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Contributors: A Bansal (U of Pennsylvania) | P Dedhia (U of Cincinnati) | A Elebiary (Lahey Clinic) | X Vela (U of El Salvador) | D Thomson (ECU) | P Jawa (ECU) | S Sridharan (Lister Hospital, UK) | F Iannuzsella (IRCCS, Italy) | D Mitema (Johns Hopkins U) | Malvinder Parmar (Northern Ontario, Canada) | Wisit Cheungpasitporn (Mayo)

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Issue 5 Volume 2 Year 2015

URL http://goo.gl/QDSB5B

Editor: Tejas Desai | Chief: Tushar Vachharajani | Free subscription by @ https: / / goo.gl/ PTVJuo

by Sivakumar Sridharan (@sayitmyway)

NOW THAT I UNDERSTAND SURVIVAL ANALYSES

hospitalization, symptomatic improvement, etc. Survival analyses have two characteristics ? 1) time to event and 2) censoring. We?ll talk about each in further detail soon.

In a survival analysis, study participants are followed until a specified period of time or until the occurrence of the specified event, whichever is earlier. The time from study entry (or randomization) to the occurrence of the outcome event is called the ?time to event? or ?survival time?. However, some participants may not experience the outcome event until the end of follow-up period. These patients provide what is termed censored observations. This is

because the information available for these participants is incomplete.

Let?s use a hypothetical example to illustrate these points. Suppose the participants of a study are followed up for 12 months after a particular treatment and that the pre-specified event is recurrence of the disease. The time to event (i.e., when the disease relapses) for six patients in the study are as follows:

In our continuing efforts to educate you about the stats used in the medical literature, this month?s feature article will be about survival analyses. If you?ve read any recent medical literature, and ?survived? through the statistical portion of the paper, you may have ended your reading more confused than when you started! Don?t worry? we?re here to break down complicated statistical tests into understandable concepts. So let?s get started.

A survival analysis refers to a wide array of statistical methods to analyze data related to timing of a pre-specified event. The pre-specified event could be any measurable event depending on the study protocol e.g. death,

Patient 1: 10

Patient 2: 12*

Patient 3: 3

Gloria Gaynor "I will Survive" Released 10/23/1978 by Polydor Records

Patient 4: 12*

Patient 5: 7

Patient 6: 5*

Patients 1, 3, and 5 had disease relapses @ 10, 3 & 7 months respectively during the follow-up period. Patients 2 and 4 were disease-free at the end of the study period (12 months & no disease relapse). The last patient, #6, was lost to follow-up after 5 months (remember, the patients in this hypothetical study were supposed to be followed for 12 months). In those 5 months, patient 6 did not have disease relapse. For patients 2, 4, & 6, information about their disease relapse is not available. It does not mean that they did not have disease relapse ? it just did not happen in the specified time period. These three patients will be censored at the specified time points when we cease to collect information about them. Whenever you come across survival analysis data, it is important to examine that the specified follow-up period is sufficiently long for the outcome event to happen and that the censoring is applied only for appropriate events.

The survival analysis will be

reported as either survival &/or hazard. Reporting the data as survival provides the probability of surviving (or being event-free) up to the specified time. Reporting the data as hazard gives the potential that the event will occur assuming the participant has survived until the specified time.  Survival is expressed using Kaplan ? Meier curves & the hazard by Cox proportional hazards regression models.

In 1958, Kaplan & Meier introduced a methodology to estimate the probability of surviving event-free as a function of time. This method is now widely used & is called Kaplan-Meier curves; an example of which is shown to the right.

In a Kaplan-Meier curve, time is plotted along the X-axis and proportion of patients surviving along the Y-axis. The graph shows the difference in survival time between 2 groups of patients. Each drop in the graph is an event occurrence and each

vertical line in the graph is a censored observation.  Survival curves provide information on survival time in a clear

and easily comprehensible manner. Kaplan-Meier curves can be used to show survival curves for the entire study cohort or the difference in survival amongst various sub-groups. The survival differences between the groups can be tested using tests such as log-rank test.

The Cox proportional hazards

regression model is a useful method to explore the ?hazard? of the predictor variables in relation to the specified event. The model, although somewhat similar to parametric regression models, has a different set

of assumptions compared to linear models. An example of Cox model is given below.

The model shows the hazard ratio of death for three predictor variable (age, male gender, and BMI) in a 24-month follow-up study. As noted, hazard ratios for

age and BMI are statistically significant (because their 95% confidence intervals do not cross 1.00). A hazard ratio of more than 1 signifies increased risk and a ratio of less than 1 implies reduced risk. In the model shown, for every 1-year increase in age, there is 3.2% increase in the risk of death. Similarly, for each 1-unit (kg/m2) increase in BMI, there is 6.3% reduction in risk of

death.

As you can see, survival analyses are an essential part of biomedical statistics. You?ve probably come across them in the medical literature; hopefully you have a better handle on how to interpret the results. It is important to familiarize oneself with the basic concepts of this analysis to interpret and critically analyze the published literature.