Why Population Labels Matter
A causal effect estimated in a study refers first to the people whose data contributed to that study. A decision-maker, however, may care about a different group: all eligible patients in a health system, patients at another clinic, or people who could receive the intervention in routine practice. To reason clearly about that gap, identify three distinct groups: the study sample, the source population, and the target population.
These labels are not interchangeable. The sample is the set of individuals actually included in the analysis. The source population is the population from which study participants could have been selected or recruited. The target population is the population to which the scientific or practical question refers. A sampling indicator gives a concise way to mark inclusion in the study sample for members of the source population.
The source population is not necessarily every person who might conceivably benefit from a treatment. It needs a concrete definition, such as adults meeting specified eligibility criteria at named clinics during a stated recruitment period. The target population also needs a concrete definition: for example, all adults with the condition receiving care in a regional health system during a specified year. Naming a population precisely helps reveal whether the sample and target differ in eligibility, location, time, or other respects.
The indicator \(S\) records study inclusion, not treatment assignment. A randomized trial can have one indicator for whether a person entered the trial and a separate variable for which treatment the person was assigned. Likewise, a person with \(S=0\) is not necessarily ineligible; that person may belong to the source population but not have been selected or enrolled.
Trial Sample, Source, and Target
Worked Example: A Trial With Uninvited and Nonparticipating Patients
Suppose a hypothetical trial defines its source population as 1,200 adults who meet the clinical eligibility criteria at eight clinics during a recruitment period. Investigators invite 500 of them, and 400 of those invited enroll and are included in the trial analysis. The target population is all 4,000 eligible adults receiving care across a regional health system during that year.
Source population. The source consists of the 1,200 eligible adults at the eight study clinics. It includes people who were not invited as well as people who were invited but did not enroll.
Study sample and indicator. Define \(S=1\) for each of the 400 enrolled adults and \(S=0\) for the other 800 source-population adults. Thus, the realized study sample has 400 people, and the source population has \(400+800=1{,}200\).
Invitation and noninvitation counts. Of the 1,200 eligible adults, 500 were invited. Therefore, the number not invited is
Those 700 adults are still members of the eligible source population; they are not members of the study sample. Among the 500 invited adults, \(500-400=100\) did not enroll. Consequently, the 800 source-population adults with \(S=0\) comprise 700 not invited plus 100 invited but not enrolled.
The invitation fraction is \(500/1{,}200=0.4167\), or about 41.7%. The enrollment fraction among invitees is \(400/500=0.800\), or 80.0%. The fraction of the source population actually included is \(400/1{,}200=0.3333\), or about 33.3%. These are three different quantities because invitation and study inclusion are different events.
The target population of 4,000 regional patients is broader than the source population of 1,200 patients at the trial clinics. These definitions alone do not establish that a causal effect estimated among the 400 trial participants applies to all 4,000 target-population patients.
The trial example illustrates an important bookkeeping rule: define the indicator for the inclusion event of interest and count the people who satisfy it. If the analysis sample requires enrollment and usable data, for example, the indicator should refer to that actual analytic inclusion rule rather than merely to being invited. If invitation itself is of interest, define a separate indicator for invitation.
Site-to-Site Definitions
The same distinctions apply when a study is conducted at one site and the desired application is at another. A site can define the source population, while a different site defines the target population. The study sample is still only the individuals actually included at the source site.
Worked Example: Study at One Clinic, Target at Another
A hypothetical evaluation is conducted at Clinic A. During a defined six-month period, 240 patients meet its eligibility criteria; 180 are enrolled and included in the study. The scientific question concerns eligible patients at Clinic B, where 600 such patients receive care during the same period.
Define the source population as the 240 eligible Clinic A patients and let \(S=1\) mark the 180 included participants. The number of source-population patients not included is
The observed inclusion fraction within the source population is \(180/240=0.750\), or 75.0%. Clinic B's 600 eligible patients form the target population in this example. They are not part of Clinic A's source population under these definitions, and none is automatically part of the study sample.
A useful verbal description is: “The study sample is the 180 included Clinic A patients; the source population is all 240 eligible Clinic A patients; the target population is the 600 eligible Clinic B patients.” This makes clear that the Clinic B patients are not simply the 60 Clinic A patients who were not included. They belong to a different population.
