# Actuarial Analysis of Survival after Breast Cancer Diagnosis among Lithuanian Females

## TL;DR

This paper analyzes 5-year survival rates for Lithuanian women diagnosed with breast cancer from 1995 to 2016 using statistical survival models.

## Contribution

The study introduces a stratified Cox model to analyze survival data without dividing small datasets into unreliable subsets.

## Key findings

- Kaplan-Meier estimates were constructed for survival by cancer stage.
- A stratified Cox model was applied to account for multiple risk factors like diagnosis stage and year.
- The study highlights the importance of using appropriate statistical methods for small population data.

## Abstract

Breast cancer is the most common cause of mortality due to cancer for women both in Lithuania and worldwide. The chances of survival after diagnosis differ significantly depending on the stage of disease at the time of diagnosis and other factors. One way to estimate survival is to construct a Kaplan–Meier estimate for each factor value separately. However, in cases when it is impossible to observe a large number of patients (for example, in the case of countries with lower numbers of inhabitants), dividing the data into subsets, say, by stage at diagnosis, may lead to results where some subsets contain too few data, thus causing the results of a Kaplan–Meier (or any other) method to become statistically incredible. The problem may become even more acute if researchers want to use more risk factors, such as stage at diagnosis, sex, place of living, treatment method, etc. Alternatively, Cox models can be used to analyse survival data with covariates, and they do not require the data to be divided into subsets according to chosen risks factors (hazards). We estimate the chances of survival for up to 5 years after a breast cancer diagnosis for Lithuanian females during the period of 1995–2016. Firstly, we construct Kaplan-Meier estimates for each stage separately; then, we apply a (stratified) Cox model using stage, circumstance of diagnosis, and year of diagnosis as (potential) hazards. Some directions of further research are provided in the last section of the paper.