Competing Risk Bias in Prognostic Models Predicting Hepatocellular Carcinoma Occurrence: Impact on Clinical Decision-making

Abstract

Background and aims: Existing models predicting hepatocellular carcinoma (HCC) occurrence do not account for competing risk events and, thus, may overestimate the probability of HCC. Our goal was to quantify this bias for patients with cirrhosis and cured hepatitis C.

Methods: We analyzed a nationwide cohort of patients with cirrhosis and cured hepatitis C infection from Scotland. Two HCC prognostic models were developed: (1) a Cox regression model ignoring competing risk events and (2) a Fine-Gray regression model accounting for non-HCC mortality as a competing risk. Both models included the same set of prognostic factors used by previously developed HCC prognostic models. Two predictions were calculated for each patient: first, the 3-year probability of HCC predicted by model 1 and second, the 3-year probability of HCC predicted by model 2.

Results: The study population comprised 1629 patients with cirrhosis and cured HCV, followed for 3.8 years on average. A total of 82 incident HCC events and 159 competing risk events (ie, non-HCC deaths) were observed. The mean predicted 3-year probability of HCC was 3.37% for model 1 (Cox) and 3.24% for model 2 (Fine-Gray). For most patients (76%), the difference in the 3-year probability of HCC predicted by model 1 and model 2 was minimal (ie, within 0 to ±0.3%). A total of 2.6% of patients had a large discrepancy exceeding 2%; however, these were all patients with a 3-year probability exceeding >5% in both models.

Conclusion: Prognostic models that ignore competing risks do overestimate the future probability of developing HCC. However, the degree of overestimation-and the way it is patterned-means that the impact on HCC screening decisions is likely to be modest.

Keywords: Competing Risks; Fine-Gray; Liver Cancer; Prognosis; Risk Stratification.

Figure 1

Cumulative incidence of HCC as per high, moderate, and low risk: model 1 vs model 2. The separation in HCC cumulative incidence between the 3 risk groups is similar for model 1 and model 2. This is consistent with both models having comparable levels of discrimination. High risk was defined as a risk score in the 67th percentile or greater (ie, top tertile); low risk was defined as a risk score in the 33rd percentile or lower (ie, bottom tertile). Moderate-risk patients are those whose risk score was in the middle tertile.

Figure 2

The histogram of 3-year predicted HCC risk (model 2 minus model 1).

Figure 3

The scatter plot (Bland-Altman plot) of model 1 minus model 2 predicted 3-year HCC probability (vertical axis) and mean of model 1 and model 2 HCC probability (horizontal axis). There are 1629 circles in this scatter plot, one for each participant in the sample. The horizontal black line denotes the point at which model 1 and model 2 predictions are equal. Points below the black line indicate the Cox model (model 1) prediction is greater than the Fine-Gray model (model 2). In addition, vice versa, points above the black line indicate Cox model (model 1) prediction is less than the Fine-Gray model (model 2). The dashed red line is the mean value for the model 2 prediction minus the model 1 prediction.

Figure 4

Three-year predicted HCC probability for patients where there is at least a 2% absolute difference between model 1 and model 2 prediction (N=43). There are 43 rows in this graph; each row indicates the 3-year risk of HCC predicted by model 1 (blue dot) and the 3-year risk predicted by model 2 (red dot) for a specific patient. Only patients with >2% absolute difference in 3-year risk predicted by model 1 and model 2 are shown in this plot.