The counts describe who was studied and who is of interest. They do not show whether the sites have comparable patients or whether the study result can be applied at Clinic B. Those are additional causal and substantive questions, not consequences of the population labels or the arithmetic.
What the Indicator Tells Us About Composition
A sampling indicator can also describe how the sample's composition relates to the source population. Let \(X\) be a measured characteristic, such as age category. Among source-population members, the distribution of \(X\) in the included sample may differ from its distribution in the full source population. In probability notation, these distributions are \(P(X=x\mid S=1)\) and \(P(X=x)\), respectively.
The relationship follows directly from the definition of conditional probability and Bayes' rule. For any value \(x\) with \(P(S=1)>0\),
Thus, the sample's proportion in category \(x\) depends both on how common that category is in the source population and on its probability of study inclusion. If inclusion probabilities differ across categories, the sample distribution can differ from the source distribution. This identity describes a possible composition difference; by itself, it does not say whether that difference changes a causal effect.
Worked Example: Comparing a Sample Characteristic With Its Source Population
Suppose a hypothetical source population contains 1,000 patients: 400 are aged 65 or older and 600 are younger than 65. A study includes 200 of the older patients and 180 of the younger patients, for a sample of 380.
In the source population, the proportion aged 65 or older is \(400/1{,}000=0.400\), or 40.0%. In the study sample, it is \(200/380=0.5263\), or about 52.6%. The sample includes a larger share of older patients than the source population does.
The inclusion fractions by age category are \(200/400=0.500\) among older patients and \(180/600=0.300\) among younger patients. The overall study inclusion fraction is \(380/1{,}000=0.380\). Substituting the older category into the probability identity gives
This agrees with the direct sample calculation, \(200/380=0.5263\). The arithmetic shows how unequal inclusion fractions can produce a different sample composition. It does not establish that age is related to the causal effect, nor does it determine whether the study effect generalizes to another population.
A Practical Way to Specify the Populations
Before interpreting a study result beyond its participants, write down each population in words and then define the indicator. The following sequence keeps the concepts separate.
Name the people, setting, eligibility criteria, and relevant time period to which the causal question refers.
Describe the population from which study participants could have been selected or recruited. Do not silently equate it with the target.
Specify exactly what makes \(S=1\), such as enrollment and inclusion in the analysis. Distinguish that event from invitation or eligibility if they differ.
Verify that the sample is contained in the source population under the stated definition, and that source-population members with \(S=0\) are not mistakenly counted as sample members.
This process is useful even when a study is a randomized trial. Random assignment concerns treatment allocation among the trial participants; it does not make the enrolled participants identical to the source population or to a target population elsewhere. A clearly defined sampling indicator helps keep those separate questions visible.
Common Mistakes
- Calling everyone eligible a study participant. Eligibility defines who could qualify under the study criteria; it does not mean that every eligible person was invited, enrolled, or analyzed.
- Subtracting the wrong count. If 1,200 people are eligible and 500 are invited, \(1{,}200-500=700\) were not invited. If 400 of the 500 invited enroll, the other 100 were invited but did not enroll. The 200 figure is not the number uninvited under these counts.
- Using “source” and “target” as synonyms. The source population describes the study's recruitment context; the target population describes where the causal question is intended to apply. They may overlap, but they need not be the same.
- Treating \(S\) as treatment assignment. \(S=1\) marks study inclusion. It does not mean that the individual received treatment, and \(S=0\) does not mean the individual received control.
- Assuming the labels prove generalizability. Defining a sample, source, and target makes the question precise; it does not, on its own, justify extending a causal conclusion from one population to another.
Check Your Understanding
Use the distinctions and indicator notation from this tutorial to answer the following questions.
- A study has 900 eligible people, invites 360, and enrolls 300. How many eligible people were not invited, and how many invitees did not enroll?
- In a trial conducted at one hospital, define a plausible source population and target population for a question about applying the result across a state.
- Explain why \(S=1\) should not be interpreted as “received treatment” in a randomized trial.
- A sample has 30% older adults, while the source population has 20%. Does this alone show that the treatment effect differs by age? Explain.
- What details should be included when describing a target population so that its scope is clear?