## An introduction to the concepts of Survival Analysis and its implementation in lifelines package for Python.

Survival Analysis is used to estimate the lifespan of a particular population under study. It is also called **‘Time to Event’ Analysis** as the goal is to estimate the time for an individual or a group of individuals to experience an event of interest. This time estimate is the duration between birth and death events[1]. Survival Analysis was originally developed and used by Medical Researchers and Data Analysts to measure the lifetimes of a certain population[1]. But, over the years, it has been used in various other applications such as predicting churning customers/employees, estimation of the lifetime of a Machine, etc. The birth event can be thought of as the time of a customer starts their membership with a company, and the death event can be considered as the customer leaving the company.

In survival analysis, we do not need the exact starting points and ending points. All the observation do not always start at zero. A subject can enter at any time in the study. All the duration are relative[7]. All the subjects are bought to a common starting point where the time t is zero (t = 0) and all subjects have the survival probabilities equal to one, i.e their chances of not experiencing the event of interest (death, churn, etc) is 100%.

There may arise situations where the volume of the data prevents it to be used completely in Survival Analysis. For such situations, Stratified Sampling may help. In Stratified Sampling, your goal is to have an equal or nearly equal amount of subjects from each group of subjects in the whole population. Each group is called a Strata. The whole population is stratified (divided) into groups based on some characteristic. Now, in order to pick a certain number of subjects from each group, you can use Simple Random Sampling. The total number of subjects is specified at the start and you split the total number required among each group and you pick that number of subjects randomly from each group[12].

It is important to understand that not every member of the population will experience the Event of Interest (death, churn, etc) during the study period. For example, there will be customers who are still a member of the company, or employees still working for the company, or machines that are still functioning during the observation/study period. We do not know when they will experience the event of interest as of the time of the study. All we know that they haven’t experienced it yet. Their survival times are longer than their time in the study. Their survival times are thus, labelled as ‘Censored’[2]. This indicates that their survival times were cut-off. Therefore, Censorship allows you to measure lifetimes for the population who haven’t experienced the event of interest yet.

It is worth mentioning that the people/subjects who didn’t experience the event of interest need to be a part of the study as removing them completely would bias the results towards everyone in the study experiencing the event of interest. So, we cannot ignore those members and the only way to distinguish them from the ones who experienced the event of interest is to have a variable that indicates censorship or death (the event of interest).

There are different types of Censorship done in Survival Analysis as explained below[3]. Note that Censoring must be independent of the future value of the hazard for that particular subject [24].

**Right Censoring:**This happens when the subject enters at t=0 i.e at the start of the study and terminates before the event of interest occurs. This can be either not experiencing the event of interest during the study, i.e they lived longer than the duration of the study, or could not be a part of the study completely and left early without experiencing the event of interest, i.e they left and we could not study them any longer.**Left Censoring:**This happens when the birth event wasn’t observed. Another concept known as Length-Biased Sampling should also be mentioned here. This type of sampling occurs when the goal of the study is to perform analysis on the people/subjects who already experienced the event and we wish to see whether they will experience it again. The lifelines package has support for left-censored datasets by adding the keyword*left_censoring=True*. Note that by default, it is set to False. Example[9]:

**Interval Censoring:**This happens when the follow-up period, i.e time between observation, is**not continuous**. This can be weekly, monthly, quarterly, etc.**Left Truncation:**It is referred to as**late entry**. The subjects may have experienced the event of interest before entering the study. There is an argument named ‘entry’ that specifies the duration between birth and entering the study. If we fill in the truncated region then it will make us overconfident about what occurs in the early period after diagnosis. That’s why we truncate them[9].

In short, subjects who have not experienced the event of interest during the study period are right-censored and subjects whose birth has not been seen are left-censored[7]. Survival Analysis was developed to mainly solve the problem of right-censoring[7].

The Survival Function is given by,

Survival Function defines **the probability that the event of interest has not occurred at time t**. It can also be interpreted as the **probability of survival after time t **[7]. Here, T is the random lifetime taken from the population and it **cannot be negative.** Note that S(t) is between zero and one (inclusive), and S(t) is a non-increasing function of t[7].

The Hazard Function also called the intensity function, is defined as the probability that the subject will experience an event of interest within a small time interval, provided that the individual has survived until the beginning of that interval [2]. It is the instantaneous rate calculated over a time period and this rate is considered constant [13]. It can also be considered as the risk of experiencing the event of interest at time t. It is the number of subjects experiencing an event in the interval beginning at time t divided by the product of the number of subjects surviving at time t and interval width[2].

