The term ‘survival analysis’ has been used for data involving time to a certain event such as death, onset of a disease or relapse of a condition. The development of survival analysis dates back to the 17th century with the first life table ever produced by John Graunt in 1662.

Throughout the centuries, survival analysis was solely linked to the investigation of mortality rates; however, in the last few decades, applications of the statistical methods for survival data analysis have been ex­tended beyond biomedical re­search to other fields such as criminology, sociology, marketing, institutional research and health insurance practice.

Survival analysis plays an im­portant role when analysing data on events observed over time, such as death, cardiac arrest, relapse of drug addiction or failure of an electronic de­vice. Besides identifying the significant risk factors, the survival model ranks these hazards by their importance in predicting survival durations. This information is essential to surgeons, psychologists and manufacturers to address these risk factors optimally.

The contributions of Kaplan and Meier in 1958 in estimating survival probabilities and hazard rates led to ground-breaking im­provements in survival analysis. The Nelson-Aalen estimator is an alternative non-parametric estimator of the cumulative hazard rate. The proportional hazard model proposed by Cox in 1972 was another significant contribution to survival analysis. This semi-parametric model consists of two parts. The first component is the baseline hazard, which is a function of time and describes how risk varies over time. The second component is an exponential function of a linear combination of the predictors and is independent of time.

In essence, the Cox model can be used to compare the relative forces of mortality of two lives or two homogeneous groups of lives. These non-parametric and semi-parametric survival models assume that the members in a population are similar and so are inappropriate in the presence of unobserved diversity.

Further developments in survival analysis include the shared and unshared frailty models introduced by Vaupel in 1979 and extended by Hougaard in 1984. These models are more appropriate in accommodating heteroge­neity and random effects as they eliminate biases in estimation.

Liberato Camilleri is an associate professor at the Department of Statistics and Operations Re­search at the Faculty of Science of the University of Malta.

Sound bites

• From the international scene:

Survival analysis is a useful statistical technique for answering questions that deal with the duration of events. The Kaplan-Meier and Nelson-Aalen estimators are the traditional statistical techniques for estimating hazard rates and survival probabilities; while the Cox pro­portional hazard model assumes that the effect of each predictor is multiplicative with respect to the hazard rate. A recent development in survival analysis includes the accelerated failure time models, which assume a Weibull, Log-normal or Log-Logistic distribution. Unlike the Cox model, these parametric models do not exhibit proportional hazards.

Another recent development was the introduction of unshared and shared frailty models, which address the unobserved diversity in the data. To address the impact of frailty, these models incorporate a multiplicative term in the survival distribution, where in the unshared case, each individual is assigned a unique frailty effect, while in the shared case, groups of individuals are assigned the same frailty effect.

• From the local scene:

The author of this page (Liberato Camilleri), together with other researchers, has applied these statistical models in several research fields including health, cardiology and medicine, and the results were reported in the following publications:

- Modelling survival durations using frailty models. Proceedings of the 2017 ESM Conference p.428-432.

- Does Aortic Valve Replacement Restore Normal Life Expectancy? A 20-year relative survival study. International Cardiovascular Forum Journal, Volume 6, p.46-53.

- Long-term survival following aortic valve replacement: the influence of age, prosthesis-patient mismatch and indexed effective orifice area. International Cardiovascular Forum Journal, Volume 11, p.31-36.

- Estimation of ejection fraction with ventri-culography versus echo-cardiography in patients referred for cardiac surgery. Journal of Cardiology and Therapeutics, Volume 4, p.3-7.

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Did you know?

• Smoking increases the hazard of death from coronary heart disease by four times, but reduces the hazard of developing Parkinson’s disease by 30 per cent.

• The risk for men of experiencing a sudden cardiac arrest is two to three times higher, compared to women. Moreover, this hazard increases with age, particularly for those suffering from heart disease and other cardiovascular conditions.

• Compared to women, men are three to four times more likely to be diagnosed with attention deficit disorder; four to five times more likely to be diagnosed with autism; and two to three times more likely to be dyslexic.

• Moderate alcohol drinking (one drink a day) decreases the risk of death by 20 per cent, but excessive alcohol drinking raises the hazard by 50 per cent, compared to non-alcohol drinking.

• Men are more likely than women to use illicit drugs; while women are more likely than men to crave for drugs and relapse. Moreover, the hazard of a fatal drug overdose is larger when a relapse occurs.

• Compared to non-smokers, the risk for smokers to die from lung, throat and mouth cancer are 14 times higher; and two times larger to die from bladder cancer.

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