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Study design & analysis,� part II

Carl

MMED 2024

Earlier versions by Jim Scott, Travis Porco, & Reshma Kassanjee

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  • In some population, people are dying from an illness
  • A researcher claims to have a treatment that may reduce illness-related mortality
  • He had volunteers from the population try the treatment
  • Mortality among those treated was lower than what was observed in the general population�

Should people be convinced to buy the treatment? � Why or why not?

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Study 1

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Study 1

  • Volunteers may be different in some way to the rest�of the population

  • E.g. Volunteers were younger on average compared �to people selected at random�

Was the lower mortality observed because

  • the participants were volunteers (who were younger) �-OR-
  • the treatment actually worked?

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Study 1

  • Now, what if the results had gone the other way? That is, higher mortality in that population - do we know the treatment is harmful?

  • Again: volunteers may be different in some way to the rest of the population

  • E.g. Volunteers might know they are at high risk, and seek any possible way to mitigate that risk�

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  • The researcher developed a treatment that he felt could alleviate symptoms
  • He selected a group of participants, and provided the treatment over 6 months
  • He found that symptoms measured at 6 months were reduced compared to symptoms measured at the start

… yet people were not convinced to buy the treatment. � Why?

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Study 2

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Study 2

  • If the participants were people having particularly bad weeks, then we would see them return to their average over time

  • If the participants were people who had just acquired the illness, it could be the natural course the illness

  • Maybe people were just relieved to be trying a treatment, which led them to experience their symptoms differently

Was the reduction in symptoms due to the treatment?

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Study design and analysis,�part II:�Randomised controlled trials

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Goals

  • Confounding
  • Describe randomised controlled trials (RCTs) � and the central design elements
  • Limitations, bias and variability

  • Tutorial

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Goals

  • Confounding
  • Describe randomised controlled trials (RCTs) � and the central design elements
  • Limitations, bias and variability

  • Tutorial

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Confounding

Study 1:

Was the lower mortality observed because

  • the participants were volunteers (who were younger) -OR-
  • the treatment actually worked?

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Confounding

  • A concept relevant to causal inference�I.e. when we are trying to estimate the direct impact of an exposure on an outcome
  • In a setting and analysis:

the relationship or association between the exposure and outcome ≠ the causal effect

  • There is some common cause of the exposure and the outcome

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Confounding

  • Even if there is no treatment effect, treatment will be associated with lower mortality

Exposure:�Treatment

Age

Outcome:

Mortality

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Confounding

  • Even if there is no treatment effect, treatment will be associated with lower mortality

Exposure:�Treatment

Age

Outcome:

Mortality

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Confounding

  • Backdoor non-casual paths between the exposure and outcome

Exposure:�Treatment

Age

Outcome:

Mortality

Attitude -�wellbeing

Exercise

Wealth

Free time

Access to healthcare

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Confounding

Exposure:�Treatment

Age

Outcome:

Mortality

Questions?

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Confounding

  • There are methods to account for confounding in the analysis stage: e.g. stratification, and adjusting
  • But we cannot always adjust for confounders in an analysis. Why?

Exposure:�Treatment

Confounder:Age

Outcome:

Mortality

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Exposure:�Treatment

Age

Outcome:

Mortality

Attitude -�wellbeing

Exercise

Wealth

Free time

Access to healthcare

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Exposure:�Treatment

Age

Outcome:

Mortality

Attitude -�wellbeing

Exercise

Wealth

Free time

Access to healthcare

Unknown

confounder

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  • We know how confounding occurs, �but we have not or cannot measure all the confounders

Exposure:�Treatment

Age

Outcome:

Mortality

Attitude -�wellbeing

Exercise

Wealth

Free time

Access to healthcare

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  • Do not know what other confounders there are

Exposure:�Treatment

Age

Outcome:

Mortality

Attitude -�wellbeing

Exercise

Wealth

Free time

Access to healthcare

Unknown

confounder

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Goals

  • Confounding
  • Describe randomised controlled trials (RCTs) � and the central design elements
  • Limitations, bias and variability

  • Tutorial

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Randomised controlled trials

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Randomisation

Randomly assign participants to one of the treatment groups. I.e. what treatment a person receives depends only on chance.

