Age-Stratified BRCA Testing and Olaparib Population Impact

First-pass aggregate reconstruction of the 2024 single-cohort lifetime analysis

Author

Prepared as a reproducible R/Quarto analysis

Published

August 14, 2026

Code

library(dplyr)
library(ggplot2)
library(knitr)
library(readr)
library(scales)
library(tidyr)

Code

model_inputs <- read_csv("inputs/model_inputs.csv", show_col_types = FALSE)
life_table <- read_csv("inputs/us_female_life_table_2023.csv", show_col_types = FALSE)

scalar_input <- function(input_id) {
  value <- model_inputs$value[model_inputs$input_id == input_id]
  if (length(value) != 1) {
    stop("Expected exactly one input for ", input_id, call. = FALSE)
  }
  as.numeric(value)
}

text_input <- function(input_id, column) {
  value <- model_inputs[[column]][model_inputs$input_id == input_id]
  if (length(value) != 1) {
    stop("Expected exactly one input for ", input_id, call. = FALSE)
  }
  value
}

fmt_count <- function(x) comma(round(x, 0), accuracy = 1)
fmt_decimal <- function(x, digits = 3) formatC(x, format = "f", digits = digits)
fmt_pct <- function(x, accuracy = 0.1) percent(x, accuracy = accuracy)
fmt_pp <- function(x, digits = 1) {
  paste(formatC(100 * x, format = "f", digits = digits), "percentage points")
}
fmt_years <- function(x) comma(round(x, 1), accuracy = 0.1)

source_link <- function(label, url) {
  paste0("[", label, "](", url, ")")
}

1 Purpose

This report is a first-pass R/Quarto aggregate reconstruction of Kasle et al.’s population impact model for BRCA testing and adjuvant olaparib in high-risk HER2-negative early breast cancer. The source paper estimated 3,938 olaparib-eligible patients in the 2024 US cohort and reported lifetime reductions of 272 metastatic breast cancer (mBC) recurrences, 68 non-mBC recurrences, and 8,677 life-years gained under testing and olaparib treatment versus no testing and no adjuvant treatment.

The extension here keeps that published analysis as a reproduction benchmark and layers in an exploratory age-stratified treatment-effect modifier for <45 years and >=45 years. The age-stratified evidence is uncertain and should not be read as a definitive age-specific olaparib effect.

2 Source Inputs

Code

source_summary <- model_inputs |>
  count(category, source_url, name = "inputs") |>
  arrange(category, source_url)

kable(
  source_summary,
  col.names = c("Input category", "Source", "Rows"),
  align = c("l", "l", "r")
)

Input category	Source	Rows
age_distribution	https://doi.org/10.1038/s41523-024-00632-8	4
age_modifier	info/BRCA_pilot_age_group_het_trials.docx	6
benchmark	https://doi.org/10.1080/13696998.2025.2583870	9
clinical_rate	https://doi.org/10.1080/13696998.2025.2583870	12
population	https://doi.org/10.1080/13696998.2025.2583870	3
representative_age	https://doi.org/10.1038/s41523-024-00632-8	1
representative_age	https://doi.org/10.1080/13696998.2025.2583870	1

Key sources:

Kasle et al. 2025, Journal of Medical Economics, “The estimated long-term clinical effects of BRCA testing and olaparib treatment of early breast cancer in the US population: a population impact model”: DOI 10.1080/13696998.2025.2583870.
Age-stratified treatment-effect modifier: local meta-regression report at info/BRCA_pilot_age_group_het_trials.docx and extracted subgroup data at info/d.human.trials.subgroup.data.csv.
Age-distribution proxy: Morganti et al. 2024, npj Breast Cancer, “Clinicopathological characteristics and eligibility for adjuvant olaparib of germline BRCA1/2 mutation carriers with HER2-negative early breast cancer” (n=205, Dana-Farber): median age at diagnosis 43 years overall, 39 years among patients meeting olaparib-eligibility criteria: DOI 10.1038/s41523-024-00632-8. This is matched on gBRCA1/2 status and HER2-negative early breast cancer, unlike the previous general-population ACS proxy, but does not report an exact <45/>=45 split or subtype-specific age moments, so 50%/50% is used as a round proxy consistent with the sub-45 median.
Female life expectancy: CDC/NCHS United States Life Tables, 2023, Table 3: CDC life tables and Table03.xlsx.

3 Published Model Benchmark

The published model splits the eligible cohort into HR-positive and TNBC subpopulations. This report reconstructs those pieces from the published subtype population sizes and rounded clinical inputs.

Code

subtype_inputs <- tibble(
  subtype = c("HR-positive", "TNBC"),
  patients = c(
    scalar_input("eligible_hr_positive"),
    scalar_input("eligible_tnbc")
  ),
  no_mbc_rate = c(
    scalar_input("hrp_no_treatment_mbc_rate"),
    scalar_input("tnbc_no_treatment_mbc_rate")
  ),
  no_non_mbc_rate = c(
    scalar_input("hrp_no_treatment_non_mbc_rate"),
    scalar_input("tnbc_no_treatment_non_mbc_rate")
  ),
  no_life_years_per_patient = c(
    scalar_input("hrp_no_treatment_life_years"),
    scalar_input("tnbc_no_treatment_life_years")
  ),
  olaparib_mbc_rate = c(
    scalar_input("hrp_olaparib_mbc_rate"),
    scalar_input("tnbc_olaparib_mbc_rate")
  ),
  olaparib_non_mbc_rate = c(
    scalar_input("hrp_olaparib_non_mbc_rate"),
    scalar_input("tnbc_olaparib_non_mbc_rate")
  ),
  olaparib_life_years_per_patient = c(
    scalar_input("hrp_olaparib_life_years"),
    scalar_input("tnbc_olaparib_life_years")
  )
) |>
  mutate(
    no_mbc = patients * no_mbc_rate,
    olaparib_mbc = patients * olaparib_mbc_rate,
    mbc_prevented = no_mbc - olaparib_mbc,
    no_non_mbc = patients * no_non_mbc_rate,
    olaparib_non_mbc = patients * olaparib_non_mbc_rate,
    non_mbc_prevented = no_non_mbc - olaparib_non_mbc,
    no_life_years = patients * no_life_years_per_patient,
    olaparib_life_years = patients * olaparib_life_years_per_patient,
    life_years_gained = olaparib_life_years - no_life_years
  )

