The business question

A B2B software company wants one number for its board: how long does an account last? The finance team already has an answer — average the tenure of every account that has churned. That number is wrong, and it is wrong in a predictable direction.

The reason is censoring. On the reporting date a large share of accounts are still active. Their contracts have not ended, so their lifetimes are not known — but they are not missing. An account that has been live for 900 days and has not churned tells you something exact: its lifetime is at least 900 days. Averaging only the churned accounts throws every one of those facts away, and every fact it throws away is good news. The estimate can only come out short.

The second question is the actionable one: does completing onboarding change how long an account lasts? Onboarding costs money, so it has to earn its place.

The data

One row per account, as it would come out of a subscription billing system.

column meaning
account_id the account
segment SMB / Mid-Market / Enterprise
seats licensed seats
mrr_usd monthly recurring revenue, US dollars
onboarding completed / not_completed — did the account finish guided onboarding
started_at contract start date
churned_at churn date, or empty if the account is still active
tenure_days days from start to churn, or to the reporting date if still active
churned 1 = churned (event observed), 0 = censored (still active)

Accounts start on staggered dates, so each has a different length of observation. The reporting date is fixed at 2026-06-30. Generation is seeded, so re-knitting reproduces data.csv byte-for-byte.

set.seed(20260824)

n <- 320
reporting_date <- as.Date("2026-06-30")

segment <- sample(c("SMB", "Mid-Market", "Enterprise"), n, replace = TRUE,
                  prob = c(0.55, 0.32, 0.13))
seats <- ifelse(segment == "SMB",         sample(3:25,    n, replace = TRUE),
         ifelse(segment == "Mid-Market",  sample(25:120,  n, replace = TRUE),
                                          sample(120:600, n, replace = TRUE)))
mrr_usd <- round(seats * runif(n, 28, 46), 2)

onboarding <- ifelse(runif(n) < 0.62, "completed", "not_completed")

# staggered entry: every account has a different observation window
follow_up_days <- sample(180:1500, n, replace = TRUE)
started_at     <- reporting_date - follow_up_days

# true lifetimes: Weibull, shorter for accounts that never finished onboarding
shape       <- 1.15
scale_days  <- ifelse(onboarding == "completed", 32 * 30.44, 14 * 30.44)
true_life   <- round(rweibull(n, shape = shape, scale = scale_days))

churned     <- as.integer(true_life <= follow_up_days)
tenure_days <- pmin(true_life, follow_up_days)
churned_at  <- as.Date(ifelse(churned == 1, as.character(started_at + tenure_days), NA))

accounts <- data.frame(
  account_id  = sprintf("ACC-%04d", seq_len(n)),
  segment     = segment,
  seats       = seats,
  mrr_usd     = mrr_usd,
  onboarding  = onboarding,
  started_at  = started_at,
  churned_at  = churned_at,
  tenure_days = tenure_days,
  churned     = churned,
  stringsAsFactors = FALSE
)
accounts <- accounts[order(accounts$account_id), ]
rownames(accounts) <- NULL
write.csv(accounts, "data.csv", row.names = FALSE)

n_events   <- sum(accounts$churned)
n_censored <- sum(accounts$churned == 0)
data.frame(accounts = n, churned = n_events, still_active = n_censored,
           censored_pct = round(100 * n_censored / n, 2))
##   accounts churned still_active censored_pct
## 1      320     210          110        34.38
kable(head(accounts[, c("account_id","segment","seats","mrr_usd","onboarding",
                        "started_at","churned_at","tenure_days","churned")], 8),
      caption = "First eight rows as the billing export delivers them")
First eight rows as the billing export delivers them
account_id segment seats mrr_usd onboarding started_at churned_at tenure_days churned
ACC-0001 SMB 14 638.10 completed 2023-07-03 NA 1093 0
ACC-0002 Mid-Market 75 2536.53 completed 2024-10-15 2026-01-13 455 1
ACC-0003 SMB 8 325.64 not_completed 2023-12-08 2024-06-28 203 1
ACC-0004 SMB 20 674.87 completed 2022-06-26 2025-12-13 1266 1
ACC-0005 Enterprise 387 17307.17 completed 2025-11-13 NA 229 0
ACC-0006 Mid-Market 73 2074.86 completed 2023-12-14 NA 929 0
ACC-0007 SMB 3 136.41 not_completed 2023-03-18 2024-08-29 530 1
ACC-0008 Mid-Market 94 4067.74 completed 2023-10-20 NA 984 0

