Should non-cardiovascular mortality be considered in the SCORE model? Findings from the Prevention of Renal and Vascular End-stage Disease (PREVEND) cohort

Abstract

Competing non-cardiovascular related deaths were not accounted for in the Systematic COronary Risk Evaluation (SCORE) model. In this study we assessed the impact of non-cardiovascular related deaths on the prognostic performance and yield of the SCORE model. 5,752 participants from the Prevention of Renal and Vascular End stage Disease cohort aged 40 years and older who were free of atherosclerotic cardiovascular disease (CVD) at baseline were included. A cause-specific hazards (CSH) CVD-related mortality prediction model that accounted for non-CVD-related deaths was developed. The prognostic performance of this model was then compared with a refitted SCORE model. During a median follow-up period of 12.5 years, 139 CVD and 495 non-CVD-related deaths were reported. Discriminatory performance was comparable between the models (C-index = 0.64). The models showed good calibration although the CSH model underestimated risk in the highest decile while the refitted SCORE model showed overestimation. The CSH model classified more non-events into the low risk group compared to the refitted SCORE model (n = 51), yet it was accompanied by a misclassification of six events into the low risk group. The refitted SCORE model classified more individuals as high risk. However, the potential overtreatment that may result from utilizing the refitted SCORE model, when compared with the CSH model, still falls within acceptable limits. Our findings do not support the incorporation of non-cardiovascular mortality into the estimation of total cardiovascular risk in the SCORE model.

Appendices

Appendix 1

See Fig. 4.

Fig. 4

Cumulative incidence functions of CVD (solid line) and non-CVD (dotted line) related mortality among individuals in the PREVEND cohort aged 40 years and older and free of CVD at baseline

Appendix 2: Estimation of 10-year absolute risk of CVD-related mortality based on the refitted SCORE model

• Step 1 Sex-stratified cause-specific proportional hazards Weibull models were fit for CHD and atherosclerotic non-CHD related deaths using person’s age as time-scale. For a cause of failure k, the models take the form:

  $$\lambda_{k} (age;\,p,\alpha ,\beta ,Z) = (p_{k} /\alpha_{k} )(age/\alpha_{k} )^{p} k^{ - 1} \exp (\beta_{k} Z),\quad K = 1,2$$

  where λ _k is the cause-specific hazard function for kth cause of failure, β _k represents vector of regression coefficients of each risk factor for kth cause of failure and Z represents a person’s covariate value on the respective risk factor. P and α are sex-specific shape and scale parameters of the baseline hazard function for each cause of failure. Estimates of regression coefficients, β, and parameters of the baseline hazard functions, P and α, associated with these causes of failure are presented in the results (Table 2).

• Step 2 Estimation of survival functions for CHD and atherosclerotic non-CHD related mortality

  $$S_{k} (age) = exp( - \varLambda_{k} (age)),\quad K = 1,2$$

  where, $\varLambda_{k} ({\text{age}}) = \exp (\beta_{k} Z)*(({\text{age}})/\alpha_{k} )^{p} k)$

• Step 3 Estimation of 10-year survival probabilities for CHD and atherosclerotic non-CHD related deaths

  Individual 10-year survival probability for each cause of failure, S _k10 , was estimated from the survival functions in step 2 as a conditional probability of surviving up to age + 10 years given that the person survives up to age.

  $$S_{k10} (age) = S_{k} (age + 10)/S_{k} (age)$$

• Step 4 Estimation of 10-year risk of CVD-related mortality

  $$Risk_{CVD} = 1 - (exp( - ( - ln((S_{CHD10} ) + ( - ln(S_{non{\text{-}}CHD10} ))))))$$

Estimation of 10-year absolute risk of CVD-related mortality based on the CSH model

• Step 1 The same cause-specific proportional hazards Weibull models for CHD and atherosclerotic non-CHD-related mortality were used. In addition, a cause-specific hazards model which takes the form of equation in step 1 was fit for non-CVD-related mortality. The regression coefficients, β _k , and the parameters of the baseline hazard function for this cause-specific hazards function are presented in Table 2.

• Step 2 Estimation of overall survival function

  The cause-specific hazards functions of CHD, atherosclerotic non-CHD and non-CVD-related mortality were incorporated into the overall survival function, S(age), through;

  $$S (age )= exp\left( { - \sum\limits_{k = 1}^{k} {\varLambda _k(age)} } \right),\quad {\text{where}}\,{\text{k}} = 1, 2, 3$$

• Step 3 Estimation of 10-year absolute risks of CHD and non-CHD related deaths

  The absolute risks of CHD and atherosclerotic non-CHD related mortality were estimated as cumulative incidence of each outcome at W = age + 10 years given an individual is still a survivor at age A. The competing risk of non-CVD-related mortality was accounted for in this step as the cumulative incidence functions is determined by the cause-specific hazard functions of all the three causes of failure through the overall survival function S(age). In addition, this also accounts for the competing risk effect of atherosclerotic non-CHD related deaths on CHD-related death and vice versa.

  $$I_k(A < T \le A + W,D = K/T > A) = \frac{{\int_{A}^{A + W} {\lambda _k(s)S(s)d(s)} }}{S(A)},\quad {\text{where}}\,{\text{k}} = 1,2$$

• Step 4 Estimation of 10-year risk of CVD-related mortality

  $$Risk_{CVD} = I_{CHD} + I_{non{\text{-}}CHD}$$