subtype_display <- subtype_inputs |>
  transmute(
    Subtype = subtype,
    Patients = fmt_count(patients),
    `mBC avoided` = fmt_count(mbc_prevented),
    `non-mBC avoided` = fmt_count(non_mbc_prevented),
    `Life-years gained` = fmt_count(life_years_gained)
  )

kable(subtype_display, align = c("l", "r", "r", "r", "r"))

Subtype	Patients	mBC avoided	non-mBC avoided	Life-years gained
HR-positive	1,433	77	19	2,579
TNBC	2,505	195	48	6,012

Code

calculated_totals <- subtype_inputs |>
  summarise(
    `mBC recurrences, no testing` = sum(no_mbc),
    `mBC recurrences, olaparib` = sum(olaparib_mbc),
    `mBC recurrences avoided` = sum(mbc_prevented),
    `non-mBC recurrences, no testing` = sum(no_non_mbc),
    `non-mBC recurrences, olaparib` = sum(olaparib_non_mbc),
    `non-mBC recurrences avoided` = sum(non_mbc_prevented),
    `Life-years, no testing` = sum(no_life_years),
    `Life-years, olaparib` = sum(olaparib_life_years),
    `Life-years gained` = sum(life_years_gained)
  ) |>
  pivot_longer(everything(), names_to = "metric", values_to = "calculated")

published_totals <- tibble(
  metric = c(
    "mBC recurrences, no testing",
    "mBC recurrences, olaparib",
    "mBC recurrences avoided",
    "non-mBC recurrences, no testing",
    "non-mBC recurrences, olaparib",
    "non-mBC recurrences avoided",
    "Life-years, no testing",
    "Life-years, olaparib",
    "Life-years gained"
  ),
  published = c(
    scalar_input("published_mbc_no_testing"),
    scalar_input("published_mbc_olaparib"),
    scalar_input("published_mbc_prevented"),
    scalar_input("published_non_mbc_no_testing"),
    scalar_input("published_non_mbc_olaparib"),
    scalar_input("published_non_mbc_prevented"),
    scalar_input("published_life_years_no_testing"),
    scalar_input("published_life_years_olaparib"),
    scalar_input("published_life_years_gained")
  )
)

benchmark_comparison <- calculated_totals |>
  left_join(published_totals, by = "metric") |>
  mutate(
    difference = calculated - published,
    relative_difference = difference / published
  )

kable(
  benchmark_comparison |>
    transmute(
      Metric = metric,
      Calculated = fmt_count(calculated),
      Published = fmt_count(published),
      Difference = fmt_count(difference),
      `Relative difference` = fmt_pct(relative_difference, accuracy = 0.1)
    ),
  align = c("l", "r", "r", "r", "r")
)

Metric	Calculated	Published	Difference	Relative difference
mBC recurrences, no testing	1,220	1,218	2	0.2%
mBC recurrences, olaparib	947	946	1	0.1%
mBC recurrences avoided	273	272	1	0.3%
non-mBC recurrences, no testing	304	304	0	0.0%
non-mBC recurrences, olaparib	238	236	2	0.7%
non-mBC recurrences avoided	66	68	-2	-2.6%
Life-years, no testing	99,055	99,084	-29	0.0%
Life-years, olaparib	107,646	107,761	-115	-0.1%
Life-years gained	8,591	8,677	-86	-1.0%

The reconstruction is close for recurrence outputs because the published table gives subtype-specific recurrence rates. Life-years differ modestly because the report only exposes rounded life-year inputs and aggregate published totals.

4 Mathematical Model

This report uses an aggregate population-impact model rather than a cycle-based health-state model. The model first reconstructs all-age recurrence outputs from subtype-specific published inputs, then redistributes the treatment effect across age strata while preserving the published all-age treatment effect on the log-hazard-ratio scale.

Let \(s \in \mathcal{S}\) index subtype strata, where \(\mathcal{S} = \{\text{HR-positive}, \text{TNBC}\}\), and let \(a \in \mathcal{A}\) index age strata, where \(\mathcal{A} = \{<45, \ge 45\}\). Let \(e \in \mathcal{E}\) index recurrence endpoints, where \(\mathcal{E} = \{\text{mBC recurrence}, \text{non-mBC recurrence}\}\).

For each subtype \(s\):

\(N_s\) is the number of olaparib-eligible patients.
\(w_{s,a}\) is the share of subtype \(s\) in age stratum \(a\), with \(\sum_a w_{s,a} = 1\).
\(r^0_{s,e}\) is the no-testing/no-olaparib recurrence rate for endpoint \(e\).

The expected untreated recurrence count in each subtype-age-endpoint cell is:

\[ B_{s,a,e} = N_s w_{s,a} r^0_{s,e}. \]

4.1 Calibrating Age-Specific Treatment Effects

The published all-age recurrence effect is represented as a base hazard ratio:

\[ H_0 = 1 - \frac{P^{\text{pub}}_{\text{mBC}} + P^{\text{pub}}_{\text{non-mBC}}} {B^{\text{pub}}_{\text{mBC}} + B^{\text{pub}}_{\text{non-mBC}}}, \]

where \(P^{\text{pub}}_e\) is the published number of recurrences avoided for endpoint \(e\), and \(B^{\text{pub}}_e\) is the published no-testing recurrence count for endpoint \(e\). Let \(L = \log(H_0)\).

