Survival Analysis of Customer Lifetime and Churn Prediction in the Telecom Industry

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ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Special Issue | Volume XIV, Issue XIII, October 2025

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Survival Analysis of Customer Lifetime and Churn Prediction in
the Telecom Industry

Akshata Lembhe*, Yogita Lagad, Rupali Kamthe, Abhijeet Swami

Department of Statistics, Dr. D. Y. Patil Arts, Commerce and Science College, Pimpri, Pune-18, Maharashtra, India

DOI: https://doi.org/10.51583/IJLTEMAS.2025.1413SP041

Received: 26 June 2025; Accepted: 30 June 2025; Published: 27 October 2025

Abstract: Customer churn poses a significant concern for the telecom industry, as it directly affects both revenue generation and
the efficiency of operations. To better understand and address this issue, the present analysis applies survival analysis methods to
study customer tenure and the likelihood of churn. Specifically, the Kaplan-Meier estimator is utilized to estimate the survival
function of telecom customers over time, while the Cox Proportional Hazards model is used to assess the influence of various
customer attributes on the risk of churn. The study highlights that several customer-related factors play a crucial role in
determining the probability of churn. Among these, the type of contract (e.g., month-to-month vs. long-term), mode of payment
(e.g., electronic check, credit card), and access to additional services (like internet or tech support) emerged as statistically
significant determinants. For instance, customers on short-term contracts or using certain payment methods exhibited higher
churn probabilities compared to those with long-term commitments or bundled services.

The findings emphasize the importance for telecom companies to tailor their retention strategies by focusing on at-risk customer
segments. By understanding the survival patterns and the variables most strongly associated with early churn, service providers
can design targeted interventions—such as loyalty programs, contract incentives, or personalized communication—to extend
customer relationships and improve overall Customer Lifetime Value (CLV). Ultimately, this evidence-based approach can
support telecom firms in minimizing customer loss and maintaining long-term profitability.

Keywords: Survival Analysis, Customer Churn, Kaplan-Meier Estimator, Cox Proportional Hazards Model, Retention Strategies.

I. Introduction

Due to intense competition, the telecom industry faces challenges in retaining customers. Survival analysis, a statistical and
machine learning approach, models the time until events like customer churn occur, offering insights into customer behavior and
retention strategies. Demographics, usage patterns, service quality, and pricing influence key metrics, such as customer lifetime.

Churn prediction identifies at-risk customers, while survival analysis provides a timeline for churn likelihood, enabling targeted
interventions like personalized offers and loyalty programs. Techniques such as Kaplan-Meier estimators and Cox proportional
hazards models help estimate survival probabilities and hazard rates, offering actionable intelligence for reducing churn.

By integrating these methods with tools like Power BI, telecom companies can make data-driven decisions, optimize customer
retention, and align services with evolving customer expectations. Survival analysis and churn prediction collectively enhance
customer relationships, product strategies, and profitability.

II. Literature Review

Survival analysis has been widely used across various domains, including healthcare, engineering, and business, to model time-
to-event data. Its application in the telecom industry has gained traction due to its ability to predict customer churn and
understand retention dynamics. Studies reveal that techniques like the Kaplan-Meier estimator are effective in estimating survival
probabilities, providing insights into customer longevity, and identifying critical churn periods. The Cox Proportional Hazards
model further enriches this analysis by quantifying the relationship between multiple predictors and churn risk.

Research highlights several key factors influencing churn, such as contract type, payment method, and additional services. Long-
term contracts and automated payment methods have been shown to significantly improve retention, while customers using
month-to-month contracts or electronic checks are more likely to churn. Furthermore, studies emphasize the importance of
bundling additional services like online security and device protection to enhance customer engagement and reduce attrition.