Since the probability of a continuous random variable to equal a particular value is zero. That’s why we consider the probability of the event happening at a particular interval of time from T till (T + ΔT). Since our goal is to find the risk of an event and we don’t want the risk to get bigger as the time interval ΔT gets bigger. Thus, in order to adjust for that, we divide the equation by ΔT. This scales the equation by ΔT[14]. The equation of the Hazard Rate is given as:

The limit ΔT approaches zero implies that our goal is to measure the risk of an event happening at a particular point in time. So, taking the limit ΔT approaches zero yields an infinitesimally small period of time [14].

One thing to point out here is that the Hazard is not a probability. This is because, even though we have the probability in the numerator, but the ΔT in the denominator could result in a value which is greater than one.

Kaplan-Meier Estimate is used to measure the fraction of subjects who survived for a certain amount of survival time t[4] under the same circumstances[2]. **It is used to give an average view of the population[7]**. This method is also called the product limit. It allows a table called, life table, and a graph, called survival curve, to be produced for a better view of the population at risk[2]. **Survival Time is defined as the time starting from a predefined point to the occurrence of the event of interest[5]**. **The Kaplan-Meier Survival Curve is the probability of surviving in a given length of time where time is considered in small intervals.** For survival Analysis using Kaplan-Meier Estimate, there are three assumptions [4]:

- Subjects that are censored have the same survival prospects as those who continue to be followed.
- Survival probability is the same all the subjects, irrespective of when they are recruited in the study.
- The event of interest happens at the specified time. This is because the event can happen between two examinations. The estimated survival time can be more accurately measured if the examination happens frequently i.e if the time gap between examinations is very small.

The **survival probability** at any particular time is calculated as the number of subjects surviving divided by the number of people at risk. The censored subjects are not counted in the denominator[4]. The equation is given as follows:

Here, ni represents the number of subjects at risk prior to time t. di represents the number of the event of interest at time t.

For the Survival Curve for the Kaplan-Meier Estimate, the y-axis represents the probability the subject still hasn’t experienced the event of interest after time t, where time t is on the x-axis[9]. In order to see how uncertain we are about the point estimates, we use the confidence intervals[10]. The median time is the time where on average, half of the population has experienced the event of interest[9].

Like the Kaplan-Meier Fitter, Nelson Aalen Fitter also gives us an average view of the population[7]. It is given by the number of deaths at time t divided by the number of subjects at risk. It is a non-parametric model. This means that there isn’t a functional form with parameters that we are fitting the data to. It doesn’t have any parameters to fit[7].

Here, ni represents the number of subjects at risk prior to time t. di represents the number of the event of interest at time t.

Survival Regression involves utilizing not only the duration and the censorship variables but using additional data (Gender, Age, Salary, etc) as covariates. We ‘regress’ these covariates against the duration variable.

The dataset used for Survival Regression needs to be in the form of a (Pandas) DataFrame with a column denoting the duration the subjects, an optional column indicating whether or not the event of interest was observed, as well as additional covariates you need to regress against. Like with other regression techniques, you need to preprocess your data before feeding it to the model.

The Cox Proportional Hazards Regression Analysis Model was introduced by Cox and it takes into account the effect of several variables at a time[2] and examines the relationship of the survival distribution to these variables[24]. It is similar to Multiple Regression Analysis, but the difference is that the depended variable is the Hazard Function at a given time t. It is based on very small intervals of time, called time-clicks, which contains at most one event of interest. It is a semi-parametric approach for the estimation of weights in a Proportional Hazard Model[16]. The parameter estimates are obtained by maximizing the partial likelihood of the weights[16].

Gradient Descent is used to fit the Cox Model to the data[11]. The explanation of Gradient Descent is beyond the scope of this article but it finds the weights such that the error is minimized.

The formula for the Cox Proportional Hazards Regression Model is given as follows. The model works such that the log-hazard of an individual subject is a linear function of their static covariates and a population-level baseline hazard function that changes over time. These covariates can be estimated by partial likelihood[24].

β0(t) is the baseline hazard function and it is defined as the probability of experiencing the event of interest when all other covariates equal zero. And It is the only time-dependent component in the model. The model makes no assumption about the baseline hazard function and assumes a parametric form for the effect of the covariates on the hazard[25]. The partial hazard is a time-invariant scalar factor that only increases or decreases the baseline hazard. It is similar to the intercept in ordinary regression[2]. The covariates or the regression coefficients x give the proportional change that can be expected in the hazard[2].