  • Ensures that the treatment assignment is independent of all possible confounders
  • Groups are essentially the ‘same’ with respect to all variables – they differ only by chance
  • Only difference between the groups is in what treatment they receive

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Randomisation

Exposure:�Treatment

Age

Outcome:

Mortality

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Randomisation

Exposure:�Treatment

Age

Outcome:

Mortality

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Randomisation

Exposure:�Treatment

Age

Outcome:

Mortality

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Exposure:�Treatment

Age

Outcome:

Mortality

Attitude -�wellbeing

Exercise

Wealth

Free time

Access to healthcare

Unknown

confounder

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Exposure:�Treatment

Age

Outcome:

Mortality

Attitude -�wellbeing

Exercise

Wealth

Free time

Access to healthcare

Unknown

confounder

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Randomisation

Exposure:�Treatment

Age

Outcome:

Mortality

Questions?

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Study designs

  • Correlational/ecological
  • Cross-sectional
  • Case-control
  • Cohort

  • RCTs (clinical trials) Experimental

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Observational

Ethics

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Randomised controlled trials

Randomisation

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Randomised controlled trials

?

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Study 2:

Was the reduction in symptoms due to the treatment?

What can we include in our study design to help us answer this?

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Randomised controlled trials

Suitable ‘control’ group (or arm) for comparisons

Ethical considerations

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Masking and placebos

  • Knowing the treatment assignments may lead to a biased (often inflated) estimate of the treatment effect
  • Participants or evaluators may be biased in reporting or measuring of outcomes (e.g. symptoms)

Masking/blinding: Participants (and evaluators) do not know to which treatment group each participant has been assigned�

  • Single-blind (participants), double-blind (and evaluators), triple-blind (and data analysts)

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Masking and placebos

Placebo: a ‘treatment’ that has no therapeutic effect, that resembles and is administered in the same way as the treatment being tested

  • Assists with masking
  • Accounts for the placebo-effect: change in a �person’s outcomes because of the perception of the intervention

  • Not always possible or ethical to mask treatment

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Let’s talk through a simple randomized controlled trial….

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Population of interest

Study participants

Randomizer

Treatment

A

Treatment

B

Compare

outcomes

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Ethics

Ethics is central to the purpose and design of �clinical trials

  • Many shocking examples of unethical trials �(e.g. Tuskeegee study)�

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Ethics

  • Institutional, national and international ethical requirements
  • Different oversight bodies: E.g. Internal Review Board (IRB), Data Safety Monitoring Board (DSMB)
  • Internationally, the Declaration of Helsinki (1964) is widely accepted as a statement of key ethical principles for research on human subjects
  • In the USA, the Belmont Report (1978) forms the basis of ethical decisions

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Ethics

Study participants must provide informed consent

  • Voluntarily agree to participate in the research study, fully understanding the potential risks and benefits

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Goals

  • Confounding
  • Describe randomised controlled trials (RCTs) � and the central design elements
  • Limitations, bias and variability

  • Tutorial

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Interpretation limited to study population

Participants are often not representative of the population

Why?

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Population

of interest

Study sample

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Interpretation limited to study population

Participants are often not representative of the population

  • Specific ‘type’ of person that chooses to participate
  • Exclusion criteria: Safety (e.g. pregnant women) and�ethics (e.g. informed consent)

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Population

of interest

Study sample

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estimate =

truth

bias

random error

+

+

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Various other sources of bias

�RCTs are still prone to many of the biases that occur in other study designs

  • E.g. Information bias from inaccurate data collection, selection bias because some participants gets ‘lost’

  • Try to mitigate these biases. E.g. standardized and tested instruments or tools for measuring outcomes, train evaluators

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Compare outcomes

Estimate an effect and its uncertainty

E.g. Time to treatment failure is 1.4 (95% CI: 1.2, 1.6) times larger when using Drug A rather than Drug B