The age-modifier meta-regression estimates the older-versus-younger log-hazard-ratio contrast:

\[ \delta = \log(H_{\ge 45}) - \log(H_{<45}). \]

Let \(W_a\) be the total olaparib-eligible cohort share in age stratum \(a\):

\[ W_a = \frac{\sum_s N_s w_{s,a}}{\sum_s N_s}. \]

The age-specific hazard ratios are centered around the published all-age effect:

\[ \log(H_{<45}) = L - W_{\ge 45}\delta, \]

\[ \log(H_{\ge 45}) = L + W_{<45}\delta. \]

This construction preserves both the estimated age contrast and the all-age anchor:

\[ \log(H_{\ge 45}) - \log(H_{<45}) = \delta, \]

\[ W_{<45}\log(H_{<45}) + W_{\ge 45}\log(H_{\ge 45}) = L. \]

4.2 Recurrences Avoided

For the age-stratified treatment-effect analysis, expected olaparib-treated recurrences are:

\[ T_{s,a,e} = B_{s,a,e} H_a. \]

Recurrences avoided are therefore:

\[ P_{s,a,e} = B_{s,a,e} - T_{s,a,e} = B_{s,a,e}(1 - H_a). \]

Aggregate age-stratified recurrence outputs are:

\[ P_{a,e} = \sum_s P_{s,a,e}. \]

The homogeneous-effect counterfactual used in the HTE communication section applies the same all-age hazard ratio \(H_0\) to every age stratum:

\[ P^{\text{hom}}_{s,a,e} = B_{s,a,e}(1 - H_0). \]

This counterfactual keeps age-specific life expectancy but removes age-specific treatment-effect heterogeneity.

4.3 Life-Years Saved

The published model gives an aggregate life-year gain per recurrence avoided:

\[ c_0 = \frac{Y^{\text{pub}}} {P^{\text{pub}}_{\text{mBC}} + P^{\text{pub}}_{\text{non-mBC}}}, \]

where \(Y^{\text{pub}}\) is the published total life-years gained.

Let \(\ell_a\) be the remaining life expectancy for the representative age of stratum \(a\), taken from the US female life table. The age-specific life-year gain per recurrence avoided is scaled from \(c_0\) by relative remaining life expectancy:

\[ c_a = c_0 \frac{\ell_a}{\sum_a W_a \ell_a}. \]

Finally, life-years saved in age stratum \(a\) are:

\[ Y_a = c_a \sum_e P_{a,e}. \]

This life-year translation is directional: it is designed to illustrate how age-specific recurrence prevention changes expected population impact, not to replace a disease-specific survival model.

5 Age-Modifier Calibration

The local meta-regression estimates an older-versus-younger age contrast of 0.2073 on the log-hazard-ratio scale, where >=45 years has the higher log-HR and therefore the smaller recurrence benefit. The deterministic base case uses the point estimate and communicates the uncertainty separately: standard error 0.0984, model p-value 0.0352, and permutation-test p-value 0.0604.

Code

published_total_recurrences_no_testing <-
  scalar_input("published_mbc_no_testing") +
  scalar_input("published_non_mbc_no_testing")

published_total_recurrences_prevented <-
  scalar_input("published_mbc_prevented") +
  scalar_input("published_non_mbc_prevented")

base_recurrence_hr <- 1 - (
  published_total_recurrences_prevented /
    published_total_recurrences_no_testing
)

age_distribution <- model_inputs |>
  filter(category == "age_distribution") |>
  transmute(
    subtype,
    age_group,
    age_share = as.numeric(value)
  )

age_weights <- subtype_inputs |>
  select(subtype, patients) |>
  inner_join(age_distribution, by = "subtype") |>
  group_by(age_group) |>
  summarise(
    patients = sum(patients * age_share),
    cohort_share = patients / sum(subtype_inputs$patients),
    .groups = "drop"
  ) |>
  arrange(factor(age_group, levels = c("<45", ">=45")))

delta_log_hr <- scalar_input("age_contrast_log_hr")
weight_young <- age_weights$cohort_share[age_weights$age_group == "<45"]
weight_older <- age_weights$cohort_share[age_weights$age_group == ">=45"]
base_log_hr <- log(base_recurrence_hr)

age_effects <- age_weights |>
  mutate(
    log_hazard_ratio = if_else(
      age_group == "<45",
      base_log_hr - weight_older * delta_log_hr,
      base_log_hr + weight_young * delta_log_hr
    ),
    hazard_ratio = exp(log_hazard_ratio),
    recurrence_reduction = 1 - hazard_ratio
  )

age_calibration_check <- age_effects |>
  summarise(
    weighted_log_hr = sum(cohort_share * log_hazard_ratio),
    base_log_hr = base_log_hr,
    difference = weighted_log_hr - base_log_hr,
    observed_delta = log_hazard_ratio[age_group == ">=45"] -
      log_hazard_ratio[age_group == "<45"]
  )

kable(
  age_effects |>
    transmute(
      `Age group` = age_group,
      `Cohort share` = fmt_pct(cohort_share),
      `Log-HR` = fmt_decimal(log_hazard_ratio, 3),
      HR = fmt_decimal(hazard_ratio, 3),
      `Relative recurrence reduction` = fmt_pct(recurrence_reduction)
    ),
  align = c("l", "r", "r", "r", "r")
)

Age group	Cohort share	Log-HR	HR	Relative recurrence reduction
<45	50.0%	-0.356	0.700	30.0%
>=45	50.0%	-0.149	0.861	13.9%

Calibration check: the weighted log-HR is -0.252817, the base log-HR is -0.252817, and the age contrast is 0.2073.