Recent advancements incorporate machine learning models to complement survival analysis, improving the accuracy of churn
predictions. These approaches leverage historical data to identify at-risk customers, allowing companies to implement targeted
retention strategies. Integrating survival analysis with visualization tools like Power BI also facilitates better communication of
insights, enabling stakeholders to make informed, data-driven decisions. This study builds on existing literature by applying
survival analysis to the telecom sector, identifying significant churn factors, and offering actionable recommendations to enhance
customer retention.

III. Methodology

The Telco Customer Churn dataset from Kaggle served as the foundation for this study, comprising 7,043 customer records and

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21 variables, including demographic attributes, service usage patterns, and churn status. Key variables such as tenure, monthly
charges, total charges, contract type, payment method, and churn (Yes/No) were analyzed. To ensure the dataset's readiness for
analysis, preprocessing steps were undertaken. Missing values were addressed using mean imputation for numerical variables and
mode imputation for categorical variables. Categorical variables were encoded using one-hot encoding, while continuous
variables, such as Monthly Charges, were normalized to enhance model performance.

Survival analysis was conducted using two key methods. The Kaplan-Meier estimator, a non-parametric technique, was employed
to calculate survival probabilities and examine customer churn trends over time. This approach provided insights into the
likelihood of customers remaining subscribed at various time intervals. The Cox Proportional Hazards model, a semi-parametric
regression technique, was applied to evaluate the influence of covariates on survival time. This model identified significant
predictors of churn, such as contract type, payment methods, and additional services, offering actionable insights for retention
strategies. By combining these techniques, the study achieved a comprehensive understanding of customer churn and provided a
robust framework for predictive analysis.

Dataset-Telco Customer Churn

Dataset link- https://www.kaggle.com/datasets/blastchar/telco-customer-churn

Objective

1) The primary objective of this report is to identify the key factors that influence customer churn in the telecom industry.
Understanding what drives customers to leave their service providers is crucial for developing targeted retention strategies
and minimizing churn.

2) This study aims to estimate survival probabilities to predict how likely customers are to stay with the service over time. By
assessing customer retention patterns, this analysis will help anticipate churn and inform proactive strategies to extend
customer lifecycles.

3) This report seeks to understand customer churn behaviour through segment analysis, which examines how different
customer groups (based on demographics, service usage, etc.) behave concerning churn. This helps identify specific groups
that may require tailored retention efforts.

4) The objective of this study is to visualize key findings using clear and informative visuals. By presenting the results in an
intuitive and accessible format, the report aims to make the insights actionable for decision-makers in the telecom industry.

5) This project aims to calculate the Customer Lifetime Value (CLV) for each customer, providing a quantitative measure of
the value a customer brings over their entire relationship with the service provider. This information is essential for
optimizing customer retention strategies and improving business profitability.

Exploratory Data Analysis

Interpretations:

a) The mean tenure of customers with the telecom service stands at 32.37 months.

b) Customers' tenures span from 0 to 72 months, with the shortest tenure being 0 months and the longest 72 months.

c) A significant number of customers, with an average monthly charge of $64.76, have moderate to high monthly charges,
with many paying between $35.50 and $89.85.

d) The proportion of senior citizens among customers averages 16.2%, indicating that a smaller portion of the customer
base is made up of senior citizen

Senior Citizen Tenur Monthly Charges
count 7043.000000 7043.000000 7043.000000

mean 0.162147 32.371149 64.761692
std 0.368612 24.559481 30.090047
min 0.000000 0.000000 18.250000
25% 0.000000 9.000000 35.500000
50% 0.000000 29.000000 70.350000
75% 0.000000 55.000000 89.850000
max 1.000000 72.000000 118.750000

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Data Visualization

fig1.1 Gender and Churn Distribution

Interpretation: The gender distribution shows no significant bias, which is beneficial for generalizing insights across gender.

The churn rate, at 26.5%, suggests that the company might still face challenges in retaining over a quarter of its customers.

Strategies to further investigate the reasons behind this churn and mitigate it should be explored.

