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Biomarker Matching in Lung-MAP

Learn to define and estimate the proportion of screened Lung-MAP patients who could enter a biomarker-matched randomized comparison, while keeping each stage of the screening-to-assignment pathway distinct.

Advanced 12 min read

What You'll Learn

  • Define a biomarker-matching rate with an explicit screened-patient denominator.
  • Separate a genomic match from clinical eligibility, an open substudy, and randomization.
  • Calculate conditional and overall rates from a screening-to-assignment flow.
  • Handle overlapping biomarkers without counting the same patient twice.
  • Quantify uncertainty in an observed proportion and recognize limits to interpretation.
  • Diagnose common errors in comparing matching rates across protocol versions or sites.

From a Genomic Result to a Randomized Comparison

Lung-MAP used a shared screening platform to direct patients with advanced squamous lung cancer toward substudies, including biomarker-matched comparisons. The key question here is narrower than whether genomic testing found an alteration: among the patients screened, how many could proceed to a biomarker-matched randomized treatment comparison? Answering it requires tracking several distinct events rather than treating “matched” as a single outcome.

The earlier material on Lung-MAP's screening protocol for squamous lung cancer establishes the setting and the role of genomic screening. For measuring matching, the important practical point is that the routing rules belong to a particular protocol version. Alteration definitions, available substudies, eligibility criteria, and assignment rules may change; a reported rate therefore needs a specified period or protocol version.

A genomic result can indicate that a patient fits a substudy's biomarker definition, but that alone does not show that the patient was eligible to enroll, that the substudy was open, or that the patient was randomized. These distinctions matter when interpreting a “matching rate”: a high rate of biomarker findings can coexist with a lower rate of entry into a randomized comparison.

Definition: For a specified population of screened patients and a specified protocol version, a biomarker match occurs when an evaluable genomic result meets the protocol's biomarker rule for at least one relevant substudy. A patient is eligible for a matched randomized comparison only if the patient also meets that substudy's applicable clinical and operational criteria, including its being open to enrollment. The matched-randomization rate is the number of screened patients randomized in a biomarker-matched comparison divided by the number screened in the stated population.

These definitions distinguish related but non-equivalent quantities. A screening program might report the fraction with an evaluable result, the fraction with a biomarker match among evaluable patients, or the fraction of all screened patients randomized in a matched substudy. Each answers a different question. The denominator must be named whenever a rate is reported.

Define the Pathway and the Denominator

A useful flow separates the stages that occur between screening and randomization. Let \(S\) denote being screened, \(E\) having an evaluable genomic result, \(C\) meeting the clinical eligibility criteria for the relevant comparison, \(O\) having an applicable substudy open and available, and \(R\) being randomized. A patient can reach \(R\) only after the preceding requirements are met. Not every program records each stage in the same way, so the operational definitions should be stated before calculation.

$$ P(R\mid S) = P(E\mid S)\, P(C\mid E,S)\, P(O\mid C,E,S)\, P(R\mid O,C,E,S) $$

This factorization is the chain rule for conditional probabilities. It does not assume that stages are independent: each factor is conditional on reaching the preceding stages. In a biomarker-matched analysis, the flow also requires a match \(M\), so the relevant sequence includes \(P(M\mid E,S)\) and eligibility and availability conditional on a match. Reporting the product is useful for showing where patients leave the pathway, but the overall rate is most directly calculated as the number randomized divided by the number screened.

In practice, assignment rules need particular care. If a patient has more than one alteration, the protocol may specify a priority rule, allow more than one possible substudy, or classify the patient in a separate group. Count people, not alteration records: one person who matches two categories must not be counted twice in a person-level rate. Also, a match is not necessarily a random assignment to the experimental treatment. Randomization means allocation to one of the comparison groups within the relevant substudy.

Worked Example: Calculating the Overall Matched-Randomization Rate

Suppose, hypothetically, that 1,000 patients are screened under one protocol version. Of these, 800 have an evaluable genomic result; 280 have at least one result meeting a matched-substudy rule; 240 of those 280 meet the relevant clinical criteria while a matching substudy is open; and 192 are randomized in that matched comparison. What proportion of all screened patients entered a biomarker-matched randomized comparison?

