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4. Statistical principles

4.1 Adjustment of P-values for multiplicity, and confidence intervals

In presentation of results (with the exception of the safety analyses of hundreds of different causes of death; Section 6.9), formal allowance will not be made for multiple testing.  However, allowance may, where appropriate, be made for multiple testing and any other potential sources of bias in discussion and interpretation of results. Other things being equal, the more extreme the P-value the more reliable the evidence will be considered to be of a real effect on breast-cancer-related outcomes. Although all confidence intervals will be 95%, this does not imply that P-values slightly above or slightly below 0.05 will be interpreted very differently.

4.2 Main analyses population

All analyses will strictly respect the random allocation, thereby avoiding bias. The main analyses are those of the primary and main subsidiary endpoints (Sections 6.1 and 6.2). These will be restricted to the “main analyses population” (Section 5.2), which includes only the 2 million younger and 1 million older participants who had been eligible and linkable to NHS England datasets, with no record there of prior cancer or breast disease, and who were considered likely to attend screening if invited (based on uptake of their previous breast or cervical screening invitation). Details of those included and excluded are in Table 1. All these inclusions and exclusions were based on information that could not have been affected by the random allocation.

4.3 Adherence and protocol deviations

Invitees and non-invitees (controls) are defined as those who were randomly allocated to be, or not to be, invited, regardless of whether an invitation actually reached them. Within the main analyses population, let P and p denote, respectively, the proportions of the invitees and controls who (without having had a diagnosis of breast cancer recorded as being after randomisation but before getting screened) actually had an NHS breast screening clinic visit within one year of randomisation. The proportion of invitees adherent to their random allocation is then P, the proportion of controls adherent to their random allocation is 1-p, and the difference P-p indicates the effectiveness of the random allocation as a determinant of screening rates.

The proportions of invitees and of controls screened by various times after randomisation will be described by Kaplan-Meier plots of proportions having had a screening visit against time since randomisation (calculated from routinely collected NHS England electronic records of screening visits). The delay between randomisation and screening for those who would attend within 1 year if and only if invited will also be estimated (see Section 6.3.1 on adherence-corrected analyses).

In this section