Hazard ratio | EPFL Graph Search

In survival analysis, the hazard ratio (HR) is the ratio of the hazard rates corresponding to the conditions characterised by two distinct levels of a treatment variable of interest. For example, in a clinical study of a drug, the treated population may die at twice the rate per unit time of the control population. The hazard ratio would be 2, indicating higher hazard of death from the treatment. A scientific paper might utilise a Hazard Ratio (HR) to state something as follows. "Adequate COVID-19 vaccination status was associated with significantly decreased risk for the composite of severe COVID-19 or mortality with a[n] HR of 0.20 (95% CI, 0.17-0.22)." In layman's English, this means: People in the study who were vaccinated were 80% less likely to get severe Covid-19 or to die, compared to people who weren't vaccinated in the same study. So, for a hazardous outcome (e.g. death), a Hazard Ratio below 1 indicates that the treatment (e.g. vaccination) might be favorable (less hazard

Comparative study of joint analysis of microarray gene expression data in survival prediction and risk assessment of breast cancer patients

Haleh Yasrebi

Microarray gene expression data sets are jointly analyzed to increase statistical power. They could either be merged together or analyzed by meta-analysis. For a given ensemble of data sets, it cannot be foreseen which of these paradigms, merging or meta-analysis, works better. In this article, three joint analysis methods, Z-score normalization, ComBat and the inverse normal method (meta-analysis) were selected for survival prognosis and risk assessment of breast cancer patients. The methods were applied to eight microarray gene expression data sets, totaling 1324 patients with two clinical endpoints, overall survival and relapse-free survival. The performance derived from the joint analysis methods was evaluated using Cox regression for survival analysis and independent validation used as bias estimation. Overall, Z-score normalization had a better performance than ComBat and meta-analysis. Higher Area Under the Receiver Operating Characteristic curve and hazard ratio were also obtained when independent validation was used as bias estimation. With a lower time and memory complexity, Z-score normalization is a simple method for joint analysis of microarray gene expression data sets. The derived findings suggest further assessment of this method in future survival prediction and cancer classification applications.

Oxford Univ Press2016

Can survival prediction be improved by merging gene expression data sets?

Philipp Bucher, Haleh Yasrebi

BACKGROUND: High-throughput gene expression profiling technologies generating a wealth of data, are increasingly used for characterization of tumor biopsies for clinical trials. By applying machine learning algorithms to such clinically documented data sets, one hopes to improve tumor diagnosis, prognosis, as well as prediction of treatment response. However, the limited number of patients enrolled in a single trial study limits the power of machine learning approaches due to over-fitting. One could partially overcome this limitation by merging data from different studies. Nevertheless, such data sets differ from each other with regard to technical biases, patient selection criteria and follow-up treatment. It is therefore not clear at all whether the advantage of increased sample size outweighs the disadvantage of higher heterogeneity of merged data sets. Here, we present a systematic study to answer this question specifically for breast cancer data sets. We use survival prediction based on Cox regression as an assay to measure the added value of merged data sets. RESULTS: Using time-dependent Receiver Operating Characteristic-Area Under the Curve (ROC-AUC) and hazard ratio as performance measures, we see in overall no significant improvement or deterioration of survival prediction with merged data sets as compared to individual data sets. This apparently was due to the fact that a few genes with strong prognostic power were not available on all microarray platforms and thus were not retained in the merged data sets. Surprisingly, we found that the overall best performance was achieved with a single-gene predictor consisting of CYB5D1. CONCLUSIONS: Merging did not deteriorate performance on average despite (a) The diversity of microarray platforms used. (b) The heterogeneity of patients cohorts. (c) The heterogeneity of breast cancer disease. (d) Substantial variation of time to death or relapse. (e) The reduced number of genes in the merged data sets. Predictors derived from the merged data sets were more robust, consistent and reproducible across microarray platforms. Moreover, merging data sets from different studies helps to better understand the biases of individual studies and can lead to the identification of strong survival factors like CYB5D1 expression.

Public Library of Science2009

Transforming cumulative hazard estimates

Pal Christie Ryalen, Mats Julius Stensrud

Time-to-event outcomes are often evaluated on the hazard scale, but interpreting hazards may be difficult. Recently in the causal inference literature concerns have been raised that hazards actually have a built-in selection bias that prevents simple causal interpretations. This is a problem even in randomized controlled trials, where hazard ratios have become a standard measure of treatment effects. Modelling on the hazard scale is nevertheless convenient, for example to adjust for covariates; using hazards for intermediate calculations may therefore be desirable. In this paper we present a generic method for transforming hazard estimates consistently to other scales at which these built-in selection biases are avoided. The method is based on differential equations and generalizes a well-known relation between the Nelson–Aalen and Kaplan–Meier estimators. Using the martingale central limit theorem, we show that covariances can be estimated consistently for a large class of estimators, thus allowing for rapid calculation of confidence intervals. Hence, given cumulative hazard estimates based on, for example, Aalen’s additive hazard model, we can obtain many other parameters without much more effort. We give several examples and the associated estimators. Coverage and convergence speed are explored via simulations, and the results suggest that reliable estimates can be obtained in real-life scenarios.

2018

Can survival prediction be improved by merging gene expression data sets?

Philipp Bucher, Haleh Yasrebi

Public Library of Science2009