The numerator is the number randomized in matched comparisons, 192. The denominator is all 1,000 screened patients. Thus

$$ \widehat{P}(R\mid S)=\frac{192}{1000}=0.192=19.2\%. $$

So, in this hypothetical cohort, 19.2% of screened patients were randomized in a biomarker-matched comparison. The intermediate proportions clarify the pathway: \(800/1000=80.0\%\) had an evaluable result, \(280/800=35.0\%\) of evaluable patients had a match, and \(240/280=85.7\%\) of matched patients met the specified eligibility-and-availability condition. Finally, \(192/240=80.0\%\) of that eligible, available group were randomized.

The 35.0% figure is a biomarker-match rate among evaluable patients, not the overall matched-randomization rate. The 19.2% figure answers the question about all screened patients reaching randomization. Neither figure should be described without its denominator.

Deriving and Interpreting the Rate

For a fixed screened cohort, let \(N_S\) be the number of screened patients and \(N_R\) the number randomized in a biomarker-matched comparison. The observed rate is \(\hat{p}=N_R/N_S\). To see why the pathway factors cannot simply be substituted without checking their denominators, write each stage as a conditional proportion. If \(N_E\) have evaluable results, \(N_M\) have a match, \(N_A\) are matched and eligible with an available substudy, and \(N_R\) are randomized, then

$$ \frac{N_R}{N_S} = \frac{N_E}{N_S} \cdot \frac{N_M}{N_E} \cdot \frac{N_A}{N_M} \cdot \frac{N_R}{N_A}. $$

When each count refers to the same cohort and each stage is nested in the preceding stage, adjacent denominators cancel, leaving \(N_R/N_S\). This identity is a consistency check, not a license to combine incompatible summaries. For example, a match rate from one protocol period and an enrollment rate from another cannot be multiplied to reconstruct a meaningful cohort rate.

If screened patients are treated as independent observations from a wider population of similar patients, an interval can describe sampling uncertainty in the observed proportion. For a proportion \(\hat{p}\) based on \(N_S\) patients, the Wilson 95% interval is

$$ \frac{ \hat{p}+\frac{z^2}{2N_S} \ \pm\ z\sqrt{\frac{\hat{p}(1-\hat{p})}{N_S}+\frac{z^2}{4N_S^2}} }{ 1+\frac{z^2}{N_S} }, \qquad z=1.96. $$

This interval concerns the proportion under the stated sampling interpretation. It does not account for differences in site practices, protocol eras, or patient populations; nor does it turn a descriptive rate from one trial cohort into a universal probability for future patients.

Worked Example: An Uncertainty Interval for a Cohort Rate

Suppose, hypothetically, that 196 of 1,000 screened patients were randomized in matched comparisons. The observed rate is \(\hat{p}=196/1000=0.196\), or 19.6%. Using the Wilson interval with \(z=1.96\), the center is

$$ \frac{0.196+\frac{1.96^2}{2(1000)}}{1+\frac{1.96^2}{1000}} = \frac{0.197921}{1.003842} \approx 0.1972. $$

The half-width is

$$ \frac{1.96\sqrt{\frac{0.196(0.804)}{1000}+\frac{1.96^2}{4(1000)^2}}}{1+\frac{1.96^2}{1000}} \approx 0.02458. $$

The resulting interval is approximately \(0.1972\pm0.02458\), or 17.3% to 22.2%. Under the binomial sampling interpretation, this is a 95% confidence interval for the underlying matched-randomization proportion in a comparable population. It is not a 95% probability statement about the fixed proportion in the observed cohort.

Worked Routing and Overlapping Biomarkers

Worked Example: Why Unique Patients Must Be Counted

Imagine a hypothetical set of 300 screened patients with evaluable results. A table of alteration records shows 72 patients meeting one biomarker rule and 48 meeting another. Twelve patients meet both rules. If the protocol routes each patient meeting either rule to one of these matched categories, how many unique patients have a match, and what is the match rate among those with evaluable results?

