A method for checking regression models in survival analysis based on the risk score

Grønnesby, Jon Ketil; Borgan, Ørnulf

doi:10.1007/bf00127305

Cited by 186 publications

(148 citation statements)

References 14 publications

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“…19 Calibration is the agreement between the predicted risks and the observed risks of MACE and was tested with the calibration plot and Gronnesby and Borgan test. 22 For presentation and application of our model, we developed a score chart using previously described methods 23 and subsequently divided patients into 4 risk groups. Although cutoff points for primary cardiovascular risk estimation have been described in population-based studies, 24,25 no cutoff points are available for risk estimation of secondary cardiovascular events.…”

Section: Model Validation and Presentationmentioning

confidence: 99%

Clinical Prediction Rule to Estimate the Absolute 3-Year Risk of Major Cardiovascular Events After Carotid Endarterectomy

Lammeren

Catanzariti

Peelen

et al. 2012

Stroke

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Background and Purpose-Prognosis after carotid endarterectomy is mainly determined by the occurrence of major adverse cardiovascular events (MACEs). Optimal medical treatment to reduce risk is the mainstay of MACE prevention. The level of risk of MACE may determine the initiation and aggressiveness of medical treatment, yet a prediction rule to assess that absolute MACE risk after carotid endarterectomy is currently unavailable. Methods-The prediction model was developed in a consecutive cohort of 1138 patients who underwent carotid endarterectomy between 2002 and 2009. Primary end point was MACE and encompassed myocardial infarction, stroke, and cardiovascular death. Fourteen potential clinical predictors were entered into a Cox proportional hazard model. After backward stepwise regression, internal validation was conducted with bootstrapping techniques to correct for overfitting. To provide an easily applicable clinical tool, a score chart was constructed, dividing patients into 4 risk groups. Model performance was assessed in terms of discrimination, calibration, and risk stratification. Results-During a mean follow-up of 2.28 (Ϯ0.95) years, 148 events occurred, corresponding to a cumulative incidence of 13%. Clinical predictors in the final model were age, history of coronary or peripheral artery disease, smoking, systolic blood pressure, use of antihypertensive drugs, clinical presentation, presence of contralateral carotid stenosis, and serum creatinine levels. Discrimination of the final model, in terms of a C statistic, was 0.69 (0.64 -0.73) and calibration showed a good overall fit (Gronnesby and Borgan, Pϭ0.39). The observed incidence of MACE in the 4 risk groups was 6%, 9%, 19%, and 35%, respectively, indicating good overall risk stratification. Conclusions-The clinical prediction model for MACE in the first 3 years after carotid endarterectomy may be used to identify high-risk patients to help optimize medical treatment and risk factor management as part of secondary prevention to increase life expectancy free from MACE. Despite our success in stratifying risk among these patients, even the lowest stratum remains at high risk and all of these patients should receive maximal secondary preventive measures. (Stroke. 2012;43:1273-1278.)

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Section: Model Validation and Presentationmentioning

confidence: 99%

Clinical Prediction Rule to Estimate the Absolute 3-Year Risk of Major Cardiovascular Events After Carotid Endarterectomy

Lammeren

Catanzariti

Peelen

et al. 2012

Stroke

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“…One can perform more formal tests to assess normality (e.g., KolmogorovSmirnov, Cramér-von Mises, Anderson-Darling). Grønnesby and Borgan (1996) concluded that when β is one-dimensional, (3.7) only checks the coding of the covariate. However, when β is of higher dimension, W(z) cannot detect whether the effects of covariates vanish with time or not.…”

Section: Diagnostics Based On Martingale Residualsmentioning

confidence: 99%

“…However, when β is of higher dimension, W(z) cannot detect whether the effects of covariates vanish with time or not. Grønnesby and Borgan (1996) grouped the individuals after their linear predictions, i.e., replaced I(β…”

