How Might Missing Deaths Affect Median Predicted Survival?

I wanted to understand how a few infant deaths potentially missing from a patient registry might affect its median predicted survival. I also wanted to explore a practical question about the way I work: could I assess that effect with AI, without commissioning a separate statistical analysis? This is a specific question about a particular task. Researchers who know their data may be able to work through some statistical problems independently with AI. Other problems require expertise they do not have. I wanted to understand where this example sits, and what would make its answer credible. The cystic fibrosis example allowed me to combine my knowledge of the data with an AI-assisted derivation. It also made clear which questions a calculation could answer and which required information that was not available.

The knowledge I brought to the problem

In nearly 18 years working with the CF Patient Registry, I observed that infant deaths were rarely recorded. There are specific reasons why these deaths may not be captured, related to how patients enter the registry, but those are beyond the scope of this article. That experience is why I raised the question. Here, “missing” means potentially absent from the registry, not absent from the national death-certificate file. I downloaded the CDC’s 2024 Multiple Cause of Death file into a local database. Among U.S.-resident deaths, CF appeared as the underlying cause or another standardized cause in 294 records. It was the underlying cause in 226. Four CF-mentioned deaths occurred before age one; three had CF as the underlying cause. [2] The Cystic Fibrosis Foundation’s 2024 registry report separately listed 226 deaths among 33,989 participants. The matching death total does not establish that these are the same people. [1]

Figure 1. Age distribution of U.S.-resident deaths with cystic fibrosis recorded on the death certificate, 2024. CF was mentioned in 294 deaths and was the underlying cause in 226. Age 0 represents infants under one. The underlying-cause series is included within the all-mentions series. This distribution describes recorded deaths, not age-specific mortality risk or life expectancy.

Registry participation requires consent from the individual or a legal guardian and care at accredited CF centers. A death certificate can mention CF for someone outside that population; a registry participant can die without CF appearing on the certificate. Subtracting 226 from 294 would not count missing registry deaths. [3] My experience raised the concern. Establishing whether these particular infants were absent would require linkage or another direct check. Because registry survival concerns deaths from any cause, all four CF-mentioned infant deaths could be relevant if they were confirmed, eligible and missing, not only the three CF-underlying deaths.

The question I asked AI

Suppose three infant deaths were genuinely missing. How much could they change median predicted survival, and could we assess that without individual registry records? Median predicted survival is not the median age among people who died. It comes from an age-specific survival curve, asking when survival reaches 50% under the mortality conditions of the selected period. The CFF report gives 68.0 years for 2024 alone and 65.4 years for 2020–2024. Those periods cannot be interchanged. [1, 4] AI helped develop a sensitivity analysis: calculate what follows under specified assumptions. That is a legitimate statistical task, although narrower than reconstructing the registry’s published estimate. The distinction determines what the answer can mean.

The calculation and its limits

For an illustrative single-year scenario, assume 500 infant person-years of exposure, three additional deaths, unchanged mortality after infancy, and an annual mortality hazard near the median between 0.02 and 0.05. The hazard is the instantaneous death rate among people still alive at that age. These are assumed inputs, not measured registry values. A count of infants born or diagnosed during a year is not their accumulated person-time at risk. Over the one-year infant interval, the approximate extra cumulative hazard is (3 deaths / 500 person-years) × 1 year = 0.006. Dividing by the assumed hazard near the median gives an approximate median reduction of 0.12–0.30 years, or 1.44–3.60 months. Four additional deaths would give 1.92–4.80 months under the same assumptions. If the infants were already captured, no adjustment for those deaths is warranted. Extra infant mortality lowers the fraction surviving to later ages, so the curve reaches 50% earlier. The size of that shift depends on both the infant denominator and the curve near its midpoint. The ranges above reflect chosen assumptions, not confidence intervals or a measured correction to CFF’s estimate. There is another denominator issue. If omitted infants are added, they may contribute person-time as well as deaths. The revised infant rate is (D + k) / (Y + E), where D and Y are the original deaths and exposure, k is additional deaths, and E is their additional exposure. The shortcut above neglects E. The technical note makes that approximation explicit. Individual records are not always necessary if adequate aggregate risk-set information is available. A published median alone is insufficient. We also have to define whether we are estimating survival within the registry or in the national CF population, and keep the analysis period consistent. Three deaths potentially missing from 2024 cannot be added to every year of a five-year calculation.

What I learned from the exercise

The result was not unexpected. What interested me more was how AI helped me work through the method and examine the assumptions myself. I reviewed the reasoning and found no obvious flaw. My PhD is not in statistics, so I also need to recognize the limits of that review. This example illustrates a conditional calculation; it does not establish how reliably AI would handle every kind of statistical problem. The useful sequence was to bring knowledge of the data, define the target quantity, obtain a derivation, inspect its assumptions and reproduce the arithmetic. AI made that process more accessible. The ability to question the answer remained essential. In this case, a convincing answer could still be wrong by treating all four infant deaths as confirmed omissions, using births as person-years, confusing median age at death with predicted survival, or presenting an assumed hazard as an observed one. These are concrete checks a researcher must be able to make, rather than simply accepting a plausible explanation.