The sign of the regression coefficients, βi, plays a role in the hazard of a subject. A change in these regression coefficients or covariates will either increase or decrease the baseline hazard[2]. A positive sign for βi means that the risk of an event is higher, and thus the prognosis for the event of interest for that particular subject is higher. Similarly, a negative sign means that the risk of the event is lower. Also, note that the magnitude, i.e the value itself plays a role as well[2]. For example, for the value of a variable equaling to one would mean that it’ll have no effect on the Hazard. For a value less than one, it’ll reduce the Hazard and for a value greater than one, it’ll increase the Hazard[15]. These regression coefficients, β, are estimated by maximizing the partial likelihood[23].

Cox Proportional Hazards Model is a semi-parametric model in the sense that the baseline hazard function does not have to be specified i.e it can vary, allowing a different parameter to be used for each unique survival time. But, it assumes that the rate ratio remains proportional throughout the follow-up period[13]. This results in increased flexibility of the model. A fully-parametric proportional hazards model also assumes that the baseline hazard function can be parameterized according to a particular model for the distribution of the survival times[2].

Cox Model can handle right-censored data but cannot handle left-censored or interval-censored data directly[19].

There are some covariates that may not obey the proportional hazard assumption. They are allowed to still be a part of the model, but without estimating its effect. This is called stratification. The dataset is split into N smaller datasets based on unique values of the stratifying covariates. Each smaller dataset has its own baseline hazard, which makes up the non-parametric part of the model, and they all have common regression parameters, which makes up the parametric part of the model. There is no regression parameter for the covariates stratified on.

The term “proportional hazards” refers to the assumption of a constant relationship between the dependent variable and the regression coefficients[2]. Thus, this implies that the hazard functions for any two subjects at any point in time are proportional. The proportional hazards model assumes that there is a multiplicative effect of the covariates on the hazard function[16].

There are three assumptions made by the Cox Model[23]

- The Hazard Ratio of two subjects remains the same at all times.
- The Explanatory Variables act multiplicatively on the Hazard Function.
- Failure times of individual subjects are independent of each other.

**Some built-in functionality provided by the lifelines package [11]**

**print_summary**prints a tabular view of coefficients and related stats.**hazards_**will print the coefficients**baseline_hazard_**will print the baseline hazard**baseline_cumulative_hazard_**will print the N baseline hazards for the N datasets**_log_likelihood**will print the value of the maximum log-likelihood after fitting the model**variance_matrix**will present the variance matrix of the coefficients after fitting the model**score_**will print out the concordance index of the fitted model- Gradient Descent is used to fit the Cox Model to the data. You can even see the fitting using the variable
**show_progress=True**in the**fit**function. **predict_partial_hazard**and**predict_survival_function**are used to inference the fitted model.**plot**method can be used to view the coefficients and their ranges.- the
**plot_covariate_groups**method is used to show what the survival curves look like when we vary a single (or multiple) covariate while holding everything else equal. This way we can understand the impact of a covariate in a model. **the check_assumptions**method will output violations of the proportional hazard assumption.**weights_col=’column_name’**specifies the weight column that contains integer or float values that represents some sampling weights. You also need to specify**robust=True**in the fit method to change the standard error calculations.

Like the Cox model, this model is also a regression model but unlike the Cox model, it defines the hazard rate as an additive instead of a multiplicative linear model. The hazard is defined as:

During estimation, the linear regression is computed at each step. The regression can become unstable due to small sample sizes or high colinearity in the dataset. Adding the coef_penalizer term helps control stability. Start with a small term and increase if it becomes too unstable[11].

This is a parametric model, which means that it has a functional form with parameters that we are fitting the data to. Parametric models allow us to extend the survival function, hazard function, or the cumulative hazard function past our maximum observed duration. This concept is called Extrapolation[9]. The Survival Function of the Weibull Model looks like the following:

Here, λ and ρ are both positive and greater than zero. Their values are estimated when the model is fit to the data. The Hazard Function is given as:

If we are given two separate populations A and B, each having its own survival functions given by SA(t) and SB(t) and they are related to one another by some accelerated failure rate, λ, such that,

It can slow down or speed up the moving along the survival function. λ can be modelled as a function of covariates[11]. It describes stretching out or contraction of the survival time as a function of the predictor variables[19].

