Pediatric Vaccine Trial With Age-Dependent Follow-Up

Why age-related follow-up patterns matter

In a pediatric vaccine trial, missed visits can reflect more than a general tendency to drop out. Appointment burden, illness, and family logistics may differ with a child’s age; age may also be associated with the antibody response itself. If follow-up differs across ages, the people whose endpoint responses are observed may not represent all randomized children in the same way in each age group. A single overall missingness rate can conceal that structure.

This case study uses a hypothetical randomized trial with a six-month antibody endpoint. The aim is to estimate and compare mean responses for vaccine and control while making the follow-up patterns visible. The numerical estimates below illustrate identifying restrictions; they are not results from an actual trial. They also do not establish that a particular restriction is true.

For this illustration, age groups are 2–5 months and 6–11 months at enrollment. The endpoint is measured at a common, prespecified time after the final scheduled dose. This alignment matters: if the age groups have different dose schedules, a response measured at different times since vaccination would not be directly comparable without a clinically justified time-based estimand. The analysis also assumes the endpoint has the same meaning and measurement scale across ages and arms.

First describe the follow-up patterns

The following hypothetical counts are the same in both randomized arms. Each age-by-arm group has 40 children. Younger children more often have the endpoint missing, while some children in both age groups miss an intermediate visit and later attend the endpoint visit.

For an endpoint analysis, the \(E\) and \(I\) groups both contribute observed \(Y\) values. Their different histories may still help predict outcomes for children in \(L\). In practice, the prediction model could condition on age, randomized arm, baseline variables, and observed antibody measurements or visit history. The restriction is about the unobserved endpoint after conditioning on the variables included in that model.

Identifying an endpoint mean by pattern

Write \(\mu_{a,g,r}=E(Y\mid A=a,G=g,R=r)\) for the mean endpoint response in a treatment-arm, age-group, and follow-up-pattern cell. For patterns \(E\) and \(I\), this mean can be estimated from observed endpoint values, subject to ordinary sampling and model considerations. For pattern \(L\), the endpoint values are not observed, so the corresponding mean is not determined by the observed data alone.

One possible identifying restriction is missing at random conditional on the variables used in the model: within a given arm, age group, and observed history, the expected endpoint among children with a missing endpoint equals the model-predicted expected endpoint among comparable children whose endpoint is observed. This restriction does not mean the missingness is unrelated to everything; it allows dependence on included observed information. It does rule out residual dependence between endpoint values and endpoint missingness after conditioning on that information.

A pattern-specific delta restriction instead allows the mean for a missing-endpoint pattern to depart from its MAR prediction. Here \(\delta_{a,g,L}\) is an additive shift in log₂ titer units: the assumed mean for pattern \(L\) is the MAR-predicted mean plus \(\delta_{a,g,L}\). A negative value represents a lower assumed mean response among children with missing endpoints than among otherwise comparable children under MAR. The observed data do not estimate this shift; it is a sensitivity parameter chosen for clinical interpretation.

Calculate the MAR estimates

Suppose the hypothetical observed endpoint means and the model-based predictions for pattern \(L\) are as follows. The \(L\)-column values are predictions under the conditional MAR restriction. All values are in log₂ titer units.

For each arm and age group, combine the observed endpoint values and the predicted missing-endpoint values, weighting each pattern mean by its number of children. The resulting age-specific mean is

To define an age-standardized contrast, give the two age groups equal weight. This targets a hypothetical population with half its children in each age group; it is a transparent choice for this illustration, not a claim that every trial should use equal weights.

Change the restriction and examine the result

Suppose clinicians consider it plausible that vaccine recipients whose endpoint is missing had lower responses than comparable vaccine recipients with observed endpoints, even after accounting for the observed history. As one sensitivity scenario, set \(\delta_{V,g,L}=-0.8\) in both age groups and set the control-arm shifts to zero. This scenario changes only the unobserved endpoint means; observed endpoint means remain as recorded.

The size of that change can also be checked directly. For younger vaccine recipients, 10 of 40 outcomes receive a \(-0.8\) shift, reducing the age-specific mean by \(10(-0.8)/40=-0.2\). For older vaccine recipients, the corresponding reduction is \(5(-0.8)/40=-0.1\). With equal age weights, the overall reduction is \(\{(-0.2)+(-0.1)\}/2=-0.15\) log₂ units. This verifies the difference between the two standardized contrasts.

Assumptions, diagnostics, and alternative approaches

The calculations rely on several distinct conditions. Randomization supports comparison by assigned arm, but does not identify missing outcomes. The conditional MAR estimate additionally relies on a suitable prediction model, adequate observed information for predicting pattern \(L\), and overlap: children with missing endpoints must have observed counterparts with sufficiently similar age and recorded history to inform predictions. The delta scenario replaces the MAR equality for the specified pattern with an explicit alternative mean shift. Both approaches require consistent endpoint measurement and a clearly defined target population and age weights.

Diagnostics should examine whether the visit-pattern definitions match the protocol, whether endpoint availability differs by age and arm, and whether the prediction model is extrapolating beyond observed histories. Check cell counts and the range of predicted values, compare predictions with observed endpoint values in similar history groups, and investigate whether missed visits cluster around illness, treatment discontinuation, or other recorded events. A very small pattern cell can make its mean unstable; a model that predicts far outside the observed response range can signal poor fit or insufficient overlap. These checks can expose problems but cannot verify a restriction about outcomes that were never observed.

A frequent mistake is to treat every missed visit as a missing endpoint and discard the distinction between patterns \(I\) and \(L\). The correction is to classify endpoint availability separately from earlier visit attendance: a child in \(I\) contributes an observed six-month response, while a child in \(L\) requires an identifying restriction for that endpoint.

Another mistake is to read the MAR estimate as if it were determined by randomization or confirmed by a good model fit. Randomization addresses assignment, while MAR addresses the relationship between missingness and unobserved outcomes after conditioning. A well-fitting model can still rely on an incorrect restriction. The delta comparison makes this dependence visible, but no single delta value is selected by the observed data alone.

Finally, the point estimates above do not quantify sampling uncertainty. In a full analysis, uncertainty must reflect estimation of observed pattern means and missing-outcome predictions, and the chosen sensitivity scenario should be reported alongside its assumptions. The numerical contrast is in log₂ titer units; it should not be described as a probability or as proof that vaccination caused an individual child’s response.