Data Analysis – Customer Churn in an Australian Subscription Business

Research Question and Background

Subscription businesses depend on retaining customers, and the timing of cancellation is as important as whether it occurs at all. A customer who cancels in month two is far more costly to acquire and retain than one who remains for two years. For this reason, churn is best analysed as a time-to-event outcome rather than a simple yes or no. This analysis examines an Australian direct-to-consumer subscription service and asks: which customer and account characteristics are associated with the hazard of cancellation over the first 24 months of tenure?

Survival analysis is appropriate because many customers are still subscribed at the end of the observation window, so their true tenure is unknown and only right-censored. The Cox proportional hazards model was chosen because it estimates the effect of covariates on the hazard of churn without requiring a parametric form for the baseline hazard, and it produces hazard ratios that are readily interpretable for commercial audiences.

Data and Variables

The dataset contains 3,200 customers who commenced a subscription during a defined intake period and were observed for up to 24 months. The event of interest is voluntary cancellation. Customers still active at the end of the window, or lost to follow-up for administrative reasons, were treated as right-censored. In total, 1,144 customers (35.8 per cent) churned during follow-up, leaving 2,056 censored observations. Tenure was measured in months from activation to cancellation or censoring.

Seven covariates were included:

• Monthly billing, coded 1 for month-to-month plans and 0 for annual plans (reference).
• Promotional acquisition, coded 1 where the customer joined on a discounted introductory offer and 0 otherwise.
• Early support contacts, the count of support tickets raised in the first 90 days (continuous).
• Engagement score, a standardised measure of monthly product usage (mean 0, standard deviation 1).
• Payment failure, coded 1 where the customer experienced at least one failed payment and 0 otherwise.
• Add-on subscribed, coded 1 where the customer held a bundled add-on or upgrade and 0 otherwise.
• Regional location, coded 1 for customers outside a greater capital city area and 0 for metropolitan customers (reference).

The cohort was described before modelling. The median follow-up was 16 months and the mean age at activation was 39 years. Month-to-month plans accounted for 54 per cent of customers and annual plans for 46 per cent. Twenty-nine per cent joined on a promotional discount, 22 per cent experienced at least one payment failure, 34 per cent held an add-on, and 27 per cent were located outside a greater capital city. Customers raised on average 0.9 support tickets in their first 90 days. These figures were internally consistent, with no negative tenures or out-of-range values, and the small number of customers with incomplete covariate records were excluded from the fitted model.

Analytic Approach

Analyses were conducted in R version 4.3 using the survival and survminer packages. A Cox proportional hazards model was fitted with coxph, entering all seven covariates simultaneously. Hazard ratios were obtained by exponentiating the coefficients and are reported with 95 per cent confidence intervals. Kaplan and Meier curves were produced with survfit to describe unadjusted retention by billing type. Model discrimination was summarised using Harrell’s concordance statistic, and overall significance was assessed with the likelihood ratio test.

Covariates were specified in advance on the basis of commercial reasoning and prior evidence rather than by automated stepwise selection, which reduces the risk of overfitting and of unstable estimates. Continuous covariates were retained in their natural units to preserve interpretability, and no interaction terms were included in the primary model.

Assumption and Diagnostic Checks

The central assumption of the Cox model is that hazards are proportional over time. This was tested using scaled Schoenfeld residuals via the cox.zph function. The global test was not significant, chi-square (7) = 11.2, p = .131, indicating that the proportional hazards assumption was reasonable for the model as a whole. One covariate, monthly billing, showed a borderline individual result (p = .048); inspection of the residual plot showed only a mild trend, and a sensitivity analysis stratifying on billing type produced materially unchanged estimates for the other covariates, so the simpler model is reported.

The functional form of the single continuous count covariate, early support contacts, was assessed using martingale residuals, which supported a linear specification. Influential observations were examined with deviance residuals and scaled score (dfbeta) statistics; no individual customer exerted undue influence on any coefficient. Because each customer contributed a single spell, observations were treated as independent.

Results

The model was highly significant overall, likelihood ratio test = 512.3 on 7 degrees of freedom, p < .001, and discrimination was good, with a concordance of 0.71 (standard error 0.008). Table 1 reports the coefficients, hazard ratios, confidence intervals and p values.

All seven covariates were statistically significant. Monthly billing carried the largest hazard: customers on month-to-month plans had 2.10 times the hazard of cancellation compared with annual subscribers, holding other factors constant. Customers who experienced a payment failure had 1.80 times the hazard, and customers acquired on a promotional discount had 1.60 times the hazard, consistent with weaker commitment among price-motivated joiners. Each additional support ticket in the first 90 days raised the hazard by 15 per cent. Two covariates were protective: each standard deviation increase in engagement reduced the hazard by 28 per cent, and holding an add-on reduced the hazard by 35 per cent. Regional customers had a modestly higher hazard than metropolitan customers.

The Kaplan and Meier analysis illustrated these differences in absolute terms. Median tenure for month-to-month customers was approximately 14 months, whereas the median for annual subscribers was not reached within the 24-month window, meaning more than half of annual customers remained active at the end of follow-up.

Expressed as retention, the model implies materially different survival curves by plan type and engagement. A monthly-billed customer who has also experienced a payment failure carries a combined hazard several times that of an annual customer with an add-on and above-average engagement, which helps explain why a single blended churn figure can mask very different underlying risk profiles within the same base.

Interpretation

The pattern of results is coherent and commercially intelligible. Contractual commitment, captured by billing frequency and add-on ownership, is strongly associated with retention, while friction and dissatisfaction signals, captured by payment failures and early support contacts, are associated with elevated churn. The engagement result is especially actionable: because usage is measurable early and continuously, a declining engagement score may serve as a leading indicator that allows intervention before a customer cancels.

The promotional acquisition effect highlights a familiar tension in subscription growth. Discount-led acquisition can inflate early sign-ups while attracting customers with a higher propensity to leave once the introductory price expires, which suggests that the quality of acquisition channels should be evaluated on retained rather than gross additions. The regional effect, while smaller, may reflect differences in service experience or connectivity and warrants further investigation.

The practical value of the model lies in translating these associations into targeted retention activity. Because engagement, early support contacts and payment status are observable in near real time, a simple risk score built from the fitted coefficients could flag customers at elevated hazard early enough to intervene, for example by prompting a plan review before an annual renewal lapses or by resolving payment issues proactively. The evidence also cautions against judging acquisition channels on gross sign-ups alone, since promotionally acquired customers churn faster and may generate less lifetime value than their raw volume suggests.

Limitations

Several limitations should be noted. The analysis covers a single business and a 24-month window, so the estimates may not transfer to other categories or longer horizons. Voluntary and involuntary churn were combined in the primary model, although payment failure was included as a covariate; separating these mechanisms, for example through a competing-risks framework, would sharpen interpretation. The engagement score is a composite whose construction affects its coefficient, and reverse causation is possible, since customers who are already disengaging may reduce usage before cancelling. The borderline proportional hazards result for billing type indicates that its effect may vary over tenure, which a time-varying coefficient or stratified model could capture. Finally, unmeasured factors such as competitor pricing and household circumstances are not observed and may confound some associations. In addition, the model estimates average effects over the observation window and does not capture seasonality in cancellations or the influence of price changes introduced during follow-up, both of which could be incorporated through time-varying covariates in future work.

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