Statistical analysis

This section contains the following:

Introduction
Things to consider when writing a protocol
Illustrative examples - WHO pre-eclampsia trial
Illustrative examples - CRASH trial
Illustrative examples - RaPP trial
Additional resources
Further reading

Introduction

The principal features of the statistical analysis of the trial should be described in the Statistical Analysis section of the protocol. This section should include details of the proposed analysis of both the primary and secondary outcome(s) and provide some information on how any anticipated analysis problems will be handled. In general, the analysis of the primary outcome(s) should follow the intention to treat principle – the participants should remain in the group they were randomised to and not analysed as the treatment actually received. Any novel statistical techniques should be referenced in the text. A statistician should write or comment on the analysis strategy.

In addition to the Statistical Analysis section of the protocol, it is often necessary to describe a statistical analysis plan. This is usually written as a separate document that is appended to the protocol. The plan may include more detailed descriptions of the principal statistical features stated in the protocol. This plan can be finalised as the trial progresses, and might require amendment if unusual features of the data are identified during the analyses.

Things to consider when writing a protocol

Provide details of the proposed analysis for the primary and secondary outcome(s)
Give references for any non-standard statistical techniques
Supply information on how to handle anticipated problems such as missing values (see Compliance and missing data)
Any proposed analyses should correspond to the data required for the Dummy tables (see Dummy tables)
Get a statistician involved with the development of this section

Scenarios where special considerations apply

Cluster trials

A fundamental assumption of the standard statistical methods used to analyse patient randomised trials is that the outcome for an individual patient is completely unrelated to that for any other patient – they are said to be ‘independent’. This assumption is violated, however, in cluster trials because patients within any one cluster are more likely to respond in a similar manner. Cluster trials that do not account for clustering during analysis have artificially extreme p-values and over narrow confidence intervals increasing the chances of spuriously significant findings and misleading conclusions. The statistical analysis section of the protocol should provide specific details on how to account for the clustering in the data.

Equivalence trials

In equivalence trials, the statistical analysis is generally based on the use of confidence intervals. The investigator sets equivalence margins, and if the entire confidence interval lies within these margins the interventions are said to be equivalent. In contrast to the parallel group designs described above, the correct analysis is by treatment received not by intention to treat. The protocol should state the equivalence margins and specific details on how to analyse the equivalence trial.

Illustrative examples - WHO pre-eclampsia trial
An analysis plan has been finalised before recruitment starts. A draft layout of the proposed analysis plan is presented in Appendix 2 in dummy tables. Principal analyses will be on an intention-to-treat principle with comparisons made between calcium and placebo for primary and secondary outcomes. Stratification will be made for gestational age of entry into the trial by each woman and by baseline calcium intake level of populations served by the hospitals. These hospitals will be classified as serving a population of very low (< 200mg), low (200-400mg), or medium (400-599mg) calcium intake before initiation of the trial. An exploratory analysis will be conducted for the hypothesis that the effect will be larger among women who started treatment before 16th week of pregnancy and among populations with the lowest baseline calcium intake. (WHO Multicentre Randomized Trial of Calcium Supplementation for the Prevention of Pre-eclamsia - go to protocol)

Illustrative examples - WHO pre-eclampsia trial

An analysis plan has been finalised before recruitment starts. A draft layout of the proposed analysis plan is presented in Appendix 2 in dummy tables. Principal analyses will be on an intention-to-treat principle with comparisons made between calcium and placebo for primary and secondary outcomes. Stratification will be made for gestational age of entry into the trial by each woman and by baseline calcium intake level of populations served by the hospitals. These hospitals will be classified as serving a population of very low (< 200mg), low (200-400mg), or medium (400-599mg) calcium intake before initiation of the trial. An exploratory analysis will be conducted for the hypothesis that the effect will be larger among women who started treatment before 16th week of pregnancy and among populations with the lowest baseline calcium intake. (WHO Multicentre Randomized Trial of Calcium Supplementation for the Prevention of Pre-eclamsia - go to protocol)

Illustrative examples - CRASH trial
Comparisons will be made of the primary outcome measures, comparing all those allocated methylprednisolone versus all those allocated placebo, on an 'intention to treat' basis. Analyses will be stratified on time from injury to the initiation of treatment, and on severity of head injury as assessed by the Glasgow Coma Scale. Comparisons will also be made of the risks of infection and gastrointestinal bleeding. (CRASH trial - go to protocol)

Illustrative examples - CRASH trial

Comparisons will be made of the primary outcome measures, comparing all those allocated methylprednisolone versus all those allocated placebo, on an 'intention to treat' basis. Analyses will be stratified on time from injury to the initiation of treatment, and on severity of head injury as assessed by the Glasgow Coma Scale. Comparisons will also be made of the risks of infection and gastrointestinal bleeding. (CRASH trial - go to protocol)

Illustrative examples - RaPP trial
We will carry out post-test comparisons between the intervention- and control-group using cluster-adjusted chi-square and T-tests. Analysis of covariance may be used to adjust for imbalance of baseline levels between the intervention- and control-groups. (RaPP trial - go to protocol)

Additional resources

Statistical analysis checklist

This checklist was developed by Dave Sackett, who prepared it for the forthcoming 3rd edition of Clinical Epidemiology; A Basic Science for Answering Questions about Health Care, to be published by Lippincott, Williams & Wilkins in 2004.

Analysis and interpretation checklist

Analysis and interpretation text from 3rd edition of Clinical Epidemiology

This text has been contributed by Dave Sackett, who prepared it for the forthcoming 3rd edition of Clinical Epidemiology; A Basic Science for Answering Questions about Health Care, to be published by Lippincott, Williams & Wilkins in 2005.

Physiological statistics text from 3rd edition of Clinical Epidemiology

ICH Harmonised Tripartite Guideline: Statistical Principles for Clinical Trials

This document provides guidance for the design, conduct, analysis, and evaluation of clinical trials of an intervention in the context of its overall clinical development.

Papers related to statistical methods and analyses

The British Medical Journal collates a number of research papers on Statistical Methods and analyses.

Epi Info

Epi Info is a public domain software package designed for the global community of public health practitioners and researchers. It provides for easy form and database construction, data entry, and analysis with epidemiologic statistics, maps, and graphs. Within Epi Info there is an analysis program for producing statistical analyses of data, report output and graphs.