6 Age-Stratified Recurrences

The age-stratified extension uses subtype-specific untreated recurrence rates from the published model, then applies the age-specific olaparib recurrence HRs above. This keeps subtype-specific baseline recurrence behavior while making treatment benefit age-stratified.

Code

baseline_recurrence_rates <- subtype_inputs |>
  select(subtype, patients, no_mbc_rate, no_non_mbc_rate) |>
  pivot_longer(
    cols = c(no_mbc_rate, no_non_mbc_rate),
    names_to = "endpoint",
    values_to = "baseline_rate"
  ) |>
  mutate(
    endpoint = recode(
      endpoint,
      no_mbc_rate = "mBC recurrences",
      no_non_mbc_rate = "non-mBC recurrences"
    )
  )

age_recurrence_cells <- baseline_recurrence_rates |>
  inner_join(age_distribution, by = "subtype") |>
  inner_join(
    age_effects |> select(age_group, hazard_ratio, recurrence_reduction),
    by = "age_group"
  ) |>
  mutate(
    baseline_recurrences = patients * age_share * baseline_rate,
    olaparib_recurrences = baseline_recurrences * hazard_ratio,
    recurrences_prevented = baseline_recurrences - olaparib_recurrences
  )

age_recurrence_summary <- age_recurrence_cells |>
  group_by(age_group, endpoint) |>
  summarise(
    baseline_recurrences = sum(baseline_recurrences),
    olaparib_recurrences = sum(olaparib_recurrences),
    recurrences_prevented = sum(recurrences_prevented),
    .groups = "drop"
  )

age_output_wide <- age_recurrence_summary |>
  select(age_group, endpoint, recurrences_prevented) |>
  pivot_wider(names_from = endpoint, values_from = recurrences_prevented)

kable(
  age_recurrence_summary |>
    transmute(
      `Age group` = age_group,
      Endpoint = endpoint,
      `No testing recurrences` = fmt_count(baseline_recurrences),
      `Testing and olaparib recurrences` = fmt_count(olaparib_recurrences),
      `Recurrences avoided` = fmt_count(recurrences_prevented)
    ),
  align = c("l", "l", "r", "r", "r")
)

Age group	Endpoint	No testing recurrences	Testing and olaparib recurrences	Recurrences avoided
<45	mBC recurrences	610	427	183
<45	non-mBC recurrences	152	106	46
>=45	mBC recurrences	610	525	85
>=45	non-mBC recurrences	152	131	21

Code

ggplot(
  age_recurrence_summary,
  aes(x = age_group, y = recurrences_prevented, fill = endpoint)
) +
  geom_col(position = "dodge", width = 0.7) +
  scale_y_continuous(labels = comma) +
  scale_fill_manual(values = c("#1b7f79", "#be6a15")) +
  labs(
    x = "Age group",
    y = "Recurrences avoided",
    fill = "Endpoint",
    title = "Exploratory age-stratified recurrence impact"
  ) +
  theme_minimal(base_size = 12) +
  theme(
    legend.position = "bottom",
    panel.grid.minor = element_blank()
  )

7 Age-Specific Life-Year Translation

The published base case reports 8,677 life-years gained for 340 total recurrences avoided, or 25.5 life-years per recurrence avoided. This aggregate reconstruction scales that relationship by age-specific remaining life expectancy from the female US life table.

Code

representative_ages <- model_inputs |>
  filter(category == "representative_age") |>
  transmute(
    age_group,
    representative_age = as.integer(round(as.numeric(value))),
    source_note,
    assumption_note
  )

life_expectancy_by_age <- representative_ages |>
  left_join(
    life_table |> select(age, life_expectancy_years),
    by = c("representative_age" = "age")
  )

reference_life_expectancy <- age_effects |>
  select(age_group, cohort_share) |>
  left_join(life_expectancy_by_age, by = "age_group") |>
  summarise(
    value = sum(cohort_share * life_expectancy_years)
  ) |>
  pull(value)

base_life_years_per_recurrence <-
  scalar_input("published_life_years_gained") /
  published_total_recurrences_prevented

life_year_translation <- age_effects |>
  select(age_group, cohort_share) |>
  left_join(life_expectancy_by_age, by = "age_group") |>
  mutate(
    life_years_per_recurrence =
      base_life_years_per_recurrence *
      life_expectancy_years /
      reference_life_expectancy
  )

life_years_by_age <- age_recurrence_summary |>
  group_by(age_group) |>
  summarise(
    total_recurrences_prevented = sum(recurrences_prevented),
    .groups = "drop"
  ) |>
  left_join(life_year_translation, by = "age_group") |>
  mutate(
    life_years_saved = total_recurrences_prevented * life_years_per_recurrence
  )

kable(
  life_year_translation |>
    transmute(
      `Age group` = age_group,
      `Representative age` = representative_age,
      `Female life expectancy` = fmt_years(life_expectancy_years),
      `Life-years per recurrence avoided` = fmt_years(life_years_per_recurrence)
    ),
  align = c("l", "r", "r", "r")
)

Age group	Representative age	Female life expectancy	Life-years per recurrence avoided
<45	42	40.8	30.2
>=45	56	28.2	20.8

