# Biomedical Statistics

- Multiple robust estimation of confounding factors in observational studies
- Meta-analysis of biomarkers
- Survival analysis

### The application of statistical methods to analyze observational research and existing data

The relationship between biomarkers and prognosis factors such as life expectancy plays an important role in the determination of therapeutic targets. Meta-analysis of the relationship tends to be done on a small scale, however, and at few facilities, which use different cut-off values. In a meta-analysis of acute pulmonary embolism short-term mortality with troponin I and troponin T, the combined odds ratio of the troponin I expression was 4.01 (95% confidence interval: 2.23-7.23) and of the troponin T expression was 7.95 (3.795-16.65), but the clinical significance of these values is unclear (Bacattini et al., Circulation, 2007).

Hattori and Zhou (Statist Med, 2016a) showed that the difference under the ROC curve (AUC) was estimated to be 0.14, indicating that troponin T expression was a better indicator of short-term mortality risk (Fig. 1).

However, this approach did not consider the degree of bias in the ROC analysis. In a second article, the two authors proposed a solution to this problem (Statist Med, 2017).

Figure 2 shows that as the number of unpublished studies increases, the certainty of the AUC value weakens, questioning the significant effect of the two troponins. In related work, we are developing methods to estimate ROC curves using a meta-analysis of survival times (Hattori and Zhou, Statist Med, 2016b; Sadashima et al., Res Syn Med, 2016).

This approach is still nascent, but has the potential to significantly advance the meta-analysis of biomarkers.

The above problem is an example of selection bias caused by confounding in observational studies. The stratified doubly robust estimator was proposed to adjust the influence of confounding factors (Hattori and Henri, Biometrics, 2014). We are applying similar methods to cancer registration database analysis (Komukai and Hattori, Biometrics, 2017).