如何计算c-index？求Fine Gray模型的Stata计算代码

Hey there! Let's break this down clearly—first covering what c-index is and how it works, then diving straight into the Stata code for Fine Gray models since you mentioned you already have R solutions sorted out.

一、c-index的基本计算逻辑 #

The c-index (concordance statistic) measures how well a survival model predicts the order of event times. Here's the core idea:

• For any pair of subjects, if the one with a higher predicted risk experiences the target event earlier, that's a concordant pair.
• If their event times are identical, it's a half-concordant pair.
• If the higher-risk subject has a later event time, that's a discordant pair.

The formula is straightforward:

c-index = (Number of concordant pairs + 0.5 * Number of half-concordant pairs) / Total number of comparable pairs

Comparable pairs are those where at least one subject experienced the target event (we exclude pairs where both are censored or had a competing event).

二、Fine Gray模型下的Stata实现 #

Stata doesn't have a built-in command for Fine Gray c-index, but we can build it using existing tools or custom code. Here are two reliable methods:

Method 1: Use stcompet + somersd (Fast for large datasets) #

First, install the stcompet package if you haven't already:

ssc install stcompet

Then follow these steps (adjust variables to match your dataset):

1. Fit your Fine Gray model:

* Define survival data: time = event time, status=1 is target event, status=2 is competing event
stset time, failure(status==1)
* Fit the Fine Gray model with covariates x1, x2
stcrreg x1 x2, compete(status==2)

2. Generate predicted cumulative incidence functions (CIF) for each observation:

predict cif_values, cif

3. Calculate the c-index using somersd (since c-index is equivalent to 0.5 + 0.5 * Somers' D for survival data):

* Mark observations that experienced the target event
gen target_event = (status == 1)
* Compute Somers' D between predicted CIF and actual event times
somersd cif_values time if target_event | (status == 0), by(target_event)
* Calculate and display the c-index
display "Fine Gray Model c-index: " 0.5 + 0.5*r(somersd)

Method 2: Custom Loop (Precise for small datasets) #

If you want to manually count concordant pairs (great for small samples, but slow for large datasets), use this code:

* First fit your Fine Gray model as before
stset time, failure(status==1)
stcrreg x1 x2, compete(status==2)
* Generate predicted risk scores
predict risk_scores, risk

* Initialize counters
local concordant = 0
local tied_pairs = 0
local total_pairs = 0

* Loop through all subject pairs
forvalues i = 1/`=_N' {
    * Skip if subject i didn't experience the target event
    if status[`i'] != 1 continue
    
    forvalues j = 1/`=_N' {
        * Skip self-pairs and subjects with competing events
        if `i' == `j' | status[`j'] == 2 continue
        
        local total_pairs = `total_pairs' + 1
        
        * Check concordance
        if risk_scores[`i'] > risk_scores[`j'] {
            if time[`i'] < time[`j'] local concordant = `concordant' + 1
        }
        else if risk_scores[`i'] == risk_scores[`j'] {
            if time[`i'] == time[`j'] local tied_pairs = `tied_pairs' + 1
        }
        else {
            if time[`i'] > time[`j'] local concordant = `concordant' + 1
        }
    }
}

* Calculate and display c-index
local c_index = (`concordant' + 0.5*`tied_pairs') / `total_pairs'
display "Fine Gray Model c-index: " `c_index'

内容的提问来源于stack exchange，提问作者Nawar