Code

main_outputs <- age_output_wide |>
  left_join(
    life_years_by_age |> select(age_group, life_years_saved),
    by = "age_group"
  )

main_outputs <- bind_rows(
  main_outputs,
  main_outputs |>
    summarise(
      age_group = "Total",
      `mBC recurrences` = sum(`mBC recurrences`),
      `non-mBC recurrences` = sum(`non-mBC recurrences`),
      life_years_saved = sum(life_years_saved)
    )
)

kable(
  main_outputs |>
    transmute(
      `Age group` = age_group,
      `mBC recurrences avoided` = fmt_count(`mBC recurrences`),
      `non-mBC recurrences avoided` = fmt_count(`non-mBC recurrences`),
      `Life-years saved` = fmt_count(life_years_saved)
    ),
  align = c("l", "r", "r", "r")
)

Age group	mBC recurrences avoided	non-mBC recurrences avoided	Life-years saved
<45	183	46	6,899
>=45	85	21	2,201
Total	267	67	9,100

8 Subtype-by-Age Detail

Code

subtype_age_detail <- age_recurrence_cells |>
  group_by(subtype, age_group, endpoint) |>
  summarise(recurrences_prevented = sum(recurrences_prevented), .groups = "drop") |>
  pivot_wider(names_from = endpoint, values_from = recurrences_prevented)

kable(
  subtype_age_detail |>
    transmute(
      Subtype = subtype,
      `Age group` = age_group,
      `mBC recurrences avoided` = fmt_count(`mBC recurrences`),
      `non-mBC recurrences avoided` = fmt_count(`non-mBC recurrences`)
    ),
  align = c("l", "l", "r", "r")
)

Subtype	Age group	mBC recurrences avoided	non-mBC recurrences avoided
HR-positive	<45	88	22
HR-positive	>=45	41	10
TNBC	<45	95	24
TNBC	>=45	44	11

9 Why Age-Stratified Treatment Effects Matter

The age-stratified treatment-effect estimates are used here to improve population-impact estimation, not to define an age-based treatment rule. In this first-pass analysis, olaparib eligibility and treatment uptake are unchanged: eligible patients in both age groups remain candidates for olaparib, the >=45 years stratum still has a positive predicted recurrence reduction, and no better alternative treatment strategy for >=45 years is modeled.

Two distinct age-related mechanisms affect projected life-years saved. First, if recurrence is avoided earlier in life, more remaining life-years can be preserved even when the treatment effect is identical at every age. Second, if treatment benefit is heterogeneous by age, the model avoids a different number of recurrences in each age group before life expectancy is even applied. The counterfactual below separates those mechanisms.

Code

lt45_impact_share <- main_outputs |>
  filter(age_group == "<45") |>
  transmute(
    recurrence_share =
      (`mBC recurrences` + `non-mBC recurrences`) /
      sum(main_outputs$`mBC recurrences`[main_outputs$age_group != "Total"] +
            main_outputs$`non-mBC recurrences`[main_outputs$age_group != "Total"]),
    life_year_share =
      life_years_saved /
      sum(main_outputs$life_years_saved[main_outputs$age_group != "Total"])
  )

communication_table <- tibble(
  Question = c(
    "Does this change who should receive olaparib?",
    "Does this change predicted recurrences avoided?",
    "Does this change predicted life-years saved?",
    "Does this help when applying the model to another population?",
    "Does this change how uncertainty should be communicated?",
    "Does this show value in collecting subgroup evidence?"
  ),
  Answer = c(
    "No. The analysis is not an age-based rule for withholding treatment from eligible patients in the >=45 years stratum.",
    "Yes. The same all-age treatment benefit is redistributed across age strata according to the calibrated treatment-effect contrast.",
    "Yes. Life-years depend on both recurrence reductions and remaining life expectancy, so age-stratified effects can materially change the life-year estimate.",
    "Yes. A population with a different age mix may not have the same all-age population impact, even under the same treatment strategy.",
    "Yes. The report can separate the published-model benchmark from the uncertain age-stratified extension.",
    "Yes. Subgroup evidence can improve population-impact estimates even when it does not justify a different treatment rule."
  )
)

kable(communication_table, align = c("l", "l"))

Question	Answer
Does this change who should receive olaparib?	No. The analysis is not an age-based rule for withholding treatment from eligible patients in the >=45 years stratum.
Does this change predicted recurrences avoided?	Yes. The same all-age treatment benefit is redistributed across age strata according to the calibrated treatment-effect contrast.
Does this change predicted life-years saved?	Yes. Life-years depend on both recurrence reductions and remaining life expectancy, so age-stratified effects can materially change the life-year estimate.
Does this help when applying the model to another population?	Yes. A population with a different age mix may not have the same all-age population impact, even under the same treatment strategy.
Does this change how uncertainty should be communicated?	Yes. The report can separate the published-model benchmark from the uncertain age-stratified extension.
Does this show value in collecting subgroup evidence?	Yes. Subgroup evidence can improve population-impact estimates even when it does not justify a different treatment rule.

Code

homogeneous_recurrence_summary <- age_recurrence_cells |>
  group_by(age_group, endpoint) |>
  summarise(
    baseline_recurrences = sum(baseline_recurrences),
    .groups = "drop"
  ) |>
  mutate(
    recurrences_prevented = baseline_recurrences * (1 - base_recurrence_hr)
  )

homogeneous_life_years_by_age <- homogeneous_recurrence_summary |>
  group_by(age_group) |>
  summarise(
    homogeneous_recurrences_prevented = sum(recurrences_prevented),
    .groups = "drop"
  ) |>
  left_join(
    life_year_translation |> select(age_group, life_years_per_recurrence),
    by = "age_group"
  ) |>
  mutate(
    homogeneous_life_years_saved =
      homogeneous_recurrences_prevented * life_years_per_recurrence
  )