Perform hypothesis testing

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0

1

There is evidence that the treatment may impact the outcome

We think we have made� a discovery (“significant”)

There is a lack of evidence that the treatment impacts the average outcome

We still do not know

p-value

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Analogy for errors: Looking for planets

  • Use a telescope to try to discover a new planet
  • The telescope is like a statistical test�

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Analogy for errors: Looking for planets

  •  

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  • Factors that may impact your ability to see the planet

    • The resolution of your telescope � (↑ sample size, ↑ power)

    • The size of the planet� (↑ effect size, ↑ power)

    • The weather

(↓ variability, ↑ power)

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Analogy for errors: Looking for planets

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  • Factors that may impact your ability to see the planet

    • The resolution of your telescope � (↑ sample size, ↑ power)

    • The size of the planet� (↑ effect size, ↑ power)

    • The weather

(↓ variability, ↑ power)

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Analogy for errors: Looking for planets

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Statistical analysis plan

  • Pre-specified statistical analysis plan
    • Specify the sample size
    • Define outcomes to be analyzed
    • Indicate how missing data will be handled

  • The intent-to-treat principle: �once-randomized, always analyzed as part of the group

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What about mathematical modeling?

  • Data from RCTs can be integrated into your modelling exercise, or models can inform RCTs

  • Mathematical modeling may be valuable in analysis of clinical trial data for interventions against infectious diseases
  • Here, individuals are not independent, since each individual’s status (infected or not infected) affects other individuals
  • Standard statistical methods may not be appropriate

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Summary

RCTs

  • greatly reduce the chance that confounding is present via randomization of treatment assignments
  • provide us with causal evidence (observational studies provide us with associative evidence)

  • Masking/blinding can greatly reduce bias in RCTs
  • Oversight reduces exploratory data analysis, preserves the integrity of the research, and protects participants
  • Ethics is core to conducting clinical trials

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This presentation is made available through a Creative Commons Attribution-Noncommercial license. Details of the license and permitted uses are available at� http://creativecommons.org/licenses/by-nc/3.0/

Study Design and Analysis in Epidemiology II: Clinical Trials. DOI: 10.6084/m9.figshare.5044669.v3

�Attribution: R. Kassanjee, J. Scott, T. Porco

Clinic on the Meaningful Modeling of Epidemiological Data

Source URL: �https://figshare.com/collections/International_Clinics_on_Infectious_Disease_Dynamics_and_Data/3788224

For further information please contact figshare@ici3d.org.

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© 2014-2023 International Clinics on Infectious Disease Dynamics and Data

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Tutorial

  • Demonstrate and strengthen your understanding of key concepts
    • How do you implement randomization?
    • How do your potential confounders get balanced?
    • How does bias in estimating a treatment effect compare with and without randomization?

  • Explore these concepts by simulation
    • Do a ‘synthetic’ study
    • Can do many studies
    • Know the truth

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Tutorial

  • Focus on understanding the reasoning (work through the comments) and outputs – you do not need to understand every line of code (e.g. do not get distracted by the lines of code that set axis limits on plots).

  • Guide you through what you are doing in the comments

  • Okay

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Extra slides from previous years

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Goals

  • Describe the basic design of a randomized controlled trial (RCT)
  • Describe how randomization is used in an RCT and why it is essential
  • Discuss false positive and false negatives in the context of RCTS
  • RCTs and ethics

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Observational Designs

  • Observational designs may suffer from BIAS
    • Selection of subjects can influence results
    • Inaccurate data collection (e.g. recall bias, volunteer bias, etc.)
  • Observational designs may suffer from:

CONFOUNDING

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Example

  • You think some treatment reduces mortality
  • You give treatment to volunteers
  • You compare mortality rates in people getting treatment to those who didn’t get treatment
  • You find lowered mortality in the treated group but no one believes you
  • WHY?