Where,

Depending on the subjects’ covariates, the model can accelerate or decelerate failure times. An increase in xi means that the average/median survival time changes by a factor of exp(bi)[11]. We then pick a parametric form for the survival function. For this, we’ll select the Weibull form.

The first step is to install the lifelines package in Python. You can install it using pip.

One thing to point out is that the lifelines package assumes that every subject experienced the event of interest unless we specify it explicitly[8].

The input to the fit method of the survival regression, i.e CoxPHFitter, WeibullAFTFitter, and AalenAdditiveFitter must include durations, censored indicators, and covariates in the form of a Pandas DataFrame. The duration and censored indicator must be specified in the call to the fit method[8].

The lifelines package contains functions in lifelines.statistics to compare two survival curves[9]. The Log-Rank Test compares two event series’ generators. The series have different generators if the value returned from the test exceeds some pre-defined value.

It is a non-parametric statistical test which is used to compare the survival curves of two groups.

It is a commonly used most commonly for performance evaluation for survival models. It is used for the validation of the predictive ability of a survival model[18]. It is the probability of concordance between the predicted and the observed survival. It is the “fraction of all pairs of subjects whose predicted survival times are correctly ordered among all subjects that can actually be ordered”[16].

If censoring is present then we shouldn’t use the mean-squared-error or the mean-absolute-error losses. We should opt for the concordance-index (or the c-index for short). The Concordance Index evaluates the accuracy of the ordering of predicted time. It is interpreted as follows[11]:

- Random Predictions: 0.5
- Perfect Concordance: 1.0
- Perfect Anti-Concordance: 0.0 (in this case we should multiply the predictions by -1 to get a perfect 1.0)

Usually, the fitted models have a concordance index between 0.55 and 0.7 which is due to the noise present in the data.

We can also use K-Fold Cross-Validation with the Cox Model and the Aalen Additive Model. The function splits the data into a training set and a testing set and fits itself on the training set and evaluates itself on the testing set. The function repeats this for each fold.

## In the second part, we’ll implement Survival (Regression) Analysis in Python to Predict Customer Churn.

[1] Lifelines: Survival Analysis in Python: https://www.youtube.com/watch?v=XQfxndJH4UA

[2] What is a Cox model?, Stephen J Walters. www.whatisseries.co.uk

[3] Applied Survival Analysis: Regression Modeling of Time-to-Event Data By David W. Hosmer, Jr., Stanley Lemeshow, Susanne May

[4] Understanding survival analysis: Kaplan-Meier estimate: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3059453/

[5] Statistics review 12: survival analysis. Bewick V, Cheek L, Ball J. Crit Care. 2004 Oct; 8(5):389–94.

[6] Altman DG. London (UK): Chapman and Hall; 1992. Analysis of Survival times.In:Practical statistics for Medical research; pp. 365–93.

[7] lifelines — Survival Analysis Intro

[8] lifelines — Quick Start

[9] lifelines — Survival Analysis with lifelines

[10] The Greenwood and Exponential Greenwood. Confidence Intervals in Survival Analysis — S. Sawyer — September 4, 2003

[11] lifelines — Survival Regression

[12] Stratified Sampling, https://www.youtube.com/watch?v=sYRUYJYOpG0

[13] Survival analysis, part 3: Cox regression Article in American Journal of Orthodontics and Dentofacial Orthopedics · November 2017

[14] The Definition of the Hazard Function in Survival Analysis: https://www.youtube.com/watch?v=KM23TDz75Fs

[15] Cox Proportional-Hazards Model — STHDA

[16] On Ranking in Survival Analysis: Bounds on the Concordance Index — Vikas C. Raykar, Harald Steck, Balaji Krishnapuram CAD and Knowledge Solutions (IKM CKS), Siemens Medical Solutions Inc., Malvern, USA & Cary Dehing-Oberije, Philippe Lambin Maastro Clinic, University Hospital Maastricht, University Maastricht, GROW, The Netherlands

[17] lifelines — Time Varying Survival Regression

[18] Concordance Index

[19] Parametric Survival Models — Christoph Dätwyler and Timon Stucki. 9. May 2011

[20] StatQuest: Maximum Likelihood, clearly explained! https://www.youtube.com/watch?v=XepXtl9YKwc

[21] Cox (1972)

[22] Partial likelihood by D. R. Cox (1975)

