[임상통계] DELTA2 guidance on choosing the target difference and ... reporting the sample size calculation for a RCT 리뷰

**관련 LINK**

논문 link

https://www.bmj.com/content/363/bmj.k3750

DELTA2 Project Link

https://www.ndorms.ox.ac.uk/csm/delta2-guidance

**논문 소개**

DELTA2 Guidance는 RCT(Randomised Clinical Trial) 임상 연구에서 목표하는 차이값(target difference)과 이에 따라 계산되는 표본 수 산출(sample size calculation)에 대한 Guidance로 University of Oxford의 Centre for Statistics in Medicine 에서 2019년에 최종 버전이 발표되었습니다. 이 논문에서는 이 Guidance의 주요 내용(target difference 설정 및 표본수 산출)에 대해 설명하고 있습니다.

**The DELTA2 project**

the United Kingdom’s Medical Research Council/National Institute for Health Research Methodology Research Programme 의 지원을 받아 진행되었음

기존 Guidance(Delta guidance)의 개정 (target difference, sample size calculation을 다룸)

on specifying and reporting the

**target difference (the effect size)**in the

**sample size calculation**of a randomised controlled trial.

**Box 1: DELTA2 recommendations for researchers undertaking a sample size calculation and choosing the target difference **

Begin by

**searching for relevant literature**to inform the specification of the target differenceTarget difference을 찾기 위해

**우선 문헌 고찰**을 시작할 것Relevant literature can: relate to a

**candidate primary outcome**or the comparison of interest, andinform what is an

**important or realistic difference**for that outcome, comparison, and population.

Candidate

**primary outcomes**should be considered in turn, and**주 평가변수 선택지(Candidate primary outcomes)**를 검토할 것the

**corresponding sample size**explored.Where multiple candidate outcomes are considered,

the choice of the primary outcome and target difference should be based on

consideration of the views of relevant stakeholder groups (eg, patients), as well as

the practicality of undertaking such a study with the required sample size.

The choice should not be based solely on

which outcome yields the minimum sample size.

Ideally, the final sample size will be sufficient for all key outcomes,

although this is not always practical.

**The importance of observing a particular magnitude**of a difference in an outcome결과변수의

**차이값 크기를 특정하는 것(Particular magnitude of a difference)**은 중요함with the exception of mortality and other serious adverse events,

cannot be presumed to be self evident.

Therefore, the target difference for all other outcomes needs

additional justification to infer importance to a stakeholder group.

The target difference for a definitive trial (eg, phase III) should be one

considered to be important to at least one key stakeholder group.

The target difference does

**not necessarily have to be the minimum value**목표 차이값은

**필요한 값의 최소값(the minimum value)보다 커도 무방**함that would be considered important

if a larger difference is considered a realistic possibility or would be necessary to alter practice.

Where

**additional research**is needed to inform what would be an important difference**추가 연구**가 필요할 경우,**anchor and opinion seeking method**가 더 나은 방법임**the anchor and opinion seeking methods**are to be favoured.The distribution method should not be used.

**The anchor and the distribution method 관련 link**

Specifying the target difference based solely on a

standardised effect size approach should be considered a last resort,

Where additional research is needed to inform what would be a realistic difference,

the

**opinion seeking and the review of the evidence base methods**are recommended.Pilot trials are typically too small to inform what would be a realistic difference and

primarily address other aspects of trial design and conduct.

**Use existing studies**to inform the value of key nuisance parameters**기존 연구(existing studies)**결과치(e.g., 탐색 연구 pilot trial)를 표본수 계산에 활용할 것that are part of the sample size calculation.

For example, a pilot trial can be used

to inform the choice of the standard deviation value for a continuous outcome and

the control group proportion for a binary outcome,

along with other relevant inputs such as the amount of missing outcome data.