The naive answer, and how far off it is

churned_only <- accounts$tenure_days[accounts$churned == 1]
naive_mean   <- mean(churned_only)
naive_median <- median(churned_only)
c(naive_mean_days = round(naive_mean, 2), naive_median_days = round(naive_median, 2),
  naive_mean_months = round(naive_mean / 30.44, 2))
##   naive_mean_days naive_median_days naive_mean_months 
##            380.30            301.00             12.49

This is the finance team’s number: it answers “how long did the accounts that already left last?” — a question about the dead, not about the book of business.

Kaplan-Meier: count every account for as long as it was actually observed

fit_all <- survfit(Surv(tenure_days, churned) ~ 1, data = accounts)
km_med  <- summary(fit_all)$table
km_med[c("records", "events", "median", "0.95LCL", "0.95UCL")]
## records  events  median 0.95LCL 0.95UCL 
##     320     210     540     451     637
anchors <- summary(fit_all, times = c(365, 730, 1095))
data.frame(day = anchors$time,
           n_at_risk = anchors$n.risk,
           survival = round(anchors$surv, 4),
           lower = round(anchors$lower, 4),
           upper = round(anchors$upper, 4))
##    day n_at_risk survival  lower  upper
## 1  365       175   0.6137 0.5618 0.6703
## 2  730        73   0.3671 0.3125 0.4313
## 3 1095        24   0.2305 0.1788 0.2973
km_median_days <- unname(km_med["median"])
gap_pct <- 100 * (km_median_days - naive_median) / km_median_days
c(naive_median_days = naive_median, km_median_days = km_median_days,
  naive_understates_pct = round(gap_pct, 2))
##     naive_median_days        km_median_days naive_understates_pct 
##                301.00                540.00                 44.26

Restricted mean survival over a fixed two-year horizon

The median answers “half the book outlasts this.” If you need an average instead, the honest one is the restricted mean — the area under the survival curve out to a stated horizon. The horizon is part of the number; quoting it without the horizon is meaningless.

rmst <- function(fit, horizon) {
  t <- c(0, fit$time); s <- c(1, fit$surv)
  keep <- t <= horizon
  t <- c(t[keep], horizon); s <- c(s[keep], tail(s[keep], 1))
  sum(diff(t) * head(s, -1))          # left-continuous step integral
}
rmst_all <- rmst(fit_all, 730)
c(rmst_730_days = round(rmst_all, 2), rmst_730_months = round(rmst_all / 30.44, 2))
##   rmst_730_days rmst_730_months 
##          470.03           15.44

Does onboarding change account lifetime?