Adding 72 and 48 gives 120 alteration-category records, but this counts the 12 patients meeting both rules twice. The number of unique matched patients is therefore

$$ 72+48-12=108. $$

The match rate among evaluable patients is \(108/300=0.360\), or 36.0%. If the protocol uses a priority rule, each dual-match patient must then be assigned according to that rule for category-specific counts. If it permits multiple possible substudy routes, report unique patients for the overall rate and describe the overlap separately. Without that distinction, the sum of subgroup counts may exceed the number of people who matched.

Worked Example: Separating Match, Eligibility, and Randomization

In a hypothetical screened cohort of 600 patients, 450 have an evaluable result, 135 have a biomarker match, 108 of the matched patients meet clinical criteria while the relevant substudy is open, and 81 are randomized. Calculate the match rate among evaluable patients and the matched-randomization rate among all screened patients.

The match rate among patients with an evaluable result is \(135/450=0.300\), or 30.0%. The overall matched-randomization rate is \(81/600=0.135\), or 13.5%. The conditional randomization proportion among matched, eligible patients with an open substudy is \(81/108=0.750\), or 75.0%.

These rates describe different transitions. Saying “30.0% of screened patients could enter a matched comparison” would be incorrect: 30.0% uses only patients with evaluable results and counts matches, not randomized patients. The all-screened figure for actual randomization is 13.5%.

Diagnostics, Comparisons, and Limitations

Before interpreting a rate, check that the counts form a coherent patient flow. The number with evaluable results should not exceed the number screened; the number with a match should not exceed the evaluable count; and the randomized count should not exceed the number eligible for an open matched comparison. If stages are not nested because of repeat testing, multiple assignments, or differing analysis populations, explain how the counts were constructed rather than forcing them into a single funnel.

The main alternative summaries answer different questions. A biomarker-match rate among evaluable patients describes the yield of genomic classification once testing produced a usable result. A rate among all screened patients includes failures to obtain an evaluable result. A rate among biomarker-matched patients reaching randomization describes progression after matching, not the chance that a screened patient reaches a comparison. These measures are complementary, not interchangeable.

Comparisons across periods or sites require particular caution. Protocol amendments can change which biomarkers qualify, which substudies are available, and which clinical criteria apply. Testing failures, referral patterns, and the timing of enrollment relative to substudy openings can also differ. A difference between two rates may therefore reflect changes in definitions or opportunity, as well as differences in the patients screened. State the protocol version, period, cohort, and denominator for each rate.

Finally, matched-randomization rates are measures of trial pathway performance, not treatment effectiveness. They do not show whether a matched treatment improved outcomes; that requires analysis of the randomized comparison. They also do not directly measure how many patients would benefit from a treatment in routine care. A patient not randomized may have lacked an evaluable result, failed eligibility criteria, had no open matching substudy, or declined enrollment; these reasons should not be collapsed into “no biomarker match.”

Common Pitfall

Common mistake: “Thirty-five percent of patients had a genomic match, so 35% of screened patients could enter a matched randomized comparison.” This reasoning silently changes the denominator and treats a molecular match as equivalent to eligibility and randomization. Correction: name the denominator for the 35% figure, then separately calculate the number randomized in matched comparisons divided by all screened patients. Report the intervening stages when the goal is to explain why the rates differ.

Check Your Understanding

Answer each question using the stated denominators. Solutions follow the questions.

  1. In a hypothetical cohort, 900 patients were screened, 720 had evaluable results, and 216 had a match. What is the match rate among evaluable patients?
  2. Of 216 matched patients, 162 were eligible while a relevant substudy was open, and 135 were randomized. What is the overall matched-randomization rate among the 900 screened patients?
  3. Two biomarker categories contain 50 and 40 patients, with 10 patients in both. How many unique patients match at least one category?
  4. Why can a match rate among patients with evaluable genomic results be higher than the matched-randomization rate among all screened patients?

Solutions. (1) \(216/720=0.300\), so 30.0% of evaluable patients had a match. (2) \(135/900=0.150\), so 15.0% of all screened patients were randomized in a matched comparison. (3) \(50+40-10=80\) unique patients match at least one category. (4) The first rate excludes patients without evaluable results and counts biomarker matches; the second includes all screened patients and requires progression through eligibility, substudy availability, and randomization. Thus its numerator is narrower and its denominator broader.

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