**Sensitivity analyses,**used in the sample size calculation, should be carried out.- 표본수 계산에 사용된 값(e.g., the target difference, 대조군 반응율 등)들에 대한
**민감도 분석(Sensitivity Analysis)**을 수행해야 함which consider the effect of uncertainty around key inputs

(eg, the target difference and the control group proportion for a binary outcome)

**Specification of the sample size calculation,**including the target difference,- 표본수 계산에 사용된 값들(e.g., target difference)은 양식에 따라 관련 문서(임상시험 계획서 등)에 보고되어야 함
should be reported according to the guidance for reporting items (see table 1)

when preparing key trial documents (grant applications, protocols, and result manuscripts).

**The target difference and sample size calculations in randomised controlled trials **

**RCT 연구에서의 목표 차이값과 표본수 산출 **

**The role of the sample size calculation is****표본수 산출의 역할**to determine how many patients are required

for the

**planned analysis of the primary outcome**to be informativeIt is typically achieved by

specifying a

**target difference for the key (primary) outcome**that can be reliably detected and the required sample size calculated

The

**precise research question**that the trial is primarily set up to answerwill determine what needs to be estimated in the planned primary analysis,

which is known formally as the

**“estimand”**The target difference should be a difference that is appropriate for that estimand.

**The target difference**should be viewed as important byat least one (and preferably more) key stakeholder groups—

that is, patients, health professionals, regulatory agencies, and healthcare funders.

In practice, the target difference is not always formally considered and

in many cases appears, at least from trial reports, to be determined on convenience, the research budget, or some other informal basis.

The target difference can be expressed as an

**absolute difference**(eg, mean difference or difference in proportions) or

**relative difference**(eg, hazard or risk ratio)

is also often referred to, rather imprecisely, as the trial “effect size

**Statistical calculation of the sample size**is far from an exact science**통계적인 피험자수 산출의 한계 (가정 assumption이 사용되고 가정된 값의 차이에 민감)**Firstly, investigators typically make assumptions

that are a simplification of the anticipated analysis.

For example, the impact of adjusting for baseline factors is difficult to quantify upfront,

and even though the analysis is intended to be an adjusted one

(such as when randomisation has been stratified or minimised),

the sample size calculation is often conducted on the basis of an unadjusted analysis.

Secondly, the calculated sample size can be sensitive to the assumptions made in the calculations

a small change in one of the assumptions can lead

to substantial change in the calculated sample size.

Often a simple formula can be used to calculate the required sample size.

it is necessary for researchers

**to balance**통계적 가설 검정 setting에서 제1종 오류와 제2종 오류 사이에서 균형을 맞춰야 함

the risk of incorrectly concluding that there is a difference (Type I error)

when no actual difference between the treatments exists,

with the risk of failing to identify a meaningful treatment difference when the treatments do differ(Type II error)

Under the conventional approach, referred to as the statistical hypothesis testing framework

the probabilities of these two errors are controlled by setting

the

**significance level (type I error)**and**statistical power (1 minus type II error)**at appropriate levels(typical values are two sided 5% significance and 80% or 90% power, respectively).

Once these two inputs have been set, the sample size can be determined given

the

**magnitude of the between group difference**in the outcome it is desired to detect(the target difference).

The calculation (reflecting the intended analysis) is conventionally done

on

**the basis of testing for a difference**of any magnitude

A key question of interest is

**what magnitude of difference**can be ruled out.The expected (predicted) width of the confidence interval can be determined

for a given target difference and sample size calculation,

The required sample size is very sensitive to the target difference.

Under the conventional approach,

halving the target difference quadruples the sample size for a two arm, 1:1, parallel group superiority trial with a continuous outcome.