When I would involve a statistician

I would seek statistical expertise when the task requires judgment I cannot supply or verify: choosing a defensible design, handling censoring or selection in a way I do not understand, resolving an identification problem, or investigating a result I cannot explain. For a complex or consequential analysis, that contribution can be indispensable. Not every bounded calculation requires a separate consultation. The appropriate level of review depends on the unresolved questions and the consequences of being wrong. Where I cannot assess the method, asking AI to reassure me again is not a substitute for competent scrutiny. I see an opportunity for researchers to do more of the initial analytical work themselves and, when needed, bring a better-defined problem to a statistician. Domain knowledge and statistical judgment can complement each other. AI may make that exchange more productive as well as expand what a researcher can do independently. I also think AI-assisted methods deserve consideration in scientific journals when the evidence, derivation and calculations can be examined and reproduced. Human authors remain responsible for the claims and for explaining how the analysis was performed.

A further question the data cannot answer alone

Prenatal CFTR modulator treatment provides another useful test of these boundaries. Early reports of off-label treatment describe improvement in fetal bowel obstruction in some cases, but do not establish an infant mortality benefit or long-term safety. [5] Could such treatment eventually reduce CF-associated infant deaths? Future CDC files could reveal changes in recorded deaths, but do not identify prenatal exposure. With such small counts, chance, diagnosis, coding and changes in CF births also matter. Establishing a treatment effect would require exposure and outcome data, not just an AI analysis of a national trend.

What I take from this

For this bounded sensitivity analysis, AI helped me do meaningful statistical work independently. Turning the scenario into an actual registry adjustment would require additional evidence and a method appropriate to the registry’s data. That is the distinction I find useful. Before deciding whether I need a statistician, I can define the task, examine what I can verify myself and identify where additional expertise would improve the answer. AI gives me another way to start that process, while the quality of the reasoning and evidence remains the standard.

Technical note and sources Illustrative sensitivity analysis This scenario is conditional, not a recalculation of the CFF estimate. It assumes genuinely omitted, eligible infant deaths; 500 infant person-years in a single year; unchanged mortality after infancy; and a mortality hazard near the median between 0.02 and 0.05 per year. The denominator and hazard range are illustrative, not estimated from the registry.

Ranges reflect assumed hazards, not confidence intervals. Rounded values in the article are 1.4–3.6 and 1.9–4.8 months.

The approximation

For a one-year infant interval, approximate additional cumulative hazard is ΔH ≈ (k / Y) × 1 year. The median reduction is approximately ΔH / h(m), where k is additional deaths, Y is infant person-years, and h(m) is the annual hazard near the original median m. For three deaths: ΔH ≈ (3 deaths / 500 person-years) × 1 year = 0.006, giving 0.12–0.30 years, or 1.44–3.60 months. This shortcut neglects any additional exposure from omitted participants. With D infant deaths and Y infant person-years originally observed, the revised rate is λ = (D + k) / (Y + E), where E is the omitted person-time. Compare it with λ = D / Y before calculating an added cumulative hazard. Counts of births or diagnoses are not substitutes for person-time. Under unchanged mortality after infancy, S(a) = exp(−ΔH) S(a) for a ≥ 1. The revised median is the age where the original survival curve reaches 0.5 exp(ΔH), rather than 0.5. Locally, m* − m ≈ −ΔH / h(m). The survival scaling is an identity under the model assumptions; the median shift is a local approximation. Neither establishes that the assumptions hold. A true update requires population eligibility and overlap checks plus adequate risk-set or exposure data. Sufficient aggregate information may reproduce a specified estimator; a separate age-specific life table need not match the registry’s estimator. The published median alone is insufficient. Deaths potentially missing only in 2024 must not be repeated in every year of a pooled 2020–2024 calculation.

Sources and evidence boundaries

[1] Cystic Fibrosis Foundation 2024 Patient Registry Annual Data Report Printed pages 8 and 96: registry population and deaths. Page 93: single-year and pooled median predicted survival estimates.

[2] CDC and NCHS 2024 mortality public use data Author’s analysis of 2024 U.S.-resident records, using the E84 ICD-10 code family in underlying or standardized record-axis causes and counting each death once. National records were not linked to registry participants.

[3] Cystic Fibrosis Foundation Patient Registry Data Requests Registry data are collected at accredited care centers with informed consent from participants or legal guardians.

[4] Cystic Fibrosis Foundation Patient Registry survival methods Pages 18–19 describe applying recent age-specific mortality to a hypothetical newborn’s lifetime. Annual report inclusion alone does not completely specify the survival risk sets.

[5] Metcalf and colleagues 2025 prenatal CFTR modulator case series Three fetuses with meconium ileus received maternal elexacaftor/tezacaftor/ivacaftor exposure. Outcomes varied; this case series does not establish an infant mortality benefit. File layout reference: 2024 NCHS mortality public-use documentation