Time-to-Resignation in a Six-Year Hiring Cohort, with a Non-Proportional Covariate
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Capstone 40 · Technical Report
Technical Report

Time-to-Resignation in a Six-Year Hiring Cohort, with a Non-Proportional Covariate

Kaplan-Meier estimation under 57 percent right-censoring, log-rank comparison, Cox regression with a Schoenfeld test, and episode splitting to recover a reversing effect.

Data  3,191 employees hired January 2020 to January 2026, monthly resolution
Event  Voluntary resignation. Involuntary exits and active employment treated as censoring
Models  Kaplan-Meier, log-rank, Cox proportional hazards, Cox with time-varying covariates
Where this comes from
Chapter Chapter 203 · Survival Analysis: Time to Event
Part Part XXXIII · Capstone Projects: Specialized Methods
Dataset capstone-survival-analysis-time-to-event.xlsx
Notebook View the analysis

Abstract

Objective. To estimate tenure distribution and covariate effects on voluntary resignation, and to evaluate a remote-work policy whose effect the standard summaries report as null.

Design. All 3,200 employees hired into a six-year window were followed to a fixed administrative cut-off. Tenure was computed from hire and exit dates; voluntary resignation was the event of interest, with involuntary exits and continuing employment treated as right-censored. Kaplan-Meier estimation, multivariate log-rank testing, and Cox proportional hazards regression were applied, followed by a Schoenfeld residual test of proportionality and, where it failed, episode splitting at 18 months fitted by a time-varying Cox model.

Result. 1,375 resignations, 83 involuntary exits and 1,733 censored, giving 56.9 percent censoring. Median tenure was 29.0 months against 19.1 for the mean among leavers. The proportionality test rejected for work mode (statistic 67.5, p < 0.0001) while the adjusted hazard ratio for remote work was 1.08 (p = 0.238) and the log-rank test returned p = 0.165. After episode splitting, remote work carried a hazard ratio of 0.487 (95% CI 0.390 to 0.607) in months 0 to 18 and 2.016 (1.708 to 2.379) thereafter.

1. Data and preprocessing

The extract contained 3,211 rows. Eleven duplicate employee identifiers were removed. The Operations department appeared under two spellings following a mid-period rename and was consolidated. Nine records carried an exit date preceding the hire date and were dropped. Work mode was absent for 58 employees and was retained as an explicit category rather than deleted or imputed. Tenure was computed in months to the exit date or to the 1 January 2026 cut-off, giving 3,191 employees with follow-up from 0.9 to 72.0 months, median 18.0.

2. Kaplan-Meier estimation

Months since hireSurvival95% CI
1284.2%
2458.5%56.4% to 60.5%
3641.4%
4836.0%
Product-limit estimates of the probability of not having resigned.

Median survival is 29.0 months. The mean tenure among the 1,375 employees who resigned is 19.1 months, an understatement of 34 percent relative to the median. The discrepancy is structural: restricting to completed durations conditions on the event having occurred within the observation window, which excludes long durations by construction.

3. Group comparison and a follow-up-time artifact

DepartmentnMean tenure at exitResignation rateMean follow-up12-month survival
Platform3396.95.3%8.993.4%
Customer Support54218.060.0%20.775.6%
Operations59119.644.2%24.885.0%
Sales59919.653.8%22.183.7%
Engineering1,12019.840.1%25.386.5%
Platform ranks last on mean tenure at exit and first on survival. It was created 18 months before the cut-off.

The multivariate log-rank test across departments gives chi-square 109.4 on 4 degrees of freedom, p = 9.9e-23. The department comparison is therefore real; the ordering implied by mean tenure at exit is not.

4. Cox regression and the proportionality test

CovariateHazard ratio95% CIp
Job level, per level0.8370.804 to 0.871<0.001
Salary percentile, per point0.9920.989 to 0.995<0.001
Manager changes, each1.2141.129 to 1.307<0.001
Customer Support vs Engineering1.8361.591 to 2.119<0.001
Sales vs Engineering1.6131.397 to 1.862<0.001
Platform vs Engineering0.5370.334 to 0.8650.011
Remote vs onsite1.0840.948 to 1.2380.238
Concordance 0.620. Reference categories Engineering and onsite.

Schoenfeld residual tests with rank time transformation reject proportionality for remote work (statistic 67.49, p < 0.0001) and, far more weakly, for Sales (7.47, p = 0.0063). All remaining covariates return p between 0.15 and 0.91. The reported hazard ratio for remote work is therefore an average over a non-constant effect.

5. Episode splitting

Follow-up was partitioned at 18 months, expanding 3,191 employees into 4,761 rows, with the event indicator assigned to the interval containing the exit. Remote status was interacted with interval membership.

EstimateHazard ratio95% CIp
Remote, months 0 to 180.4870.390 to 0.607<0.001
Remote, months 18 onward2.0161.708 to 2.379<0.001
Hybrid vs onsite0.9130.805 to 1.0350.156
A ratio of 4.1 between the two regimes, previously summarized as 1.08.

Kaplan-Meier estimates by work mode confirm the crossing directly: remote survival exceeds onsite by 9.2 points at 12 months and 13.7 at 18 months, and trails it by 10.4 at 36 months and 12.5 at 48. The log-rank statistic, which integrates the difference over follow-up, is correspondingly near zero at 1.92.

6. Comparison with a completed-durations analysis

Restricting to the 1,375 resignations and regressing tenure on the same covariates by ordinary least squares returns a remote coefficient of +3.83 months (p < 0.001), discarding 1,816 employees and reversing the sign of the practical conclusion. This is selection on the outcome and is presented as a contrast rather than an analysis.

7. Limitations

Involuntary exits are a competing risk treated as censoring, which requires them to be independent of the resignation hazard conditional on covariates; a Fine and Gray subdistribution model or cause-specific modeling of both events would relax this. The 18-month split point was selected after inspecting the survival curves, so the two hazard ratios are optimistically sharp relative to a pre-specified split or a smooth time-varying coefficient. Left truncation is absent by construction since only employees hired within the window are included, which excludes the longest-tenured population. Work mode is self-selected and the estimates are associational.

From Statistics, Data Science and AI: A Visual Handbook by John Fisher. Every statistic, table, and figure in this report is reproduced by the companion notebook.