follow-up was started. During the follow-up, subjects cannot drop out and T2D cannot censor death (semi-competing process). There are five states that subjects could experience during the study and its follow-up: healthy (state 1), T2D (state 2), DO (state 3), DO-T2D (state 4; subjects developing T2D after DO), and death (state 5). All subjects were healthy at enrolment (state 1), and during the study, they could stay healthy (state 1), develop T2D (state 2), drop out (state 3), or die (state 5). The study ended once a subject moved from state 1 to any other state. After the study (during follow-up), subjects with T2D could stay in state 2 or die (state 5), subjects who dropped out could remain healthy in state 3, develop T2D (state 4) or die (state 5) and subjects who dropped out and then developed T2D could stay in state 4 or die (state 5). These restrictions defined the nature of the different risks and the model’s system of differential equations. Different hazard distributions and predictors were investigated for the transition intensities (λij) from state i to state j. We tested three hypotheses: the risk of death for healthy subjects is independent of DO (i.e. λ15=λ35), the risk of death for subjects with T2D is independent of DO (i.e. λ25=λ45) and dropout out is non-informative for developing T2D (i.e. λ12=λ34). Yearly measured covariates including the nine indices for measurement of SI were tested one by one prospectively on the different λs.
The model could jointly describe the semi-competing terminal process of death and the two competing non-terminal processes of developing T2D and DO while accounting for the interval-censoring. The model was non-stationary in λ12 and λ15 and homogenous in λ13 and λ34. Transition intensities to death were indeed independent of DO and were described by scaling Gompertz-Makeham formula estimated from the Swedish population, to adapt for the different death incidences observed in the FDPS data. The estimated scaling parameters reflected a 20% higher risk of death among subjects with T2D than others, that was not significant when the data was analyzed by the standard survival cox models . The model showed that informative DO is present and subjects are more likely to drop out if they were healthier and thus, after DO they were at ~ 3.5 lower risk for developing T2D than subjects who stayed in state 1. The model identified age and sex as predictors on dying, intervention and baseline BMI on λ13, and intervention, baseline BMI, time-dependent HbA1c and time-dependent SI measurements to be the significant covariates on λ12. QUICKI, HOMA and Avignon indices as time-varying measurements of SI surpassed the other investigated indices, while baseline QUICKI and HOMA were the best to predict the future onset of T2D. The effects of the significant covariates on the competing risks at different combinations can be easily assessed by plugging the desired covariates’ values in the model’s system of equations. Visual predictive checks of the model stratified by subjects’ treatment group showed a nice agreement between the simulated and observed proportion of subjects in the different states at different times.
We successfully developed a multi-state model for competing risks analysis of data from the FDPS. The model described the data, characterized mechanisms leading to incomplete observations and accounted for the occurrence probability of the non-terminal processes in the interval between visits as only death dates can be retrieved exactly. The model allowed simultaneous estimation of covariate effects on all λs. Though with a different methodology, we successfully identified the same covariates recently used for stratifying patients with T2D into subgroups with differing disease progression and risk of diabetic complications . Finally, our model is naturally extendable for PK/PD joint modeling of drugs, biomarkers and competing clinical outcomes. This framework, with suitable adaptions, may find widespread applicability for competing risks interval-censored longitudinal data instead of the currently used misspecififed standard survival models.
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