# Re-implementing a cox-proportional hazard model (Suita Score) from the coefficients provided in a paper

I am trying to implement a model (Suita Score) shared in this paper:

https://www.jstage.jst.go.jp/article/jat/21/8/21_19356/_pdf/-char/en

for predicting the 10-year probability of CHD they given the probability function:

P = 1 - S(t) ^ exp(X, M) f(X, M) = β1 * (X1 - M1) + ... + βn * (Xn - Mn)

Where:

S(t) = survival rate for the mean of values of risk factors in the Suita cohort βs = the regression coefficients Xs = the observed risk factor values Ms = the mean risk factor values in the Suita cohort

In the tables of data provided they give:

• The mean values for all risk factors in their study (Table 1)
• The cox regression model coefficients (Table 4)

They also state:

"The beta coefficients corresponding to the Cox model were multiplied 10 times for categorical covariates and were rounded. For the age category, the midpoint of each category was multiplied by the β coefficients in Table 4, and then multiplied 10 times. We added all these values corresponding to each individual risk, divided the number by 10, and then the corresponding probability of CHD was calculated from the equation: P = 1 - S(t)^exp((sum of points)/10) where S(t) is the baseline survival function of the Suita cohort."

There are a few things confusing me about re-implementing this:

1. How to I calculate the baseline survival function?
2. Why all the multiplication and division by 10?
3. What are they doing to the age category and why?

Any replies much appreciated even if you tell me it is not possible to re-implement from this information.

3. Although the Cox models included age as a continuous predictor linearly associated with log hazard, it seems that the authors chose to categorize age for their clinical Suita scoring system. That's not generally a good idea, although at least the authors seem to have done the categorization after rather than before developing the Cox model. They might have chosen the score for age as the contribution from age to the linear predictor at the midpoint of each age category, although that wasn't clear on a quick look at the paper. That leads to massive step changes in scores at age cutoffs. Does it really make sense, for example, that reaching your 46th birthday instantaneously increases your "TC Suita score" by 9 points? (See Table 5.)