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Example

  • Volunteers are more likely to be healthier on average than participants selected at random
  • Improved health is associated with being a volunteer
  • Those with improved health are also less likely to experience mortality
  • Is lower mortality observed because the participants were volunteers (who tend healthier) -OR-
  • Is lower mortality observed because the treatment actually worked?
  • You can’t tell! CONFOUNDING

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Confounding

  • Variable is related to the treatment (i.e. exposure)
  • Variable is related to the outcome
  • Variable is not on the causal pathway
    • Exp -> Variable Z -> Dis Z is not a confounding variable

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Exp

Dis

Variable Z

Variable Z is a confounding

variable

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Solution: Randomization

  • Randomly assign participants to one of the treatment groups
  • Ensures that treatment assignment is independent of all possible counfounders
  • Groups are essentially the same with respect to all variables – they differ only by chance
  • Only difference between them is that one group receives treatment and the other doesn’t
  • Applet http://www.rossmanchance.com/applets/Subjects.html

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Confounding

  • Randomization ensures groups are balanced
  • No variable is associated with treatment status

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Treatment

Disease

Potential

Confounder

No Confounding!!!

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Randomization

  • Randomization of treatment assignment allows us to make causal conclusions
  • Randomized Controlled Trials provide us with causal evidence
  • Observational studies (i.e. studies that don’t employ randomization of treatment assignment) are subject to confounding -> Associations only
    • Cohort studies
    • Case-control studies
    • Cross-sectional studies
    • Correlational studies

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Non-inferiority Design

  • Compare new drug against existing drug (“active control”)
  • New drug may be cheaper or have fewer side effects
  • Must specify noninferiority margin in advance

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Population of interest

Study participants

Randomizer

Tx

No TX

TX: Outcome

No Tx: Outcome

Compare

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Compare Outcomes

  • You’ll either determine that:
    • 1) there is no evidence that the average outcome (e.g. mortality) differs between groups
    • 2) there is evidence that the average outcome differs between groups

  • However….
    • You won’t ever know the truth

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Making Mistakes

  • If the truth is that the treatment has no effect and you somehow find an effect….that’s a mistake
    • Type I error – False positive
  • You control the rate at which you make these errors
    • Known as “alpha”. Usually set at 0.05

  • If the truth is that the treatment has an effect and you somehow determine that there is no effect…that’s a mistake
    • Type II error – False negative
    • Known as “beta” – variance, effect size, and sample size influence beta
    • 1 – beta = Power

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Power

  • The power of a statistical test is the probability that you correctly find a difference between groups when a difference actually exists

  • Usually, RCTs are designed so power is at least 0.80

  • Analogy

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Compare Outcomes

We never know the truth!

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Different treatments�🡪 different average outcomes

(Null is not “true”)

Different treatments�🡪 ‘same’ average outcomes

(Null is “true”)

Find evidence of differences in outcomes�(Reject null)

Fail to find evidence of differences in outcomes �(Fail to reject null)

In reality

In study

Errors

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Compare Outcomes

We never know the truth!

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Different treatments�🡪 different average outcomes

(Null is not “true”)

Different treatments�🡪 ‘same’ average outcomes

(Null is “true”)

Find evidence of differences in outcomes�(Reject null)

Fail to find evidence of differences in outcomes �(Fail to reject null)

In reality

In study

Errors

 

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Compare Outcomes

We never know the truth!

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Different treatments�🡪 different average outcomes

(Null is not “true”)

Different treatments�🡪 ‘same’ average outcomes

(Null is “true”)

Find evidence of differences in outcomes�(Reject null)

Fail to find evidence of differences in outcomes �(Fail to reject null)

In reality

In study

Errors

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Compare Outcomes

We never know the truth!

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Different treatments�🡪 different average outcomes

(Null is not “true”)

Find evidence of differences in outcomes�(Reject null)

Fail to find evidence of differences in outcomes �(Fail to reject null)

In reality

Errors

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Compare Outcomes

We never know the truth!

