Site Activation and Calendar-Time Effects

Why Site Activation and Calendar Time Must Be Examined Together

In a platform trial, sites may begin recruiting at different dates. A period with few recruits may therefore reflect limited site availability rather than low interest or a change in eligibility. Likewise, the mix of participants can change when new sites open: later recruits may come from different regions, have different baseline characteristics, or enter under different local care practices. If outcomes also change over calendar time, a simple comparison of aggregate results can blend these distinct processes.

The task here is to describe how site activation shapes recruitment and participant composition, and to separate those shifts from temporal changes observed within sites. This is a design and interpretation problem as well as an analysis problem: the dates and patterns of activation determine which site-by-time comparisons are possible. The earlier material on site and regional variation in nonconcurrent controls and treatment-by-period interaction models provides relevant context, but the central focus here is the site activation schedule itself.

Site activity and observed recruitment are different quantities. The activation schedule records when a site could recruit; the counts \(n_{jt}\) record what happened. A site may be active but recruit no participants in a particular period. Conversely, before activation it cannot contribute trial participants, so its count is structurally zero. Keeping these cases distinct matters when diagnosing slow recruitment and when deciding which comparisons the data can support.

Summarizing Recruitment and Participant Mix

Begin with a site-by-period table of recruitment counts, activation status, and relevant participant characteristics. Useful summaries include the number of active sites, the number and proportion of recruits by site, total recruitment per period, and recruitment per active site. A low total can arise because few sites are open, because open sites recruit slowly, or both. Counts alone cannot identify the explanation, but they show where to investigate.

For a binary participant characteristic, such as residence in a rural area, let \(x_{jt}\) be the number of participants with that characteristic at site \(j\) in period \(t\). When \(n_{jt}>0\), the site-specific proportion is \(\hat p_{jt}=x_{jt}/n_{jt}\). The overall proportion in period \(t\) is calculated from participant counts:

The second expression sums only over sites with \(n_{jt}>0\), so it never requires a proportion for an empty site-period. The first expression is often the safest computational form: a site with no recruits contributes zero to both its characteristic count and its participant count. If \(n_t=0\), the overall proportion for that period is undefined.

Recruitment composition can be summarized similarly. For instance, \(w_{jt}\) tells what fraction of period \(t\)'s participants came from site \(j\). Changes in these weights show shifts in the source of participants, not necessarily changes in the characteristics of participants within a site. To examine participant mix more fully, calculate characteristics within site and period where data exist, then compare those summaries while noting empty or sparse cells.

Separating Within-Site Time Change from Composition Change

For a quantitative outcome, let \(\bar Y_{jt}\) denote the observed mean at site \(j\) in period \(t\), when \(n_{jt}>0\). The aggregate period mean is a weighted mean of the site-period means:

An aggregate mean can change because outcomes change within sites, because the site weights change, or both. To make the distinction precise, suppose the same set of sites has observed means in periods 0 and 1, with positive recruitment in both periods. Then an exact decomposition is

The first term is the change in site-specific means, weighted by the period-0 site shares. The second is the change due to different site shares, evaluated using period-1 site means. The choice of reference weights is a convention; a different reference can yield a different allocation between components, even though the total difference stays the same. The identity is an arithmetic decomposition, not a causal analysis.

To verify it, add and subtract \(\sum_j w_{j0}\bar Y_{j1}\) from the difference of aggregate means:

The common-site requirement is important. If a site has no participants in one period, its mean for that period is not observed, and the corresponding within-site change cannot be calculated from these data. Restricting the decomposition to sites observed in both periods changes the target population and may discard a meaningful part of recruitment. Standardizing to fixed site weights is also possible, but it requires outcome information for the sites and periods receiving positive standardization weight; weights cannot create data in an empty cell.

Calendar-Time Models, Overlap, and Diagnostics

A site-by-period table is a useful first diagnostic, but a model can summarize patterns across several periods. For a quantitative outcome, one descriptive mean model is

where \(\alpha_j\) represents a site-specific mean component and \(\gamma_t\) a calendar-period component. A reference site and period, or equivalent constraints, are needed to identify the parameters. This additive model assumes that site differences do not vary across periods on the model's scale; if that is implausible, site-by-period terms or plots may reveal different patterns. A model for treatment effects may also need treatment-by-period terms, but it does not remove the need to examine which sites and periods contribute data.

The most important diagnostic is overlap: which sites are observed in which periods? If all sites open at the same time, site and calendar time may be separable in the data. If each site contributes only in a unique period, site and period effects can be aliased: different combinations of \(\alpha_j\) and \(\gamma_t\) may fit the same observed means. No modeling choice can recover a distinction that the design does not identify without additional assumptions. Sparse site-periods also make estimated means unstable, even when the model is technically identifiable.

Other useful checks include comparing recruitment counts with the activation schedule; plotting site-specific recruitment and outcome summaries over calendar time; checking whether baseline characteristics change within sites; and documenting changes in local standard care, eligibility, measurement, or follow-up. These checks help distinguish a broad temporal pattern shared across sites from a change driven by which sites contribute participants. They do not prove that all relevant temporal differences have been measured.

Control availability requires its own site-period check. In a randomized platform, a control arm may be available at a site only during periods when the relevant arms are open for randomization there. Tabulate the number of active sites and the number of control participants by period, alongside activation and arm-opening dates. A large total control count does not guarantee that controls are available in every site-period or for every treatment comparison. Conversely, a site being active does not itself establish that a suitable control was randomized there. This is a descriptive availability check, not a rule for selecting or combining control participants.

What the Analysis Can and Cannot Establish

The main alternatives answer different questions. Raw period summaries describe the participants actually recruited in each period and are transparent about changing composition. Site-stratified summaries compare periods within sites, but they cannot estimate a within-site change where a site-period is empty. Fixed-weight standardization asks what the period means would be under a chosen common site distribution, provided the required site-period estimates exist. A regression model can pool information and adjust for measured factors, but its conclusions depend on its mean structure, overlap, and uncertainty calculation. These approaches are complementary rather than interchangeable.

When modeling participant-level outcomes, account for the trial's randomization and data structure. For example, participants within a site may have correlated outcomes; treating all observations as independent can understate uncertainty. Model-based standard errors should reflect relevant clustering and design features. A correct standard error does not resolve confounding or lack of overlap, and a visually plausible trend does not establish a causal calendar-time effect.

Staggered activation can be related to site capacity, geography, staffing, or expected recruitment. Those same features may relate to participant mix and outcomes. Calendar time can also coincide with changing care or measurement practices. Thus, observed site and time patterns are valuable for describing the data and assessing design support, but they do not alone identify why a trend occurred. In particular, standardization adjusts only for the dimensions and populations represented in its data; it does not recover outcomes for a site before activation or for any other unobserved site-period.

Common Pitfall

Wrong reasoning: “The overall outcome improved after new sites opened, so outcomes must have improved over time within sites.” This conclusion mistakes a change in the composition of participants for a within-site temporal change. The new sites may have different typical outcomes, even if each existing site's outcomes stayed constant.

Correction: Report the aggregate change, then inspect site-specific summaries and site weights. If the same sites are observed in both periods, a decomposition can show how much of the arithmetic change is associated with within-site differences versus changed site shares. State the reference weights and the common-site requirement. Treat any causal interpretation as a separate question requiring defensible assumptions and adequate overlap.