차이값을 절반으로 설정하면, 표본수 산출 결과는 4배로 커짐(*아래 공식 참조)

Appropriate sample size formulas vary depending on

the proposed trial design and

statistical analysis

In more complex scenarios,

**simulations**can be used더 복잡한 연구 시나리오의 경우

**, S****imulations**도 사용 가능함It is prudent to undertake

**sensitivity calculations**to assess가정값들 확인을 위해

**민감도 분석, 계산**(**sensitivity calculations)**을 하는 것이 현명함the potential effect of misspecification of

**key assumptions**such asthe control response rate for a binary outcome or

the anticipated variance of a continuous outcome

**Specifying the target difference for a randomised controlled trial**

**RCT 연구에서 목표 차이값 설정하기 **

the specification of the target difference for a randomised controlled trial,

a series of recommendations is provided in box 1 and table 1.

Seven broad types of methods can be used

to justify the choice of a particular value as the target difference, which are summarised in box 2

**Box 2: Methods that can help inform the choice of the target difference**Methods that inform what is an important difference

**Anchor**using either a patients' or health professional’s judgment to define what an important difference is

by comparing a patients' health before and after treatment and then

linking this change to participants who showed improvement or deterioration using a more familiar outcome

**Distribution**determine a value based on distributional variation

use a value that is larger than the inherent imprecision in the measurement and therefore

likely to represent a minimal level needed for a noticeable difference

**Health economic**use the principles of economic evaluation

compare cost with

health outcomes and

define a threshold value for the cost of a unit of healt effect that a decision maker is willing to pay

to estimate the overall incremental net benefit of one treatment versus the comparator

**Standardised effect size**the magnitude of the effect on a standardised scale defines the value of the difference

For continuous outcome, the standardised difference can be used

e.g., Cohen’s d effect size

the mean difference/the S.D

For binary or survival(time-to-event) outcome, odds, risk or hazard ratio can be used

no widely recognised cutoff points exist

Methods that inform what is a realistic difference

**Pilot Study**to guide expectations and determine an appropriate target difference for the trial

Phase 2 study could be used to inform Phase 3 study

Methods that inform what is an important or a realistic difference

**Opinion seeking**the target difference can be based on opinions elicited from health professionals, patients, or others

Possible approaches

forming a panel of experts

surveying the membership of a professional or patient body

intervewing individuals

**Review of evidence base**the target difference can be derived from current evidence on the research question

Ideally, from a systematic review or meta-analysis of randomised controlled trials

In the absence of randomised evidence, evidence from observational studies could be used in a similar manner

**Reporting the sample size calculation **

**표본수 산출 결과를 보고할 때 포함되어야 할 사항들 **

**The approach**taken to determine the sample size and the assumptions made should be clearly specified.all

**the inputs and formula**or**simulation results**,so that it is clear what the sample size was based on.

allows the sample size calculation to be replicated, and

clarifies the primary (statistical) aim of the study.

approach with a standard trial design (1:1 allocation, two arm, parallel group, superiority design) and unadjusted statistical analysis,

the core items are

**the primary outcome**, the target difference appropriately specified according tothe outcome type,

the associated nuisance parameter

(that is, a parameter that, together with the target difference, uniquely specifies the difference on the original outcome scale

eg, the event rate in the control group for a binary primary outcome), and

the statistical significance and power

More complicated designs can have additional inputs

such as the intracluster correlation for a cluster randomised design

If the sample size is determined on the basis of

**a series of simulations,**this method should be described

**in sufficient detail**to provide an equivalent level of transparency and assessment

**Discussion**

**논의**

Researchers are faced with a number of difficult decisions when designing a randomised controlled trial, the most important decisions are

The

**choice of trial design**,**primary outcome**, and**sample size**

The sample size is largely driven by

**the choice of the target difference**

The

**DELTA2 guidance**provides help onspecifying a target difference and

undertaking and reporting the sample size calculation for a randomised controlled trial.

The guidance was developed in response to a growing recognition from funders, researchers, and other key stakeholders (such as patients and the respective clinical communities) of a

real need for practical and accessible advice to inform a difficult decision.

The key message for researchers is the need

to be

**more explicit about the rationale**and**justification**of the target differencewhen undertaking and reporting a sample size calculation.

Increasing focus is being placed on the

**target difference**in the clinical interpretation of the trial result,

whether statistically significant or not.

00