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Table 3 Example calculation of an individual 10-year risk of all-cause mortality

From: Development and validation of prediction model to estimate 10-year risk of all-cause mortality using modern statistical learning methods: a large population-based cohort study and external validation

Patient description:

An individual is a male aged 75-years old, smoker who comes from a middle-class social-economic status. He has at least 1 limiting illness and previously had a cancer or a malignant tumour (excluding minor skin cancers) but has an intact memory. He stated that he never had a chance to do things that he never experienced before. The patient reports difficulties doing work around house and garden and struggles to walk 100 yards. Overall, he describes his health as poor; though he never experienced stroke and chronic lung disease.

Estimated Beta coefficient × variable for this person:

Using the nomogram (Fig. 1) and information from Table 2, we can estimate this patient’s probability to die in the following 10 years by adding points assigned in the nomogram to each factor in the model. Thus, in this example, the patient would have a total point score of 2 point (male gender) +  100 points (aged 75 years old) +  4 points (being a smoker) +  0 points (middle-class social-economic status) +  3 points (having at least one limiting illness) +  7 points (having previously had a cancer or a malignant tumour) +  0 points (maximum score for memory) +  10 points (never had a chance to do things that he never experienced before) +  5 points (difficulties doing work around house and garden) +  14 points (struggling to walk 100 yards) +  19 points (describing health as poor) +  0 points (having never experienced stroke) +  0 points (no history of chronic lung disease) = 164. This corresponds to a normalized prognostic index of 1.69 (linear predictor line) for all-cause mortality, meaning that the participant has a probability to die in the following 10 years in the range 35.68–62.48%.

A more precise way to compute the probabilities of death during the next 10 years for this patient is to use the following formula, as presented in Additional file 14, for absolute risk predictions at time t:

\( 1-{S}_0{(t)}^{\exp \left({b}_1{x}_1+{b}_2{x}_2+{b}_3{x}_3+\dots \right)} \),

where S0(t) is the baseline survival probability at time t, xi are the variables and bi are the log hazard ratios, i.e. the Cox-Lasso estimated coefficients (Table 2).

Therefore, given S0(t) = 0.9985, for the same individual as above, the probability of death during the next 10 years will be precisely 57.19%:

1 − 0.9985exp(0.0695 × 75 + 0.1787 × 1 − 0.0116 × 0 + 0.0532 × 1 + 0.0435 × 0 + 0.0316 × 1 + 0.0686 × 1 + 0.0509 × 0 + 0.0861 × 1 + 0.1198 × 1 + 0.2498 × 1 + 0.3369 × 1 + 0.3158 × 0) = 0.5719 = 57.19%