Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors

External validation of the International Prediction Tool in Korean patients with immunoglobulin A nephropathy

Background

The International IgA Nephropathy Prediction Tool (International IgA Nephropathy Prediction Tool) has been recently developed to estimate the progression risk of immunoglobulin A nephropathy (IgAN). This study aimed to evaluate the clinical performance of this prediction tool in a large IgAN cohort in Korea.

Methods

The study cohort was comprised of 2,064 patients with biopsy-proven IgAN from four medical centers between March 2012 and September 2021. We calculated the predicted risk for each patient. The primary outcome was occurrence of a 50% decline in estimated glomerular filtration rate (eGFR) from the time of biopsy or end-stage kidney disease. The model performance was evaluated for discrimination, calibration, and reclassification. We also constructed and tested an additional model with a new coefficient for the Korean race.

Results

During a median follow-up period of 3.8 years (interquartile range, 1.8–6.6 years), 363 patients developed the primary outcome. The two prediction models exhibited good discrimination power, with a C-statistic of 0.81. The two models generally underestimated the risk of the primary outcome, with lesser underestimation for the model with race. The model with race showed better performance in reclassification compared to the model without race (net reclassification index, 0.13). The updated model with the Korean coefficient showed good agreement between predicted risk and observed outcome.

Conclusion

In Korean IgAN patients, International IgA Nephropathy Prediction Tool had good discrimination power but underestimated the risk of progression. The updated model with the Korean coefficient showed acceptable calibration and warrants external validation.

A Novel Method for Identifying a Parsimonious and Accurate Predictive Model for Multiple Clinical Outcomes

BACKGROUND AND OBJECTIVE

Most methods for developing clinical prognostic models focus on identifying parsimonious and accurate models to predict a single outcome; however, patients and providers often want to predict multiple outcomes simultaneously. As an example, for older adults one is often interested in predicting nursing home admission as well as mortality. We propose and evaluate a novel predictor-selection computing method for multiple outcomes and provide the code for its implementation.

METHODS

Our proposed algorithm selected the best subset of common predictors based on the minimum average normalized Bayesian Information Criterion (BIC) across outcomes: the Best Average BIC (baBIC) method. We compared the predictive accuracy (Harrell's C-statistic) and parsimony (number of predictors) of the model obtained using the baBIC method with: 1) a subset of common predictors obtained from the union of optimal models for each outcome (Union method), 2) a subset obtained from the intersection of optimal models for each outcome (Intersection method), and 3) a model with no variable selection (Full method). We used a case-study data from the Health and Retirement Study (HRS) to demonstrate our method and conducted a simulation study to investigate performance.

RESULTS

In the case-study data and simulations, the average Harrell's C-statistics across outcomes of the models obtained with the baBIC and Union methods were comparable. Despite the similar discrimination, the baBIC method produced more parsimonious models than the Union method. In contrast, the models selected with the Intersection method were the most parsimonious, but with worst predictive accuracy, and the opposite was true in the Full method. In the simulations, the baBIC method performed well by identifying many of the predictors selected in the baBIC model of the case-study data most of the time and excluding those not selected in the majority of the simulations.

CONCLUSIONS

Our method identified a common subset of variables to predict multiple clinical outcomes with superior balance between parsimony and predictive accuracy to current methods.

A Qualitative Transcriptional Signature for Predicting CpG Island Methylator Phenotype Status of the Right-Sided Colon Cancer

A part of colorectal cancer which is characterized by simultaneous numerous hypermethylation CpG islands sites is defined as CpG island methylator phenotype (CIMP) status. Stage II and III CIMP−positive (CIMP+) right-sided colon cancer (RCC) patients have a better prognosis than CIMP−negative (CIMP−) RCC treated with surgery alone. However, there is no gold standard available in defining CIMP status. In this work, we selected the gene pairs whose relative expression orderings (REOs) were associated with the CIMP status, to develop a qualitative transcriptional signature to individually predict CIMP status for stage II and III RCC. Based on the REOs of gene pairs, a signature composed of 19 gene pairs was developed to predict the CIMP status of RCC through a feature selection process. A sample is predicted as CIMP+ when the gene expression orderings of at least 12 gene pairs vote for CIMP+; otherwise the CIMP−. The difference of prognosis between the predicted CIMP+ and CIMP− groups was more significantly different than the original CIMP status groups. There were more differential methylation and expression characteristics between the two predicted groups. The hierarchical clustering analysis showed that the signature could perform better for predicting CIMP status of RCC than current methods. In conclusion, the qualitative transcriptional signature for classifying CIMP status at the individualized level can predict outcome and guide therapy for RCC patients.

Recognizing the Continuous Nature of Expression Heterogeneity and Clinical Outcomes in Clear Cell Renal Cell Carcinoma

Clear cell renal cell carcinoma (ccRCC) has been previously classified into putative discrete prognostic subtypes by gene expression profiling. To investigate the robustness of these proposed subtype classifications, we evaluated 12 public datasets, together with a new dataset of 265 ccRCC gene expression profiles. Consensus clustering showed unstable subtype and principal component analysis (PCA) showed a continuous spectrum both within and between datasets. Considering the lack of discrete delineation and continuous spectrum observed, we developed a continuous quantitative prognosis score (Continuous Linear Enhanced Assessment of RCC, or CLEAR score). Prognostic performance was evaluated in independent cohorts from The Cancer Genome Atlas (TCGA) (n = 414) and EMBL-EBI (n = 53), CLEAR score demonstrated both superior prognostic estimates and inverse correlation with anti-angiogenic tyrosine-kinase inhibition in comparison to previously proposed discrete subtyping classifications. Inverse correlation with high-dose interleukin-2 outcomes was also observed for the CLEAR score. Multiple somatic mutations (VHL, PBRM1, SETD2, KDM5C, TP53, BAP1, PTEN, MTOR) were associated with the CLEAR score. Application of the CLEAR score to independent expression profiling of intratumoral ccRCC regions demonstrated that average intertumoral heterogeneity exceeded intratumoral expression heterogeneity. Wider investigation of cancer biology using continuous approaches may yield insights into tumor heterogeneity; single cell analysis may provide a key foundation for this approach.