hte_decomposition <- life_years_by_age |>
  select(
    age_group,
    hte_recurrences_prevented = total_recurrences_prevented,
    hte_life_years_saved = life_years_saved
  ) |>
  left_join(homogeneous_life_years_by_age, by = "age_group") |>
  mutate(
    recurrence_increment_from_hte =
      hte_recurrences_prevented - homogeneous_recurrences_prevented,
    life_year_increment_from_hte =
      hte_life_years_saved - homogeneous_life_years_saved
  )

hte_decomposition_display <- hte_decomposition |>
  bind_rows(
    hte_decomposition |>
      summarise(
        age_group = "Total",
        hte_recurrences_prevented = sum(hte_recurrences_prevented),
        homogeneous_recurrences_prevented =
          sum(homogeneous_recurrences_prevented),
        recurrence_increment_from_hte =
          sum(recurrence_increment_from_hte),
        hte_life_years_saved = sum(hte_life_years_saved),
        homogeneous_life_years_saved =
          sum(homogeneous_life_years_saved),
        life_year_increment_from_hte =
          sum(life_year_increment_from_hte)
      )
  )

lt45_homogeneous_life_year_share <- hte_decomposition |>
  filter(age_group == "<45") |>
  summarise(
    share = homogeneous_life_years_saved /
      sum(hte_decomposition$homogeneous_life_years_saved)
  ) |>
  pull(share)

lt45_life_year_share_increment_from_hte <-
  lt45_impact_share$life_year_share - lt45_homogeneous_life_year_share

lt45_recurrence_increment_from_hte <- hte_decomposition |>
  filter(age_group == "<45") |>
  pull(recurrence_increment_from_hte)

total_life_year_increment_from_hte <- hte_decomposition |>
  summarise(total = sum(life_year_increment_from_hte)) |>
  pull(total)

kable(
  hte_decomposition_display |>
    transmute(
      `Age group` = age_group,
      `Recurrences avoided with homogeneous effect` =
        fmt_count(homogeneous_recurrences_prevented),
      `Recurrences avoided with age-specific effect` =
        fmt_count(hte_recurrences_prevented),
      `Recurrence difference from HTE` =
        fmt_count(recurrence_increment_from_hte),
      `Life-years saved with homogeneous effect` =
        fmt_count(homogeneous_life_years_saved),
      `Life-years saved with age-specific effect` =
        fmt_count(hte_life_years_saved),
      `Life-year difference from HTE` =
        fmt_count(life_year_increment_from_hte)
    ),
  align = c("l", "r", "r", "r", "r", "r", "r")
)

Age group	Recurrences avoided with homogeneous effect	Recurrences avoided with age-specific effect	Recurrence difference from HTE	Life-years saved with homogeneous effect	Life-years saved with age-specific effect	Life-year difference from HTE
<45	170	228	58	5,139	6,899	1,759
>=45	170	106	-65	3,548	2,201	-1,347
Total	340	334	-6	8,688	9,100	412

In this run, <45 years represents 50.0% of the modeled eligible population. With age-specific life expectancy but a homogeneous treatment effect, that group accounts for 59.2% of life-years saved. With age-specific treatment effects, it accounts for 68.4% of avoided recurrences and 75.8% of life-years saved. That is an additional 16.7 percentage points shift toward <45 years attributable to treatment-effect heterogeneity, over and above the fact that younger patients have more life-years left. In counts, the age-specific treatment effect moves about 58 additional avoided recurrences into <45 years and adds 412 life-years in this aggregate approximation.

10 Sensitivity to the Age Contrast

The base-case age contrast is a single point estimate from an underpowered, marginally significant meta-regression (see Age-Modifier Calibration). This section recomputes the age-stratified recurrence and life-year pipeline at the lower and upper bounds of the age contrast’s 95% confidence interval, and at a null (no-heterogeneity) benchmark, to show how much of the reported <45 years shift depends on the exact point estimate used in the base case.

Code

run_age_scenario <- function(delta_log_hr) {
  log_h_lt45 <- base_log_hr - weight_older * delta_log_hr
  log_h_ge45 <- base_log_hr + weight_young * delta_log_hr

  scenario_age_effects <- age_weights |>
    mutate(
      log_hazard_ratio = if_else(age_group == "<45", log_h_lt45, log_h_ge45),
      hazard_ratio = exp(log_hazard_ratio)
    )

  scenario_cells <- baseline_recurrence_rates |>
    inner_join(age_distribution, by = "subtype", relationship = "many-to-many") |>
    inner_join(
      scenario_age_effects |> select(age_group, hazard_ratio),
      by = "age_group"
    ) |>
    mutate(
      baseline_recurrences = patients * age_share * baseline_rate,
      recurrences_prevented = baseline_recurrences * (1 - hazard_ratio)
    )

  scenario_recurrence_summary <- scenario_cells |>
    group_by(age_group) |>
    summarise(recurrences_prevented = sum(recurrences_prevented), .groups = "drop")

  scenario_reference_le <- scenario_age_effects |>
    select(age_group, cohort_share) |>
    left_join(life_expectancy_by_age, by = "age_group") |>
    summarise(value = sum(cohort_share * life_expectancy_years)) |>
    pull(value)

  scenario_life_years <- scenario_age_effects |>
    select(age_group, cohort_share) |>
    left_join(life_expectancy_by_age, by = "age_group") |>
    mutate(
      life_years_per_recurrence =
        base_life_years_per_recurrence * life_expectancy_years / scenario_reference_le
    ) |>
    left_join(scenario_recurrence_summary, by = "age_group") |>
    mutate(life_years_saved = recurrences_prevented * life_years_per_recurrence)