[23] Cox Regression Model

[24] Cox Proportional-Hazards Regression for Survival Data in R An Appendix to An R Companion to Applied Regression, third edition John Fox & Sanford Weisberg

## FAQs

### What question does survival analysis answer? ›

This topic is called reliability theory or reliability analysis in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology. Survival analysis attempts to answer certain questions, such as **what is the proportion of a population which will survive past a certain time?**

**How to interpret survival analysis? ›**

The Kaplan-Meier plot can be interpreted as follow: **The horizontal axis (x-axis) represents time in days, and the vertical axis (y-axis) shows the probability of surviving or the proportion of people surviving**. The lines represent survival curves of the two groups. A vertical drop in the curves indicates an event.

**What is the formula of survival analysis? ›**

The survival function is **S(t) = Pr(T >t)=1 − F(t)**. – The survival function gives the probability that a subject will survive past time t.

**What are the 3 main things for survival? ›**

The four basic needs of nearly all survival situations are **shelter, water, fire, and food**.

**What is the main message the writer wants to convey in survival is your own responsibility? ›**

What is the main message the writer is trying to get across in "Survival is Your Own Responsibility?" **When going into the wilderness, it is okay to take risks to improve your adventure**. Having a no-fear attitude will help you get through most survival situations.

**What is the most important assumption in survival analysis? ›**

An important assumption in survival analysis is that **the censoring is uninformative**. What this means is that their probability of being censored is unrelated to the probability of having an event.

**What is 0 and 1 in survival analysis? ›**

Introduction to Survival Data

Survival analysis focuses on two important pieces of information: Whether or not a participant suffers the event of interest during the study period (i.e., a dichotomous or indicator variable often coded as 1=event occurred or 0=**event did not occur during the study observation period**.

**What is failure in survival analysis? ›**

The failure rate is **the rate at which the population survivors at any given instant are "falling over the cliff"** The failure rate is defined for non repairable populations as the (instantaneous) rate of failure for the survivors to time t during the next instant of time.

**What is the difference between Kaplan-Meier and Cox regression? ›**

**KM Survival Analysis cannot use multiple predictors, whereas Cox Regression can**. KM Survival Analysis can run only on a single binary predictor, whereas Cox Regression can use both continuous and binary predictors. KM is a non-parametric procedure, whereas Cox Regression is a semi-parametric procedure.

**What does number at risk mean in Kaplan-Meier? ›**

The idea behind the number at risk table is that - in order to calculate survival probability using the Kaplan-Meier product limit method - we need to know how many individuals were still accounted for in the study that had not yet experienced the event of interest.

### What is the null hypothesis for survival analysis? ›

The null hypothesis is that **there is no difference in survival between the two groups or that there is no difference between the populations in the probability of death at any point**.

**What is the formula for Kaplan-Meier? ›**

With the Kaplan-Meier approach, the survival probability is computed using **S _{t}_{+}_{1} = S_{t}*((N_{t}_{+}_{1}-D_{t}_{+}_{1})/N_{t}_{+}_{1})**. Note that the calculations using the Kaplan-Meier approach are similar to those using the actuarial life table approach.

**How do you calculate percentage of surviving? ›**

It is calculated by dividing the percentage of patients with the disease who are still alive at the end of the period of time by the percentage of people in the general population of the same sex and age who are alive at the end of the same time period.

**How do you calculate sample in survival analysis? ›**

The estimated sample size per group n is calculated as: - **where α = alpha, β = 1 - power and z _{p} is the standard normal deviate for probability p**. n is rounded up to the closest integer. (1+1/m)/p is equivalent to 2/p in the first equation if the experimental and control group sizes are unequal.

**What are the 5 rules of survival? ›**

**Water, warmth, signals, shelter and food** are the commonly known top 5 priorities in a survival situation.

**What was the message the writer is trying to convey? ›**

The term **theme** can be defined as the underlying meaning of a story. It is the message the writer is trying to convey through the story. Often the theme of a story is a broad message about life. The theme of a story is important because a story's theme is part of the reason why the author wrote the story.

**What is the central theme of essay survival? ›**

When everything around you begins to crumble and fear overcomes you what is there left to do, and the answer is **to survive**. Having the courage to survive takes so much more bravery and effort than the actual process of surviving takes.

**What is the theme of survival? ›**

Survival stories are characterized as stories in which the characters face the challenge of surviving despite obstacles such as; the elements, animals, an oppressive system, or other people that try to kill them by way of drastic measures. The characters are forced fight against the odds.