Fig1.2 Gender and Churn Distribution

Interpretation: The analysis reveals that the percentage of customers who switched service providers is nearly equal across
genders. Males and females show comparable patterns in their decision to change providers.

Fig. 2 Tenure Distribution

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Interpretation: The distribution shows a high number of new customers (short tenure), a decline in mid-tenure retention, and a
spike in long-term loyal customers. This suggests retention challenges in the mid-tenure range, with opportunities to improve
retention strategies.

Fig.3 Churn rate by Tenure

Interpretation: Churn is highest within the first 10 months of customer tenure. After this period, the likelihood of customers
staying long-term increases, highlighting the importance of early retention efforts.

Fig.4 Churn rate by contract type

Interpretation: In the case of Month-to-month contracts Churn rate is very high. There is also a possibility of having customers
in the data frame who are still in their two-year or one-year contract plan. About 75% of the customers with a Month-to-Month
Contract opted to move out as compared to 13% of customers with One Year Contract and 3% with Two Year Contract.

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Fig 6.2 Total Charges

Interpretation: The customers paying high monthly fees churn more.

Customer Survival Analysis

Survival Analysis is a statistical approach that studies the time until a particular event of interest takes place. It is widely applied
in fields like medicine, engineering, and social sciences to analyse and model the duration until events such as death, system
failure, or customer churn occur.

Objectives of Survival Analysis:

To estimate and interpret the survival function.

To compare survival functions across different groups.

To explore the connection between survival time and one or more predictors, we analyse how certain variables influence the
duration until an event of interest occurs. This involves assessing the effect of predictors on survival outcomes and identifying
key factors that may impact the time frame of the event.

If the event has the probability density function f(t) and cumulative distribution function F(t), then the probability of surviving at
least to time t is: Pr(T>t) = S(t) = 1-F(t).

It is a non-increasing function where S(0) = 1 and S(ꝏ) = 0.

Cumulative hazard at time t is defined as H(t) = -ln(S(t)) and instantaneous hazard at time t is h(t)=dH(t)/dt. The instantaneous

hazard can also be written as h(t)=f(t)/S(t)

The likelihood function for survival analysis is described as:

where,

di = Censoring variable that equals 1 if the event is observed for individual i and 0 if the event is not observed (censored) for
individual i,

h(ti) = Hazard for individual i at time t,

H(ti) = Cumulative hazard for individual i at time t, and

S(ti)= Survival probability for individual i at time t.

Note that when di=0, the contribution of the i'th individual to the likelihood function is just its survival probability until time t:
S(t). If the individual has the event, the contribution to the likelihood function is given by the density function f(t)=h(t)S(t).

The log of likelihood is:

Where log is the natural logarithm.

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Kaplan-Meier curve

A Kaplan-Meier curve is a graphical representation used to estimate survival probabilities over time for a specific group,
frequently employed in medical research. This method is a non-parametric statistic that calculates the survival function based on
observed lifetime data.

Advantages and Limitations

The Kaplan-Meier estimator is widely recognized and extensively applied in survival analysis. It is particularly effective for
analysing recovery probabilities, mortality rates, and treatment outcomes. However, it has limitations, especially in adjusting
survival estimates for covariates. In such cases, parametric survival models or the Cox proportional hazards model can provide
more robust analyses by incorporating covariate adjustments.

Fig 7. Kaplan-Meier curve

Interpretation: At the beginning, there is a noticeable sharp decline, indicating that customers tend to churn rapidly after
completing just one tenure. However, the rate of churn slows down significantly afterwards. As anticipated in the telecom
industry, the overall churn rate remains relatively low. The company has successfully retained over 60% of its customers even
after 72months.To address this issue, offering greater discounts on long-term plans could be a viable strategy to encourage more
customers to opt for extended subscriptions, thereby reducing the initial churn rate.