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Different treatments�🡪 different average outcomes

(Null is not “true”)

Find evidence of differences in outcomes�(Reject null)

Fail to find evidence of differences in outcomes �(Fail to reject null)

In reality

Errors

 

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Analogy for errors: Looking for planets

  •  

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  • Factors that may impact your ability to see the planet
    • The weather (i.e. variability)
    • The size of the planet (i.e. effect size)
    • The resolution of your telescope (i.e. sample size)

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Analogy for errors: Looking for planets

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Goals

  • Describe the basic design of a randomized controlled trial (RCT)
  • Describe how randomization is used and why it is essential
  • Discuss false positive and false negative results, and power in RCTs
  • Some other important elements of RCTs (?)
  • RCTs and ethics

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Goals

  • Describe the basic design of a randomized controlled trial (RCT)
  • Describe how randomization is used and why it is essential
  • Discuss false positive and false negative results, and power in RCTs
  • Some other important elements of RCTs (?)
  • RCTs and ethics

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Goals

  • Describe the basic design of a randomized controlled trial (RCT)
  • Describe how randomization is used and why it is essential
  • Discuss false positive and false negative results, and power in RCTs
  • Some other important elements of RCTs (?)
  • RCTs and ethics

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Ethics

Central to the purpose and design of clinical trials

  • Separate oversight bodies in different countries and institutions
  • Internal Review Board (IRB)
  • Data Safety Monitoring Board (DSMB)
  • Internationally, the Declaration of Helsinki is widely accepted as a statement of key ethical principles for research on human subjects

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Declaration of Helsinki

“In medical research involving human subjects, the well-being of the individual research subject must take precedence over all other interests.”

“Medical research involving a disadvantaged or vulnerable population or community is only justified if the research is responsive to the health needs and priorities of this community and if there is a reasonable likelihood that this population or community stands to benefit from the results of the research.”

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The Belmont Report

Three fundamental principles

  • Respect for persons
  • Beneficence
  • Justice

Basis of US guidance (45 CFR 46)

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Informed Consent

  • Informed: Participant must be made aware of the potential risks and benefits of the treatment

  • Consent: Voluntary and informed consent is required for a subject to participate in a research study, they may opt out at any time

  • Overseen by study review board

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Ethics

Central to the purpose and design of clinical trials

  • Separate oversight bodies in different countries and institutions
  • Internal Review Board (IRB)
  • Data Safety Monitoring Board (DSMB)
  • Internationally, the Declaration of Helsinki is widely accepted as a statement of key ethical principles for research on human subjects

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You need to know about ethical considerations and ensure ethical studies

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Confounding

A confounder is

  • Related to the exposure (i.e. treatment)
  • Related to the outcome
  • Not on the causal pathway from exposure to outcome
    • E.g. Drug improve hair growth

Drug iron hair growth

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Exposure

Outcome

Confounder

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Confounding

A confounder is

  • Related to the exposure (i.e. treatment)
  • Related to the outcome
  • Not on the causal pathway from exposure to outcome

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Exposure

Outcome

Potential�Confounder

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Randomized Controlled Trials

Implement randomization of treatment assignments�

  • Provide us with causal evidence

  • In contrast to observational studies �which are subject to confounding�and provide only associations

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Exposure

Outcome

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Masking / blinding

  • Single-blind: Participants do not know their assignments
  • Double-blind: … and evaluators do not know assignments
  • Triple-blind: … and analysts do not know assignments

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Observational Designs

Observational studies are prone to suffer from

Bias

    • Selection �E.g. Subjects who participate in your data collection or receive the treatment not representative
    • Information Any inaccurate data collection or handling �E.g. Recall, misclassifications, ‘missing not at random’ data

Confounding

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Statistical analysis plan

  • Pre-specified statistical analysis plan
    • Specify the sample size
    • Define outcomes to be analyzed
    • Indicate how missing data will be handled
  • The intent-to-treat principle: �once-randomized, always analyzed as part of the group

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Accurate measurements

  • Standardization of measurements
  • Subjective measurements should involve training and certification, estimation of interrater agreement