fit_grp <- survfit(Surv(tenure_days, churned) ~ onboarding, data = accounts)
grp_tab <- summary(fit_grp)$table
kable(round(grp_tab[, c("records","events","median","0.95LCL","0.95UCL")], 2),
      caption = "Median account lifetime in days, by onboarding status")
Median account lifetime in days, by onboarding status
records events median 0.95LCL 0.95UCL
onboarding=completed 217 123 703 599 800
onboarding=not_completed 103 87 257 190 374 
lr <- survdiff(Surv(tenure_days, churned) ~ onboarding, data = accounts)
lr
## Call:
## survdiff(formula = Surv(tenure_days, churned) ~ onboarding, data = accounts)
## 
##                            N Observed Expected (O-E)^2/E (O-E)^2/V
## onboarding=completed     217      123    164.4      10.4      49.7
## onboarding=not_completed 103       87     45.6      37.7      49.7
## 
##  Chisq= 49.7  on 1 degrees of freedom, p= 2e-12
lr_p <- 1 - pchisq(lr$chisq, df = length(lr$n) - 1)
signif(lr_p, 6)
## [1] 1.83409e-12
cx <- coxph(Surv(tenure_days, churned) ~ onboarding, data = accounts)
summary(cx)
## Call:
## coxph(formula = Surv(tenure_days, churned) ~ onboarding, data = accounts)
## 
##   n= 320, number of events= 210 
## 
##                           coef exp(coef) se(coef)    z Pr(>|z|)    
## onboardingnot_completed 0.9775    2.6578   0.1440 6.79 1.12e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                         exp(coef) exp(-coef) lower .95 upper .95
## onboardingnot_completed     2.658     0.3763     2.004     3.524
## 
## Concordance= 0.614  (se = 0.017 )
## Likelihood ratio test= 42.75  on 1 df,   p=6e-11
## Wald test            = 46.1  on 1 df,   p=1e-11
## Score (logrank) test = 49.65  on 1 df,   p=2e-12
hr    <- unname(exp(coef(cx)))
hr_ci <- unname(exp(confint(cx)))
c(hazard_ratio_notcompleted_vs_completed = round(hr, 4),
  ci_lo = round(hr_ci[1], 4), ci_hi = round(hr_ci[2], 4))
## hazard_ratio_notcompleted_vs_completed                                  ci_lo 
##                                 2.6578                                 2.0044 
##                                  ci_hi 
##                                 3.5242
fits <- survfit(Surv(tenure_days, churned) ~ onboarding, data = accounts)
strata_names <- names(fits$strata)
idx <- rep(seq_along(fits$strata), fits$strata)
rmst_by <- sapply(seq_along(strata_names), function(k) {
  sub <- list(time = fits$time[idx == k], surv = fits$surv[idx == k])
  rmst(sub, 730)
})
names(rmst_by) <- strata_names
round(rmst_by, 2)
##     onboarding=completed onboarding=not_completed 
##                   532.60                   338.25

The charts a practitioner reads

plot(fit_grp, col = c("#F97316", "#5fa9dd"), lwd = 2.4, mark.time = TRUE,
     xlab = "days since contract start", ylab = "share of accounts still active",
     main = "Kaplan-Meier: account survival by onboarding status",
     xlim = c(0, 1200), yaxs = "i", ylim = c(0, 1.02))
abline(h = 0.5, lty = 3, col = "#888888")
legend("topright", legend = c("onboarding completed", "onboarding not completed"),
       col = c("#F97316", "#5fa9dd"), lwd = 2.4, bty = "n")
mtext("vertical ticks = censored accounts (still active at the reporting date)",
      side = 3, line = 0.2, cex = 0.8, col = "#666666")

vals <- c(`churned accounts only\n(the naive answer)` = naive_median,
          `Kaplan-Meier median\n(every account counted)` = km_median_days)
bp <- barplot(vals, col = c("#5fa9dd", "#F97316"), ylim = c(0, max(vals) * 1.25),
              ylab = "median account lifetime (days)",
              main = "Dropping the still-active accounts shortens the answer")
text(bp, vals + max(vals) * 0.05, sprintf("%.0f days", vals), font = 2)

What the lesson teaches

  1. Censored is not missing. An account still active at the reporting date carries a hard fact — at least this long. Methods that only count finished lifetimes answer a question about the accounts you already lost.
  2. Report the median off the curve, not the average of the churned. If you need an average, use the restricted mean and say the horizon.
  3. Compare groups with the log-rank test, which uses every account and every censoring time, not a single summary point.
  4. State the effect as a hazard ratio with its interval. An interval that clears 1 is what makes the difference reportable.
  5. The tool needs row-level data: one row per account, a duration, an event flag, and a group. Totals cannot be un-summed back into a survival curve.

Your turn

Bring your own data and the question you actually need answered.

CympleData Scientist Send me your data and question, I’ll send you the analytics. ds@mcpanalytics.ai