Log Rank Test

The log-rank test is a statistical method used to compare the survival distributions of two groups. It is a nonparametric hypothesis
test, making it suitable for analysing data that is right-skewed and subject to censoring. Importantly, this test assumes that the
censoring is non-informative, meaning it is unrelated to the event of interest.

1.Observed Events: At each event time, count the number of events (deaths, failures) in each group.

2.Expected Events: Calculate the expected number of events in each group, assuming that the survival experiences are the same
across groups.

The log-rank test statistic is based on the difference between the observed and expected number of events. For two groups, the
test statistic can be written as:

Where:

O1: The observed number of events in the group

E1: The expected number of events in group 1.

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V: The variance of the difference between observed and expected events. K: The number of time points where events occur.

Fig.8 Log Rank Test

Interpretation:

1. Gender: Negligible difference in survival probabilities; gender is not a significant factor in churn.

2. Payment Method: Electronic Check has the highest churn risk, while automated payment methods show better retention.

3. Contract: Month-to-month contracts have the highest churn risk. Longer contracts (One-Year, Two-Year) significantly
improve retention.

4. Internet Service: Fiber Optic customers have the highest churn risk compared to DSL and No Service customers.

5. Online Backup: Customers with Online Backup have better retention, while those without face higher churn risk.
Promoting online backup can improve customer retention.

6. Device Protection: Customers with Device Protection have higher retention, while those without are more likely to
churn. Offering device protection can reduce churn.

C) Survival Regression

Survival Regression extends survival analysis by modelling the relationship between survival time (or time until an event) and
explanatory variables (features). For analyzing customer data, I utilize the Cox proportional hazards model to conduct survival
regression. This model effectively fits the data, with the resulting coefficients displayed below.

Cox Proportional Hazards Model

This model is a popular choice for examining the relationship between multiple covariates and survival time. It operates under the
assumption of proportional hazards, which must be validated as part of the analysis process.

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Fig.9 Forest Plot

Forest Plot and Feature Interpretation in the Cox Proportional Hazards Model :

The forest plot displays the log hazard ratios (log(HR)) along with 95% confidence intervals (CI's) for each feature included in
the Cox Proportional Hazards Model.

Key Feature Interpretations:

Contract_ Two year and Contract_ One year:

Features with highly negative log(HR) values indicate that one- or two-year contracts significantly lower the risk of churn
compared to month-to-month contracts. The confidence intervals are entirely to the left of zero, emphasizing these features as
significant predictors with strong protective effects against churn.

Online Security, Tech Support, and Online Backup: These features also have negative log(HR) values, showing that they help
reduce the churn risk. Their confidence intervals do not cross zero, further confirming their statistical significance.

Payment Method_ Electronic check:

This feature has a positive log(HR), suggesting that customers using electronic check payments are more likely to churn. Since
the confidence interval does not cross zero, it is a significant predictor of failure.

Internet Service_ Fiber optic:

This feature exhibits a highly positive log(HR), indicating that fibre optic internet service greatly increases the churn risk. The
hazard ratio is notably large, showing that customers with this service are significantly more prone to churn compared to those
using other internet services.

Paperless Billing, Streaming TV, Streaming Movies:

These features have slightly positive log (HR) values, which suggests a marginally higher risk of churn. However, their
confidence intervals indicate weaker effects compared to other predictors.

Gender and Senior Citizen:

The confidence intervals for these features are close to or cross zero, implying they are not significant predictors of churn in this
model.

Multiple Lines, Device Protection, Phone Service:

These features show log(HR) values near zero or have confidence intervals crossing zero, making them insignificant predictors of

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churn.

Interpretation:

1)Strong negative predictors (reduce churn):

Long-term contracts (one or two years), online security, tech support, and online backup services are highly effective in reducing
churn risk.

2)Strong positive predictors (increase churn):

Fibre optic internet service and electronic check as a payment method are the strongest indicators of higher churn risk.

