A SAP is usually structured to reflect the protocol but will provide more granularity regarding the statistical methodology and population definition. Ideally, it includes and addresses the following elements in detail:
Statistics on who wrote the SAP, its version number, when it was approved, and who signed it.
Testable hypotheses to answer the study objectives (see Chapter 2). Defining primary and secondary objectives is important to avoid 'data dredging' and must correspond to the research question. A hypothesis is the product of deductive reasoning, going from general premises to specific results one would expect if those general premises were indeed true. This usually involves a set of possible relationships between a set of variables. It should be clearly stated how each outcome will be measured. Negative findings may be equally important as positive findings. Another reason to carefully choose the primary outcome is to minimise multiplicity effects. These occur when there are multiple statistical tests needed to assess the primary outcome, which increases the likelihood of false positives.
Definitions of study variables. Outcome variables based on historical data may involve complex transformations to approximate clinical variables not explicitly measured in the dataset used. These transformations should be discriminated from those made to improve the fit of a statistical model. In either case, the rationale should be provided. In the latter case, this will include which tests of fit will be used and under what conditions a transformation will be used. Next to the outcomes, the other variables used in the study also need to be further formalised. The formatting (e.g., categorisation, dichotomisation), modifications or derivations need to be described, with a special attention given to time-dependent variables (e.g., age, BMI).
Study design (see Chapter 4) and sample size considerations. It should be noted that in observational studies using data that already exist and where no additional data is collected, sample size is not preclusive and the ethical injunction against 'underpowered' studies has no obvious force provided the results, in particular the 'absence of effect' and 'insufficient evidence', which should be properly presented and interpreted. The anticipated overall number of study subjects, as well as the minimum number per strata for stratified analyses, can be provided as an indicative guide.
Methods for dealing with missing data.
Methods for dealing with outliers.
Procedures for dealing with protocol variations, non-compliance, and withdrawals.
Methods for estimating points and intervals.
Rules for calculating composite or derived variables, including data-driven definitions and any additional details required to minimise ambiguity.
Baseline and covariate data used.
Definition of study period (study entry/index date, follow-up period, study exit)
Inclusion of randomisation factors (if applicable).
Methods for dealing with data from several locations/sources.
Methods for dealing with treatment interactions.
Methods for multiple comparisons and subgroup analysis.
Computer systems and statistical software packages used to analyse data.
Statistical principles including confidence intervals and level of significance. The level of statistical significance to be employed, as well as whether one-tailed or two-tailed tests will be used, should be specified. Observational studies may be subject to repeated testing of accumulating data, which needs adjustment of significance levels to reduce inflated type-I errors (false positive findings). When false positives are a greater concern, a smaller confidence interval should be considered. Any planned adjustment of the significance level to control for type 1 error that can arise from comparisons across multiple subgroups or analysis of multiple predictors or outcomes (secondary analyses) should be presented. However, different objectives of the study may require a lower or higher strength of evidence – for instance, policy recommendations regarding drug licensing may require a lower chance of false positive decisions when deciding whether further investigation is needed for a product safety issue. It should be noted that statistical packages often employ standard procedures – for instance default p-values (i.e., 5%) or confidence intervals (i.e., 95%).
Sensitivity analyses. Sensitivity analyses allow to study the effect of potential violations of assumptions and/or results depending on specific observations (subjects) and are used to support the conclusions of the main analysis. Analyses to merely explore the data are considered exploratory analyses and should be described as such.
Decision criteria. If decisions are drawn from the study results, a section of the SAP should explain the different outcomes that might be selected for each decision, which statistics influence the decision-making process, and which values of the statistics will be considered to support each outcome.
Tables and figures for presentation of the study results. Skeleton tables should include a title, row labels and column entries be clearly spelled out, with only figures/numbers in the cells lacking. The analysis will produce the contents of the cells in a targeted manner, that is, hardly any other numbers will need to be generated. The same principle applies to graphs.
Consideration of the estimand framework is recommended to help informing choices regarding study design and data analysis and clarify how to interpret study findings. Tell me what you want, what you really really want: estimands in observational pharmacoepidemiologic comparative effectiveness and safety studies (Pharmacoepidemiol Drug Saf. 2023 Mar 22) discusses how defining an estimand is instrumental to the process of designing and analysing pharmacoepidemiological comparative effectiveness or safety studies. It applies the ICH Addendum on Estimands and Sensitivity Analysis in Clinical Trials to the Guideline on Statistical principles for Clinical Trial (2019) on estimands to three case studies and shows how defining an estimand ensures that the study targets a treatment effect that aligns with the treatment decision the study aims to inform.
For further reading on how to draft a SAP tailored to observational studies, see DEBATE-statistical analysis plans for observational studies (BMC Med Res Methodol. 2019;19(1):233); Guide to the statistical analysis plan (Pediatric Anesthesia 2019;29:237-42) which provides an exhaustive list of SAP items applicable to both prospective and retrospective observational studies; and The value of statistical analysis plans in observational research: defining high-quality research from the start (JAMA. 2012;308(8):773-4). A good example of a SAP where the main components are included can be found in Necrotizing soft tissue infections - a multicentre, prospective observational study (INFECT): protocol and statistical analysis plan (Acta Anaesthesiol Scand. 2018;62(2);272-79). Modern Epidemiology, 4th ed. (T. Lash, T.J. VanderWeele, S. Haneuse, K. Rothman. Wolters Kluwer, 2020) summarises the phases in a statistical analysis that should all be thought out and described beforehand.