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95% Ancillary analyses 18 Address multiplicity by reporting any other analyses performed, including subgroup analyses and adjusted analyses, indicating those pre-specifi ed and those exp

Reporting study results 87

6 Simpson AG A comparison of the ability of cranial ultrasound, neonatal neuro-logical assessment and observation of spontaneous movements to predict out-come in preterm infants University of Sheffi eld; 2004

7 Diggle PJ, Heagerty P, Liang K-J, Zeger SL Analysis of longitudinal data, 2nd ed

Oxford: Oxford University Press; 2002

8 Matthews JNS, Altman DG, Campbell MJ, Royston P Analysis of serial

measure-ments in medical research British Medical Journal 1990;300:230–5.

9 Moher D, Schulz KF, Altman DG, for the CONSORT Group The CONSORT statement: revised recommendations for improving the quality of reports of

par-allel group randomised trials Lancet 2001;357:1191–4.

10 Altman DG Practical statistics for medical research London: Chapman & Hall;

1991

11 Kapoor AS, Kanji H, Buckingham J, Devereaux PJ, McAlister FA Strength of evi-dence for perioperative use of statins to reduce cardiovascular risk: systematic

review of controlled studies British Medical Journal 2006;333:1149–55.

12 Deeks JJ, Everitt B Forest plot In: Everitt B, Palmer C, editors The encyclopaedic companion to medical statistics London: Arnold; 2005.

13 Deeks JJ Funnel plots In: Everitt B, Palmer C, editors The encyclopaedic compan-ion to medical statistics London: Arnold; 2005.

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by a simple graphical method British Medical Journal 1997;315:629–34.

88 How to Display Data

Appendix

Table A7.1 CONSORT checklist of items to include when reporting a randomised trial9

Title and abstract 1 How patients were allocated to interventions

Introduction

Background 2 Scientifi c background and explanation of rationale

Methods

Participants 3 Eligibility criteria for participants and the settings

and locations where the data were collected Interventions 4 Precise details of the interventions intended for

each group and how and when they were actually

Objectives 5 Specifi c objectives and hypotheses

Outcomes 6 Clearly defi ned primary and secondary outcome

measures and, when applicable, any methods used to enhance the quality of measurements (e.g multiple observations, training of assessors) Sample size 7 How sample size was determined and, when

applicable, explanation of any interim analyses and

Randomisation

Sequence 8 Method used to generate the random allocation generation sequence, including details of any restriction

(e.g blocking, stratifi cation)

Allocation 9 Method used to implement the random allocation concealment sequence (e.g numbered containers or central

telephone), clarifying whether the sequence was concealed until interventions were assigned Implementation 10 Who generated the allocation sequence, who

enrolled participants and who assigned participants

to their groups

Blinding (masking) 11 Whether or not participants, those administering

the interventions, and those assessing the outcomes were blinded to group assignment When relevant, how the success of blinding was

Statistical methods 12 Statistical methods used to compare groups for

primary outcome(s) Methods for additional analyses, such as subgroup analyses and adjusted

(Continued)

Reporting study results 89

Table A7.1 (Continued.)

Results

Participant fl ow 13 Flow of participants through each stage

(a diagram is strongly recommended) Specifi cally, for each group report the numbers of participants randomly assigned, receiving intended treatment, completing the study protocol and analysed for the primary outcome Describe protocol deviations from study as planned, together with reasons Recruitment 14 Dates defi ning the periods of recruitment and

Baseline data 15 Baseline demographic and clinical characteristics

of each group

Numbers analysed 16 Number of participants (denominator) in each

group included in each analysis and whether the analysis was by ‘intention-to-treat’ State the results in absolute numbers when feasible (e.g 10/20, not 50%)

Outcomes and 17 For each primary and secondary outcome, a estimation summary of results for each group, and the

estimated effect size and its precision (e.g 95%

Ancillary analyses 18 Address multiplicity by reporting any other

analyses performed, including subgroup analyses and adjusted analyses, indicating those pre-specifi ed and those exploratory

Adverse events 19 Address multiplicity by reporting any other

analyses performed, including subgroup analyses and adjusted analyses, indicating those pre-specifi ed and those exploratory

Discussion

Interpretation 20 Interpretation of results, taking into account study

hypotheses, sources of potential bias or imprecision and the dangers associated with multiplicity of analyses and outcomes

Generalisability 21 Generalisability (external validity) of the trial

fi ndings

Overall evidence 22 General interpretation of the results in the context

of current evidence

Chapter 8 Time series plots and

survival curves

8.1 Introduction

This chapter outlines good practice when displaying data that are ordered in time These data can arise either as a result of the monitoring of a particular event or events across a population over time (time series) or following up individuals over time to measure their time to a particular event (survival analysis) This chapter is not concerned with repeated measures outcome data as they have already been dealt with in Chapter 7.

8.2 Time series plots

A time series is a series of observations ordered in time It differs from

the repeated measures data discussed in the previous chapter in two ways:

1 Usually there is only one replication of the data, for example one subject’s

heart rate monitored over time, or the annual death rates of one country over time With repeated measures we have more than one subject under consideration.

2 There are many time points Typically in patient monitoring thousands

of points are sampled.

An example of a time series plot is given in Figure 8.1 The data are the number of infant deaths per day in England and Wales over a 7-week period

are that time should be on the X-axis (horizontal) and the series of events that are being monitored, the observations, are on the Y-axis (vertical) In

addition, adjacent points should be joined by straight lines If the origin has been omitted this should be made clear, as here, by two diagonal lines on the axis line Care should be taken when examining published time series plots They are often used in newspapers and a common trick is not to show the origin, so that a small trend can appear magnifi ed This is discussed in more detail in Section 2.3.

Time series plots and survival curves 91

8.3 Lowess smoothing plots

Lowess smoothing plots are a useful way of displaying some time series

applied to continuous data For time series they are useful for investigating non-linear trends, as demonstrated here Figure 8.2a shows the number of prescriptions for non-selective serotonin reuptake inhibitors (SSRIs), a type

of antidepressant, over a 3.5-year period, from 2002 to 2006 for one general practice in Yorkshire, England (Senior J., Personal Communication, 2006) The scatter plot seems to show a generally increasing trend, with more scatter towards the end However, fi tting a lowess smoothing curve with bandwidth

of 50% suggests that in fact the number of prescriptions peaked at around month 30 (Figure 8.2b) This corresponds to the time when national guide-lines were published by NICE recommending that SSRIs should be prescribed

in preference to non-SSRIs for the treatment of depression The peak is sug-gested by the data, and so lowess plots are useful for data exploration, but not

for testing hypotheses Note that as the Y-axis does not begin at the origin

(value 0) this has been indicated by two parallel lines.

45

40

35

30

25

20

15

Time (days)

Figure 8.1 Daily infant deaths in England and Wales over a 7-week period during

1979.1