Censored Cumulative-Cost Estimation

Definition and scope

Estimation of mean cost accrued over a specified horizon when some people lose cost observation before that horizon, using methods that distinguish incomplete capture from death and cost accrual. The target population, use, and analysis remain protocol decisions; this card explains the choices and their consequences rather than approving a study.

Operational specification

Define cumulative cost through a fixed horizon, time origin, perspective, observed cost history, death date, administrative end, and observation loss. For a target including costs until death or the horizon, death can complete a person's cost accumulation; it is not automatically ordinary cost censoring. Preserve interval cost histories when using partitioned estimators.

Analysis and diagnostics

Use a justified censored-cost estimator, such as Bang-Tsiatis weighting under its independent-censoring assumptions or suitable extensions with covariates/history. Assess observation probabilities and positivity, propagate nuisance-model uncertainty, and report the supported horizon. Do not apply Kaplan-Meier directly to accumulated cost as if cost were ordinary survival time.

When NOT to use and common errors

Observed cost divided by observed months and multiplied by the horizon does not generally recover mean cumulative cost. Complete-case means can select survivors or continuously insured people. Censoring weights cannot reconstruct claims that were never covered by the data source or fix an unsupported tail.

Worked example and implementation boundary

For a synthetic simple weighted teaching calculation, three complete accumulated costs of 100, 200, and 300 each have observation probability 0.5 in an original cohort of six. Compute the Horvitz-Thompson-style mean; this is not a fitted censoring model. The illustrative weighted mean is 200. Real censored-cost analysis needs the appropriate time-specific weights, assumptions, and variance estimator. The code performs that explicitly stated calculation with synthetic inputs. It is not a complete fitted analysis and does not demonstrate the identification assumptions, estimate sampling uncertainty, or certify application in another population.

Data-source and reporting requirements

Preserve the provenance, dates, units, and observation rule for each input. Claims capture services and transactions under observable benefits; absence of a record is not proof that an event or resource use did not occur. EHR and registry measurements depend on the collection process and may miss care outside the system. Linked sources add reconciliation and selection questions. Primary collection can improve a missing domain but still requires valid measurement and follow-up. Report which of these limitations affects the stated use, which evidence supports the chosen inputs, and what remains uncertain.

Worked example

Scenario

For a synthetic simple weighted teaching calculation, three complete accumulated costs of 100, 200, and 300 each have observation probability 0.5 in an original cohort of six. Compute the Horvitz-Thompson-style mean; this is not a fitted censoring model.

Dataset

Synthetic inputs with units defined in the scenario; no patient data.

Steps

Result

The illustrative weighted mean is 200. Real censored-cost analysis needs the appropriate time-specific weights, assumptions, and variance estimator.

Trade-offs

Code example

cost_sum = 600
observation_probability = 0.5
original_n = 6
result = cost_sum/observation_probability/original_n
assert abs(result - 200.0) < 1e-9
print(result)

cost_sum <- 600
observation_probability <- 0.5
original_n <- 6
result <- cost_sum/observation_probability/original_n
stopifnot(abs(result - 200.0) < 1e-9)
print(result)

Citations

1. [1]Bang H, Tsiatis AA. Estimating medical costs with censored data. Biometrika. 2000;87(2):329-343.
2. [2]Ramsey SD, Willke RJ, Glick H, et al. Cost-effectiveness analysis alongside clinical trials II — an ISPOR Good Research Practices Task Force report. Value in Health. 2015;18(2):161-172.