Section: Diagnostics Based On Martingale Residualsmentioning

confidence: 99%

Diagnostics for the Cox model

Xue

Schifano

2017

CSAM

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The most popular regression model for the analysis of time-to-event data is the Cox proportional hazards model. While the model specifies a parametric relationship between the hazard function and the predictor variables, there is no specification regarding the form of the baseline hazard function. A critical assumption of the Cox model, however, is the proportional hazards assumption: when the predictor variables do not vary over time, the hazard ratio comparing any two observations is constant with respect to time. Therefore, to perform credible estimation and inference, one must first assess whether the proportional hazards assumption is reasonable. As with other regression techniques, it is also essential to examine whether appropriate functional forms of the predictor variables have been used, and whether there are any outlying or influential observations. This article reviews diagnostic methods for assessing goodness-of-fit for the Cox proportional hazards model. We illustrate these methods with a case-study using available R functions, and provide complete R code for a simulated example as a supplement.

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“…28 Discrimination was assessed by Harrell c-statistic and the optimism-corrected c-statistic was obtained by 1000-fold bootstrap resampling.…”

Section: Assessment Of Model Performancementioning

confidence: 99%

Predicting the Effects of Blood Pressure–Lowering Treatment on Major Cardiovascular Events for Individual Patients With Type 2 Diabetes Mellitus

et al. 2015

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T ype 2 diabetes mellitus (T2DM) is a growing worldwide health problem, with an estimated 439 million people living with diabetes mellitus in 2030 1 . The lifelong incidence of vascular complications is extremely high, and >80% of patients with diabetes will die from a vascular cause.2 Blood pressure (BP) is strongly related to nonfatal vascular events, vascular, and all-cause mortality in patients with T2DM.3 The risk associated with BP already starts well below the BP level used to define hypertension, and BP-lowering agents have been shown to reduce vascular risk in patients with and without hypertension by an average of ≈15%.4-6 Yet, based on benefit and costs considerations, treatment with BP-lowering medication is only recommended according to guidelines if BP is >140/90 mm Hg. [7][8][9] This BP threshold serves as a marker to identify patients who potentially benefit from treatment.10 However, even above this threshold, individual patients vary greatly in the combinations Abstract-Blood pressure-lowering treatment reduces cardiovascular risk in patients with diabetes mellitus, but the effect varies between individuals. We sought to identify which patients benefit most from such treatment in a large clinical trial in type 2 diabetes mellitus. In Action in Diabetes and Vascular Disease: Preterax and Diamicron MR Controlled Evaluation (ADVANCE) participants (n=11 140), we estimated the individual patient 5-year absolute risk of major adverse cardiovascular events with and without treatment by perindopril-indapamide (4/1.25 mg). The difference between treated and untreated risk is the estimated individual patient's absolute risk reduction (ARR). Predictions were based on a Cox proportional hazards model inclusive of demographic and clinical characteristics together with the observed relative treatment effect. The group-level effect of selectively treating patients with an estimated ARR above a range of decision thresholds was compared with treating everyone or those with a blood pressure >140/90 mm Hg using net benefit analysis. In ADVANCE, there was wide variation in treatment effects across individual patients. According to the algorithm, 43% of patients had a large predicted 5-year ARR of ≥1% (number-needed-to-treat [NNT 5 ] ≤100) and 40% had an intermediate predicted ARR of 0.5% to 1% (NNT 5 =100-`200). The proportion of patients with a small ARR of ≤0.5% (NNT 5 ≥200) was 17%. Provided that one is prepared to treat at most 200 patients for 5 years to prevent 1 adverse outcome, prediction-based treatment yielded the highest net benefit. In conclusion, a multivariable treatment algorithm can identify those individuals who benefit most from blood pressure-lowering therapy in terms of ARR of major adverse cardiovascular events and may be used to guide treatment decisions in individual patients with diabetes.

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A method for checking regression models in survival analysis based on the risk score

Cited by 186 publications

References 14 publications

Clinical Prediction Rule to Estimate the Absolute 3-Year Risk of Major Cardiovascular Events After Carotid Endarterectomy

Clinical Prediction Rule to Estimate the Absolute 3-Year Risk of Major Cardiovascular Events After Carotid Endarterectomy

Diagnostics for the Cox model

Predicting the Effects of Blood Pressure–Lowering Treatment on Major Cardiovascular Events for Individual Patients With Type 2 Diabetes Mellitus

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