Survival analysis is an imperative statistical concept when it comes to biostatistics and healthcare statistics, to evaluate time-to-event data. It is more advanced than just simple average, enabling us to analyze the likelihood of something happening at a certain time period into the future and be aware that not everyone is affected by the event within the period of the study. Not merely in terms of the survival rate of particular patients after specific treatment has been administered, but in terms of the time to failure of medical devices, if implemented appropriately, using survival analysis can help. The current post will begin with the theoretical explanation of survival analysis and proceed straight to the real-life practical tips along with the examples, additional recommendations, and useful resources for better understanding and practical utilization of the analyzed topic for the readers involved into biostatistics.
An example of survival analysis that has seen a recent surge in use in the healthcare setting is time to recovery or death in COVID-19 patients. Some of the variables that were compared included patients age, other illnesses and various treatments with the help of survival analysis. It enabled them to use time series analysis regarding the likelihood of either recovery or death to assess the efficiency of the treatment approaches or interventions being offered to the population and, likewise, to pinpoint specific populations deserving concern and attention from healthcare providers.
Compared to other statistical methods, survival analysis is a good method of measuring the performance of treatments and, in particular, it is used in cancer research. While the comparison of survival rates between the treated and the controls groups is the key focus of the ordinary survival analysis, the later takes into account the basics like the possibility of variability of follow-up intervals and dropout rates of patients. It makes it possible for researchers to model the survival curves and probably illustrate the stark chance of survival of some different groups of patients at varied time frames.
In other words, it aids in establishing factors that predict outcomes and show if some variables define the risk of an event of interest such as death or disease progression in a patient. In addition, it helps making comparison of the treatment effects possible and to learn the difference in group and, therefore, to find out whether a new treatment statistically improves survival rates in contrast to the standard treatment or placebo. Thus, adding these analytical capabilities, survival analysis assists researchers in making more decision and innovations in healthcare field.
The first thing that needs to be done while undertaking survival analysis is to identify the problem and collect related data. Start with the definition of the particular event of interest or, in other words, define the type of event you want to assess and find out what kind of time-to-event data is required in the analysis. This entails noting the date on which the occurrence was noted or if it did not happen within the observation period by noting censored. Further implement covariates or factors that may play a part in duration to and from, for example, age, sex, and treatment regime. Aspiring to achieve high analysis quality, the given components of the dataset represent a crucial primary stage to consider.
Appropriate exploratory data analysis (EDA) should be conducted to gain insights into the dataset before jumping into more advanced methods of survival analysis. The steps involved include inspecting the data as well as the distribution of the variables to determine their basic characteristics as well as the relationships between them. One type of graphical displaying of data is important in EDA and survival analysis can be represented through Kaplan-Meier curves. The following curves show the survival probability estimates on the time axis, which gives an initial insight of differential survival rates of individuals belonging to certain groups within database. This makes the Kaplan-Meier curves a useful tool for researchers as it will be seen in the subsequent sections of this paper; by creating curves, the different data sets collected can be analysed to look for trends, patterns, and even potential outliers by researchers before further quantitative and qualitative analyses are carried out on the data.
Example: Suppose you are studying the survival times of patients undergoing two different types of cancer treatments. Plotting Kaplan-Meier curves for each treatment group can help visualize differences in survival rates.
# Example R code for Kaplan-Meier plot
library(survival)
library(survminer)
# Fit survival curves
fit <- survfit(Surv(time, status) ~ treatment, data = your_data)
# Plot Kaplan-Meier curves
ggsurvplot(fit, data = your_data, pval = TRUE, conf.int = TRUE)
Whether to use one of the models above depends on your data and research question: Choosing appropriate survival model is very critical. In case you would like to estimate the survival function without relying on the assumption of normality of the survival time distribution, then the Kaplan-Meier estimator is appropriate. When the interaction between the covariates and survival data is mutually independent while assuming that hazards are proportional, then the Cox proportional hazards model is most suitable. However, if one would prefer to make an assumption on the distribution of survival times for the respective groups, then one could opt for the parametric models such Weibull or exponential models. All of them have their strengths and the choice of which of them to use depends on the nature of the data and purpose of analysis.
Once the suitable survival model has been chosen, the next step is to model the selected on your data as well as assess validity of the models assumptions. For example, when working with the Cox proportional hazards model, it is crucial to verify an independence of the hazard rates to guarantee validity of the assumption mentioned above. Schoenfeld residuals can be used to assess whether covariates have a constant impact on the hazard function at this stage of the proposed model. Calibration of a proper model and its validation before using it for the final analysis is a significant step to achieve accurate results in performing survival analysis.
# Fit Cox proportional hazards model
cox_model <- coxph(Surv(time, status) ~ covariate1 + covariate2, data = your_data)
# Check proportional hazards assumption
cox.zph(cox_model)
After the final model has been fitted and cross validated, the final activity would be to assess what the results mean in relation to the initial research query.
In the final steps, you need to consider or interpret and get a better understanding of the outcomes that are generated by the model. You are encouraged to present your findings by integrating tables and plots including survival curves and hazard ratios to elaborate pertinent findings well. Therefore, interpret your statistical tests results broadly in laymen terms, such that those who can barely comprehend technical aspects of a study can understand the relationship between the findings and the research problem.
Example: If your Cox model indicates that treatment type significantly affects survival, explain how different treatments impact patient outcomes and the clinical relevance of these findings.
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