**What are the 4 key assumptions? ›**

The four basic assumptions that form the basis of financial accounting structure are **business entity assumption, accounting period assumption, going concern assumption, and money measurement assumption**.

**What are the 3 most common assumptions in statistical analysis? ›**

A few of the most common assumptions in statistics are **normality, linearity, and equality of variance**.

### What are the key assumption? ›

Key Assumptions means **the assumptions that are identified as key for the defined Project Plan and provide the basis for the Payment Plan**.

**What is hazard ratio less than1? ›**

A hazard ratio of one means that there is no difference in survival between the two groups. A hazard ratio of greater than one or less than one means that **survival was better in one of the groups**.

**What is Type 1 and Type 2 censoring? ›**

Two types of independent right censoring: Type I : completely random dropout (eg emigration) and/or fixed time of end of study no event having occurred. Type II: study ends when a fixed number of events amongst the subjects has occurred.

**How do you calculate hazard rate? ›**

HR, **hazard rate ratio = treatment hazard rate/placebo hazard rate**. The hazard ratio is constant under the Cox proportional hazard model.

**What are the 3 types of failure? ›**

These are **preventable, unavoidable/complexity-related, and innovative or intelligent failures**. All organisations can benefit from understanding what kinds of failures they can face.

**What are the 4 modes of failure? ›**

For mechanical devices, there are four Failure Mechanisms: **corrosion, erosion, fatigue and overload**. While those Failure mechanisms exists many places in nature, they may or may not be present in the specific working environment of an asset.

**What are the 2 types of failure? ›**

**Preventable failure**: a failure caused by deviating from a known process. For example, someone forgot to run the test suite before shipping code and the app crashed. Complex failure: a failure caused by a system breakdown.

**What are the disadvantages of Kaplan-Meier? ›**

The limitation of Kaplan Meier estimate is that **it cannot be used for multivariate analysis as it only studies the effect of one factor at the time**. Log-rank test is used to compare two or more groups by testing the null hypothesis.

**What is the advantage of Cox regression over Kaplan-Meier? ›**

In contrast to the Kaplan-Meier method, Cox proportional hazards regression can **provide an effect estimate by quantifying the difference in survival between patient groups and can adjust for confounding effects of other variables**.

**What is the p-value of Kaplan-Meier? ›**

The test produces a p-value of **.** **001**, suggesting that there is a survival difference between males and females in the general lung cancer population.

### Why does Kaplan-Meier not reach 0? ›

Whenever the last event is censored the Kaplan-Meier curve won't go to zero. You know people are alive beyond this point but you have no way of estimating their chances of dying thereafter. It's nice that most of your subjects survived--at least for them!

**How do you interpret median survival time Kaplan-Meier? ›**

Mean and median survival

The median survival is **the smallest time at which the survival probability drops to 0.5 (50%) or below**. If the survival curve does not drop to 0.5 or below then the median time cannot be computed.

**What is the 95% CI for median survival time? ›**

For 95% confidence, this value is **1.96**. For the sample data, the margin of error equals 1.96*0.5396 = 1.0576. Add and subtract the margin of error from the logarithm of the median survivals to create a confidence interval on a logarithm scale.

**What is a good null hypothesis example? ›**

The null hypothesis assumes that any kind of difference between the chosen characteristics that you see in a set of data is due to chance. For example, **if the expected earnings for the gambling game are truly equal to zero, then any difference between the average earnings in the data and zero is due to chance**.

**What is the assumption for Kaplan-Meier? ›**

Kaplan-Meier estimator has a few assumptions: **the survival probability is the same for censored and uncensored subjects**; the likelihood of the occurrence of the event is the same for the participants enrolled early and late; the probability of censoring is the same for different groups; finally, the event is assumed to ...

**What are the three null hypothesis? ›**

S.No | Null Hypothesis |
---|---|

1 | The null hypothesis is a statement. There exists no relation between two variables |

2 | Denoted by H_{0} |

3 | The observations of this hypothesis are the result of chance |

4 | The mathematical formulation of the null hypothesis is an equal sign |

**What is the difference between life table and Kaplan-Meier survival analysis? ›**

Survival data are analyzed in two ways: **the life-table method divides the time into intervals and calculates survival at each interval; the Kaplan-Meier method calculates survival each time an event occurs**.