  tibble(
    lt45_hazard_ratio =
      scenario_age_effects$hazard_ratio[scenario_age_effects$age_group == "<45"],
    ge45_hazard_ratio =
      scenario_age_effects$hazard_ratio[scenario_age_effects$age_group == ">=45"],
    lt45_recurrence_share =
      scenario_recurrence_summary$recurrences_prevented[
        scenario_recurrence_summary$age_group == "<45"
      ] / sum(scenario_recurrence_summary$recurrences_prevented),
    lt45_life_year_share =
      scenario_life_years$life_years_saved[scenario_life_years$age_group == "<45"] /
      sum(scenario_life_years$life_years_saved),
    total_life_years_saved = sum(scenario_life_years$life_years_saved)
  )
}

sensitivity_scenarios <- tibble(
  scenario = c(
    "No heterogeneity (life expectancy only)",
    "Age contrast: lower 95% CI bound",
    "Age contrast: point estimate (base case)",
    "Age contrast: upper 95% CI bound"
  ),
  delta_log_hr = c(
    0,
    scalar_input("age_contrast_ci_low"),
    scalar_input("age_contrast_log_hr"),
    scalar_input("age_contrast_ci_high")
  )
)

sensitivity_scenarios <- bind_cols(
  sensitivity_scenarios,
  bind_rows(lapply(sensitivity_scenarios$delta_log_hr, run_age_scenario))
) |>
  mutate(
    life_year_share_increment =
      lt45_life_year_share -
      lt45_life_year_share[scenario == "No heterogeneity (life expectancy only)"]
  )

kable(
  sensitivity_scenarios |>
    transmute(
      Scenario = scenario,
      `Log-HR contrast` = fmt_decimal(delta_log_hr, 4),
      `HR <45` = fmt_decimal(lt45_hazard_ratio, 3),
      `HR >=45` = fmt_decimal(ge45_hazard_ratio, 3),
      `<45 recurrence share` = fmt_pct(lt45_recurrence_share),
      `<45 life-year share` = fmt_pct(lt45_life_year_share),
      `Shift vs. no heterogeneity` = fmt_pp(life_year_share_increment)
    ),
  align = c("l", "r", "r", "r", "r", "r", "r")
)

Scenario	Log-HR contrast	HR <45	HR >=45	<45 recurrence share	<45 life-year share	Shift vs. no heterogeneity
No heterogeneity (life expectancy only)	0.0000	0.777	0.777	50.0%	59.2%	0.0 percentage points
Age contrast: lower 95% CI bound	0.0144	0.771	0.782	51.3%	60.4%	1.2 percentage points
Age contrast: point estimate (base case)	0.2073	0.700	0.861	68.4%	75.8%	16.7 percentage points
Age contrast: upper 95% CI bound	0.4002	0.636	0.949	87.6%	91.1%	32.0 percentage points

At the base-case point estimate, treatment-effect heterogeneity shifts an additional 16.7 percentage points of life-years saved toward <45 years, on top of the life-expectancy-only baseline. At the lower bound of the age contrast’s 95% confidence interval, that additional shift falls to 1.2 percentage points — close to zero — while at the upper bound it grows to 32.0 percentage points. Because the age contrast comes from a meta-regression of 21 observations drawn from only 9 trials (model p = 0.0352; permutation p = 0.0604), the treatment-effect-heterogeneity component of the <45 years life-year shift should be read as this wide range rather than as the fixed point-estimate value reported above.

11 Sensitivity to the Age-Distribution Proxy

The published Kasle et al. model is not age-stratified: it uses a single representative age (42, the OlympiA trial average) for the whole eligible cohort’s lifetime horizon, so there is no <45/>=45 population split in the original paper to reproduce. The 10%/90% split used in an earlier version of this exploratory extension was this project’s own first-pass proxy (general-population ACS statistics), not a published input. The Published Model Benchmark section above is unaffected by any age-distribution assumption and remains the directly comparable-to-Kasle output.

This section instead compares the exploratory age-stratified extension’s own outputs under that earlier general-population proxy and the current gBRCA-matched proxy, to make clear how much of the extension’s conclusions follow from this replaceable assumption rather than from the age-contrast calibration itself.

Code

run_proxy_scenario <- function(lt45_share, representative_age_ge45_years) {
  alt_age_distribution <- tibble(
    subtype = rep(c("HR-positive", "TNBC"), each = 2),
    age_group = rep(c("<45", ">=45"), times = 2),
    age_share = rep(c(lt45_share, 1 - lt45_share), times = 2)
  )

  alt_age_weights <- subtype_inputs |>
    select(subtype, patients) |>
    inner_join(alt_age_distribution, by = "subtype") |>
    group_by(age_group) |>
    summarise(
      patients = sum(patients * age_share),
      cohort_share = patients / sum(subtype_inputs$patients),
      .groups = "drop"
    )

  alt_weight_young <- alt_age_weights$cohort_share[alt_age_weights$age_group == "<45"]
  alt_weight_older <- alt_age_weights$cohort_share[alt_age_weights$age_group == ">=45"]

  alt_age_effects <- alt_age_weights |>
    mutate(
      log_hazard_ratio = if_else(
        age_group == "<45",
        base_log_hr - alt_weight_older * delta_log_hr,
        base_log_hr + alt_weight_young * delta_log_hr
      ),
      hazard_ratio = exp(log_hazard_ratio)
    )

  alt_cells <- baseline_recurrence_rates |>
    inner_join(alt_age_distribution, by = "subtype", relationship = "many-to-many") |>
    inner_join(
      alt_age_effects |> select(age_group, hazard_ratio),
      by = "age_group"
    ) |>
    mutate(
      baseline_recurrences = patients * age_share * baseline_rate,
      recurrences_prevented = baseline_recurrences * (1 - hazard_ratio)
    )

  alt_recurrence_summary <- alt_cells |>
    group_by(age_group) |>
    summarise(recurrences_prevented = sum(recurrences_prevented), .groups = "drop")

