Translating Design Specifications Into Software Inputs

From a Design Specification to a Software Input

A design specification describes what a trial is intended to do; software requires that intention to be expressed in defined fields. A mismatch can be subtle: entering a two-sided significance level where a one-sided level is expected, or treating enrollment fractions as information fractions when follow-up and event rates vary. The earlier material on turning a trial objective into a design specification establishes the choices to be translated. Here the task is to encode those choices without silently changing the design.

The translation is not a matter of finding a single universal list of software arguments. Programs differ in their input conventions, and some ask for maximum sample size while others ask for maximum information or for a target power from which a maximum is calculated. The reliable approach is to identify the statistical meaning of each specified choice, determine the corresponding field in the chosen implementation, and record any conversion or assumption.

Specify the Statistical Scale Before Entering Values

Before entering numbers, state the analysis model and the scale on which information is measured. For a two-arm comparison of a continuous outcome, suppose participants are independently randomized equally between arms, outcomes are independent with common known variance \(\sigma^2\), and the treatment effect is the difference in population means. With \(N\) participants in total, the variance of the difference in sample means is \(4\sigma^2/N\). Thus the information for that contrast is \(I=N/(4\sigma^2)\). This conversion is appropriate only under these assumptions and with the stated definition of \(N\).

For other endpoints, information may not be proportional to the number enrolled. For example, in a balanced time-to-event comparison, the log-rank information is often approximated by \(D/4\), where \(D\) is the number of events. That approximation relies on approximately balanced allocation and risk sets; the analysis model and software may use a more detailed calculation. The units matter: information for a mean difference is in inverse squared outcome units, while information for a log hazard ratio is dimensionless.

Maximum sample size, maximum event count, and maximum information are therefore not interchangeable labels. If the specification gives one quantity and the software requests another, make the conversion under the stated model and retain the original quantity as a cross-check. If assumptions needed for conversion are uncertain, do not disguise the uncertainty by entering an apparently precise value.

Representing Planned Looks and Boundaries

A group sequential design has a finite set of planned analyses. Let \(K\) denote the number of looks, let \(I_k\) denote information at look \(k\), and let \(I_{\max}=I_K\). The information fraction is \(t_k=I_k/I_{\max}\). A valid schedule has \(0<t_1<\cdots<t_K=1\). Some software asks directly for the fractions \(t_k\); other software asks for \(I_k\), sample sizes, event counts, or analysis times. Convert only after checking which scale its field represents.

This distinction is important because a fraction of participants enrolled need not equal a fraction of information. It may be a good approximation for a simple fixed-size continuous-outcome design with stable variance and complete data. It is generally not safe to assume the same for an event-driven study, changing allocation, delayed outcome measurement, or substantial missingness. Look timing should be entered on the scale specified by the design, and its operational counterpart should be checked separately.

Boundary inputs describe how evidence is assessed across the looks. At minimum, specify whether the test is one-sided or two-sided, which direction of the statistic favors the treatment, the family of efficacy boundaries or the corresponding alpha-spending choice, and whether a futility boundary is used. A nominal significance level alone does not identify a sequential design: its error probability must be controlled over the planned sequence of analyses. If the implementation accepts a named boundary family, verify that the name refers to the intended convention. If it accepts an alpha-spending function instead, supply that function’s parameters and the look fractions required by that implementation. Do not enter both incompatible specifications as though they were independent choices.

Enter Operating-Characteristic Targets Without Changing Their Meaning

Operating characteristics summarize a design’s performance under specified parameter values. Common targets include type I error under \(H_0\) and power at a stated treatment effect under \(H_a\). To make these targets interpretable, specify the endpoint scale, the direction and size of the effect, and any nuisance parameters required by the assumed model. For a continuous outcome, for example, a mean difference must be given in outcome units, and the standard deviation must use the same units.

A target power is not itself a boundary. If maximum information is fixed in the specification, power at the target effect is usually something to calculate and compare with the target. If the software offers a search for maximum information or sample size, the target power and target effect may instead be inputs to that search. Record which mode is being used. Otherwise, a user can inadvertently ask the program to solve for a different design than the one specified.

Likewise, distinguish the nominal significance level from the achieved overall type I error. The nominal level is the requested error-control target for the sequential test; the achieved value is a property to verify under the stated null model and stopping rules. State whether alpha is one-sided or two-sided. A two-sided level of \(0.05\) is often represented as \(0.025\) in each tail, but a software field asking for “alpha” may expect either the total two-sided level or a one-sided tail level. Follow the documented convention and record it explicitly.

A Short Justification for Information-Fraction Inputs

The information scale is useful because, under the canonical group sequential model, standardized statistics have standard normal marginal distributions and their dependence is determined by information timing. In particular, for looks \(i\leq j\), the covariance is

Since \(I_i=t_iI_{\max}\) and \(I_j=t_jI_{\max}\), the covariance becomes \(\sqrt{t_i/t_j}\). Thus the fractions encode the relative information timing that governs dependence between looks. This explains why substituting enrollment fractions for information fractions can alter the sequential calculation: it changes the assumed covariance structure whenever enrollment and information do not increase proportionally. The canonical model is an assumption about the analysis statistics and information process, not a guarantee supplied merely by entering fractions.

Diagnostics, Alternatives, and Common Errors

Before relying on a result, inspect the translated inputs as a set. Look fractions should be strictly increasing and end at 1; information and sample-size targets should not decrease; and a one-sided direction should agree with the coding of the treatment effect and statistic. Check that any futility rule is explicitly identified as binding or nonbinding, because its role in operating-characteristic calculations can differ. Confirm that the boundary specification is supported by the stated significance level and look schedule, and that the effect used for a power assessment is expressed on the correct scale.

The main alternatives are different ways to express the same design. A maximum sample-size representation is intuitive when enrollment drives precision and the analysis model gives a reliable sample-size-to-information conversion. An information-based representation is more direct for sequential calculations, particularly when the endpoint is event-driven. Look timing can be given as information fractions, event counts, or analysis times, but only if the software’s conversion between these quantities is appropriate. Boundary inputs can be provided as a named family, a spending function, or explicit critical values; these representations are alternatives, not automatically equivalent fields to combine.

A common mistake is to enter the planned fraction of participants enrolled as the information fraction at every look, then assume the design is unchanged. That reasoning is valid only when information is proportional to enrollment under the relevant model. The correction is to calculate or obtain information at each analysis, use the software’s documented information scale, and check the implied sample-size or event targets against the operational plan. Another mistake is to enter a target power as if it were a stopping boundary. Power describes performance over repeated trials under an alternative; a boundary determines a stopping decision from interim evidence.

Software input translation has limits. A correct input file cannot repair a misspecified endpoint model, unrealistic variance or event assumptions, an infeasible look schedule, or a mismatch between the protocol and analysis statistic. Nor does a successful calculation establish that a design is operationally suitable. Keep a record of the specification, assumptions, conversions, software field meanings, and resulting checks so that another analyst can reproduce the interpretation.