**What happens if Kaplan-Meier curves cross? ›**

If the Kaplan-Meier survival curves cross then this is **clear departure from proportional hazards**, and the log rank test should not be used. This can happen, for example, in a two drug trial for cancer, if one drug is very toxic initially but produces more long term cures.

**Does Kaplan-Meier adjust for confounding? ›**

**Simple Kaplan-Meier estimates do not take confounders into account** and therefore produce a systematically biased picture of the true treatment effect in such cases. The most popular way to adjust for confounders in medical time-to-event analysis is the use of the Cox proportional hazards model (Cox 1972).

**How do you calculate number of fatalities? ›**

Case fatality rate is calculated by dividing the number of deaths from a specified disease over a defined period of time by the number of individuals diagnosed with the disease during that time; the resulting ratio is then multiplied by 100 to yield a percentage.

### How do you convert death rate to percentage? ›

To make a rate into a percent, for the example of 18 deaths per 100,000 population, **divide by 1,000**: Be careful about the decimal point.

**How much sample do I need? ›**

A good maximum sample size is usually **around 10% of the population, as long as this does not exceed 1000**. For example, in a population of 5000, 10% would be 500. In a population of 200,000, 10% would be 20,000.

**How do you calculate sample size for a patient? ›**

The following simple formula would be used for calculating the adequate sample size in prevalence study (4); **n = Z 2 P ( 1 - P ) d 2** Where n is the sample size, Z is the statistic corresponding to level of confidence, P is expected prevalence (that can be obtained from same studies or a pilot study conducted by the ...

**What is the purpose of survival analysis? ›**

There are three primary goals of survival analysis, **to estimate and interpret survival and / or hazard functions from the survival data**; to compare survival and / or hazard functions, and to assess the relationship of explanatory variables to survival time.

**What data can be obtained from survival analysis? ›**

Introduction to Survival Data

Survival analysis focuses on two important pieces of information: **Whether or not a participant suffers the event of interest during the study period** (i.e., a dichotomous or indicator variable often coded as 1=event occurred or 0=event did not occur during the study observation period.

**What are the topics of survival analysis? ›**

Survival analysis includes a variety of specific type of data analysis including “**life table analysis,” “time to failure” methods, and “time to death” analysis**. Reliability methods and life contingencies are based on the same fundamental principles of survival analysis.

**When to do survival analysis? ›**

WHY USE SURVIVAL ANALYSIS? Survival analysis is important **when the time between exposure and event is of clinical interest**. In our example, five-year survival among patients with tumors < 1 cm was 85%, compared with 52% among those with tumors > 5 cm.

**What is the most widely used method in survival data analysis? ›**

**Cox's (9) regression model** has been the most widely used method in survival data analysis regardless of whether the survival time is discrete or continuous and whether there is censoring.

**What is risk in survival analysis? ›**

In survival analyses, **all subjects who are at risk of experiencing an event** are part of the so-called risk set. The risk set usually consists at each point in time of individuals who have been followed-up till that time and have not yet experienced the event of interest just before that time point [6].

**Which two pieces of information are measured in survival analysis? ›**

Survival times are analyzed with the Kaplan-Meier method, which yields two measures of interest: **survival rates and the median survival time**. The log-rank test is used to compare survival times across treatment groups. Cox regression is used in multivariable models.

### What is survival analysis for beginners? ›

Survival analysis is **a series of statistical methods that deals with variables that have both a time and event associated with it**. For example, it is used in cancer clinical research if we are interested in measuring the time it takes before a patient relapses following treatment.

**What are 5 survival tips? ›**

**10 Essential Wilderness Survival Tips**

- Build a fire. ...
- Craft a short-term survival shelter. ...
- Establish a hierarchy of priorities. ...
- Find a clean water source. ...
- Locate a food source. ...
- Practice excellent hygiene. ...
- Stay calm and assess the situation. ...
- Signal nearby search and rescue teams.

**What are the 7 elements of survival? ›**

**Top 7 survival priorities**

- Positive Attitude.
- First Aid.
- Shelter.
- Water.
- Warmth.
- Signals.
- Food.

**What are the two types of survival analysis? ›**

The two most common survival analysis techniques are the **Kaplan-Meier method and Cox proportional hazard model**.

**How do you determine survivability? ›**

It is calculated by dividing the percentage of patients with the disease who are still alive at the end of the period of time by the percentage of people in the general population of the same sex and age who are alive at the end of the same time period.