  alt_life_expectancy_by_age <- tibble(
    age_group = c("<45", ">=45"),
    representative_age = c(
      as.integer(round(scalar_input("representative_age_lt45"))),
      as.integer(round(representative_age_ge45_years))
    )
  ) |>
    left_join(life_table |> select(age, life_expectancy_years), by = c("representative_age" = "age"))

  alt_reference_le <- alt_age_effects |>
    select(age_group, cohort_share) |>
    left_join(alt_life_expectancy_by_age, by = "age_group") |>
    summarise(value = sum(cohort_share * life_expectancy_years)) |>
    pull(value)

  alt_life_years <- alt_age_effects |>
    select(age_group, cohort_share) |>
    left_join(alt_life_expectancy_by_age, by = "age_group") |>
    mutate(
      life_years_per_recurrence =
        base_life_years_per_recurrence * life_expectancy_years / alt_reference_le
    ) |>
    left_join(alt_recurrence_summary, by = "age_group") |>
    mutate(life_years_saved = recurrences_prevented * life_years_per_recurrence)

  tibble(
    lt45_population_share = alt_weight_young,
    lt45_recurrence_share =
      alt_recurrence_summary$recurrences_prevented[alt_recurrence_summary$age_group == "<45"] /
      sum(alt_recurrence_summary$recurrences_prevented),
    lt45_life_year_share =
      alt_life_years$life_years_saved[alt_life_years$age_group == "<45"] /
      sum(alt_life_years$life_years_saved),
    total_life_years_saved = sum(alt_life_years$life_years_saved)
  )
}

distribution_scenarios <- tibble(
  scenario = c(
    "Previous version: ACS general-population proxy (10% / 90%, representative age 63)",
    "Current base case: gBRCA-matched proxy (Morganti et al. 2024; 50% / 50%, representative age 56)"
  ),
  lt45_share = c(0.10, 0.50),
  representative_age_ge45_years = c(63, 56)
)

distribution_scenarios <- bind_cols(
  distribution_scenarios,
  bind_rows(
    Map(
      run_proxy_scenario,
      distribution_scenarios$lt45_share,
      distribution_scenarios$representative_age_ge45_years
    )
  )
)

kable(
  distribution_scenarios |>
    transmute(
      Scenario = scenario,
      `<45 population share` = fmt_pct(lt45_population_share),
      `<45 recurrence share` = fmt_pct(lt45_recurrence_share),
      `<45 life-year share` = fmt_pct(lt45_life_year_share),
      `Total life-years saved` = fmt_count(total_life_years_saved)
    ),
  align = c("l", "r", "r", "r", "r")
)

Scenario	<45 population share	<45 recurrence share	<45 life-year share	Total life-years saved
Previous version: ACS general-population proxy (10% / 90%, representative age 63)	10.0%	16.0%	25.9%	9,030
Current base case: gBRCA-matched proxy (Morganti et al. 2024; 50% / 50%, representative age 56)	50.0%	68.4%	75.8%	9,100

Under the previous ACS-based proxy, <45 years accounted for 25.9% of life-years saved; under the current gBRCA-matched proxy, that rises to 75.8%. Both figures use the same base-case age contrast (0.2073); the difference between them is attributable entirely to the age-distribution and representative-age assumptions, not to the treatment-effect calibration. Because the age-distribution proxy is now matched on gBRCA1/2 status rather than drawn from the general breast-cancer population, the current base case is judged more representative of this model’s population — but readers who want the prior version’s assumptions for their own comparison can reconstruct it from this table.

12 Interpretation

Under the first-pass age-distribution proxy, the calibrated age-specific recurrence HR is lower for <45 years than for >=45 years, so more benefit concentrates in the younger stratum than its population share alone would imply. The total age-stratified recurrence outputs remain close to the published aggregate benchmark because the age contrast is centered around the published all-age recurrence effect on the log-HR scale.

The life-year output is more exploratory than the recurrence output. It combines the published aggregate life-year-per-recurrence relationship with female general-population life expectancy, so it should be treated as a directional translation rather than a disease-specific survival projection. The main interpretive claim is therefore about estimating expected population impact more accurately and transparently, not changing olaparib treatment recommendations by age.

13 Limitations and Replaceable Inputs

This is an aggregate reconstruction, not the original Excel health-state model.
Published clinical input percentages are rounded, so exact reproduction of paper totals is not expected.
The age distribution is now matched on gBRCA1/2 status and HER2-negative early breast cancer (Morganti et al. 2024), but the source reports only overall-cohort median/mean age, not an exact <45/>=45 split or subtype-specific age moments, so 50%/50% is a round approximation rather than a directly reported figure. It is also not restricted to the olaparib-eligible subgroup specifically, which had a younger median age (39) in the same source.
Representative ages are placeholders and should be replaced with stratum-specific mean or median ages when available. representative_age_ge45 is now derived (56) from the same Morganti et al. 2024 mean/SD used for the age-distribution proxy, via a normal-distribution approximation, rather than a directly reported figure. representative_age_lt45 (42) is kept from the OlympiA trial average because it is directly reported rather than derived; applying the same normal-approximation method used for representative_age_ge45 to the <45 stratum would instead give about 34.5, so the two representative ages currently rest on different methods and a single consistent source would be an improvement.
The age-stratified treatment-effect evidence comes from a small meta-regression and should be communicated as uncertain: 21 observations from 9 trials of metastatic/advanced-disease PARP-inhibitor PFS (not adjuvant olaparib-specific, disease-free-survival evidence), several trials contributing multiple correlated rows. See Sensitivity to the Age Contrast for how much the headline <45 years life-year shift depends on this estimate’s confidence interval.
The recurrence translation uses 1 - HR as an aggregate approximation.
Life-years use a female general-population life table, not breast-cancer-specific survival.