3)Neutral or insignificant features

like gender, senior citizen status, and certain additional services (e.g., streaming services, multiple lines) have minimal or no
significant impact on churn.

C) Hazard Curve:

Fig.10 Cumulative Hazard Over Time

Interpretation: A significant increase in hazard rate after 60 months suggests a higher churn likelihood. Targeted

Retention Strategies: Focus on customer engagement and support as customers near the 60-month mark to minimize churn

D) Survival Curve:

Fig.11 Survival Probability Over Time

Interpretation:

High Early Retention: Survival probability remains near 1 initially. Churn Risk After 60 Months: Significant drop in survival

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probability, indicating increased churn likelihood.

Conclusion:

Target retention strategies: Focus on customer engagement and satisfaction around the 60-month mark to reduce churn.

Feature Importance

Fig.12 Feature Importance

Interpretation: The graph highlights that monthly charges and how long a customer has been with the company (tenure) are the
strongest predictors of customer churn. Customers with higher bills or shorter tenures are more likely to leave. Features like the
type of internet service, payment method, and contract length also play a key role in predicting churn, with longer contracts
reducing churn risk. Other factors like gender and additional services have less influence.

Customer Lifetime Value

The LTV of a test is: 7344.0 dollars.

LTV Value: The Customer Lifetime Value of $7,344.00 represents the estimated total revenue that a customer is expected to

generate over their lifetime with the telco service.

Interpretation:

High Customer Value: This indicates that each customer in this dataset is potentially very valuable, contributing significantly to
the company’s overall revenue.

Strategic Investment: Given the substantial LTV, the telco company should focus on customer retention strategies, such as
personalized offers, loyalty programs, and enhanced customer service, particularly as customers approach critical churn periods
identified in the survival analysis.

Resource Allocation: The high LTV justifies investing resources in improving customer satisfaction and engagement to maximize
retention and revenue generation.

Conclusion

The analysis highlights key factors influencing customer churn, including contract type, payment method, and additional services.

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Survival probability decreases over time, particularly for customers on month-to-month contracts, who are at higher risk of churn.
Segment-specific insights reveal that customers using fibre optic internet and electronic check payments are more likely to churn,
whereas those with one- or two-year contracts and device protection services have significantly lower churn risk. Additionally,
the customer lifetime value has been calculated at $7,344.00, providing a valuable metric for evaluating customer retention
strategies.

Retention Focus

To enhance customer retention, the focus should be on several key strategies. Promoting long-term contracts by offering
discounts for one- or two-year commitments can encourage customer loyalty. Improving the quality of fibre optic service and
introducing value-added services can enhance the overall customer experience. Targeted marketing efforts, including segmented
promotions and educational campaigns, can help customers better understand the benefits of staying with the service.
Strengthening customer support by providing 24/7 assistance and collecting regular feedback ensures issues are addressed
promptly. Implementing loyalty programs with rewards and referral bonuses further incentivizes retention. Proactive churn
prevention through predictive analytics can identify at-risk customers, allowing for timely interventions. Fostering community
engagement and providing regular updates can help build stronger customer relationships. Offering flexible payment options and
incentives for diverse payment methods can also improve satisfaction and retention.

Scope & Limitation

1)Customer Segmentation: Analyze and categorize customers based on demographics, purchasing behaviour, and engagement
levels to tailor churn prevention strategies.

2)Predictive Modeling: Develop models to estimate customer lifetime value (CLV) and predict churn risk using historical data.

3)Feature Engineering: Identify key features (e.g., purchase frequency, engagement scores) that impact customer retention and
churn likelihood.

4)Data Quality: The analysis depends on the quality of available data, which may include missing values, inaccuracies, or biases
that can affect results.

5)Assumptions of Models: Many survival analysis methods rely on assumptions (e.g., proportional hazards) that may not hold in
all cases.

6)Temporal Dynamics: Customer behaviour can change over time due to external factors that may not be fully captured in
historical data.

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