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Regression analysis Tamuno Alfred, PhD Biostatistician DataCamp - - PowerPoint PPT Presentation

Nov 29, 2023 307 likes •978 views

DataCamp Designing and Analyzing Clinical Trials in R DESIGNING AND ANALYZING CLINICAL TRIALS IN R Regression analysis Tamuno Alfred, PhD Biostatistician DataCamp Designing and Analyzing Clinical Trials in R Explanatory variables DataCamp

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DataCamp Designing and Analyzing Clinical Trials in R

Regression analysis

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

Tamuno Alfred, PhD

Biostatistician

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DataCamp Designing and Analyzing Clinical Trials in R

Explanatory variables

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DataCamp Designing and Analyzing Clinical Trials in R

Explanatory variables

Also referred to as covariates, independent or predictor variables. Examples include: age sex baseline values disease severity lifestyle factors

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DataCamp Designing and Analyzing Clinical Trials in R

Explanatory variables

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DataCamp Designing and Analyzing Clinical Trials in R

Simple linear regression

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DataCamp Designing and Analyzing Clinical Trials in R

Simple linear regression

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DataCamp Designing and Analyzing Clinical Trials in R

Simple linear regression

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DataCamp Designing and Analyzing Clinical Trials in R

Simple linear regression

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DataCamp Designing and Analyzing Clinical Trials in R

Simple linear regression

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DataCamp Designing and Analyzing Clinical Trials in R

Simple linear regression

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DataCamp Designing and Analyzing Clinical Trials in R

Simple linear regression

asthma.trial$group <- relevel(asthma.trial$group, ref="Placebo") asthma.reg1 <- lm(fev.change ~group, asthma.trial) summary(asthma.reg1)

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DataCamp Designing and Analyzing Clinical Trials in R

Simple linear regression

asthma.trial$group <- relevel(asthma.trial$group, ref="Placebo") asthma.reg1<-lm(fev.change ~group, asthma.trial) summary(asthma.reg1)

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DataCamp Designing and Analyzing Clinical Trials in R

Simple linear regression

t.test(fev.change~group, var.equal=TRUE, data=asthma.trial)

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DataCamp Designing and Analyzing Clinical Trials in R

Multivariable linear regression

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DataCamp Designing and Analyzing Clinical Trials in R

Multivariable linear regression

asthma.reg2<-lm(fev.change ~group + age, asthma.trial) summary(asthma.reg2)

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DataCamp Designing and Analyzing Clinical Trials in R

Logistic regression

Binary outcomes

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DataCamp Designing and Analyzing Clinical Trials in R

Logistic regression

asthma.logreg1=glm(attack~group + age, family=binomial(link="logit"), asthma.trial) summary(asthma.logreg1) exp(coefficients(asthma.logreg1)[2]) exp(confint(asthma.logreg1)[2,])

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DataCamp Designing and Analyzing Clinical Trials in R

Let's practice!

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

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DataCamp Designing and Analyzing Clinical Trials in R

Analysis sets, subgroups and interactions

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

Tamuno Alfred, PhD

Biostatistician

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DataCamp Designing and Analyzing Clinical Trials in R

Patient adherence

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DataCamp Designing and Analyzing Clinical Trials in R

Intention-to-treat (ITT)

Evaluate according to planned treatment Consider all patients irrespective of treatment received and compliance May lead to dilution of treatment effect estimate Reflects real-life conditions

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DataCamp Designing and Analyzing Clinical Trials in R

Analysis sets

Full Analysis Set (FAS): Generally all randomized patients May exclude patients who violate eligibility criteria or without post-baseline visits Primary efficacy analyses Follows ITT principle

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DataCamp Designing and Analyzing Clinical Trials in R

Analysis sets

Full Analysis Set (FAS): Generally all randomized patients May exclude patients who violate eligibility criteria or without post-baseline visits Primary efficacy analyses Follows ITT principle Per-Protocol Set (PP): Subset of ‘compliers’ May better reflect pure treatment effect

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DataCamp Designing and Analyzing Clinical Trials in R

Analysis sets

Conducted on 201 FAS patients

asthma.fas<-lm(fev.change ~group , asthma.trial) summary(asthma.fas)

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DataCamp Designing and Analyzing Clinical Trials in R

Analysis sets

Conducted on 201 FAS patients Conducted on 183 PP patients

asthma.fas<-lm(fev.change ~group , asthma.trial) summary(asthma.fas) asthma.pp<-lm(fev.change ~group , asthma.trial, subset = pp==1) summary(asthma.pp)

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DataCamp Designing and Analyzing Clinical Trials in R

Subgroup analysis

Evaluate treatment responses in different patient groups, e.g. Males only <50 years Non-obese patients

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DataCamp Designing and Analyzing Clinical Trials in R

Subgroup analysis

asthma.u65<-lm( fev.change ~group , asthma.trial, subset = age<65) summary(asthma.u65) asthma.o65<-lm( fev.change ~group , asthma.trial, subset = age>=65) summary(asthma.o65)

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Subgroup analysis

Rationale for subgroups Pre-specified in Statistical Analysis Plan Sufficient numbers of patients Consider impact of multiple testing

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DataCamp Designing and Analyzing Clinical Trials in R

Interaction

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DataCamp Designing and Analyzing Clinical Trials in R

Interaction

asthma.ageg <- lm( fev.change ~group + agegroup , asthma.trial) summary(asthma.ageg)

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DataCamp Designing and Analyzing Clinical Trials in R

Interaction

asthma.ageint <- lm( fev.change ~ group*agegroup , asthma.trial) summary(asthma.ageint)

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Interaction

asthma.ageint<-lm( fev.change ~group*agegroup , asthma.trial) summary(asthma.ageint)

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DataCamp Designing and Analyzing Clinical Trials in R

Now your turn!

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

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DataCamp Designing and Analyzing Clinical Trials in R

Multiplicity of data

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

Tamuno Alfred, PhD

Biostatistician

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DataCamp Designing and Analyzing Clinical Trials in R

Multiplicity of data

Multiple subgroups of patients Multiple looks at data (interim analyses) Multiple outcomes of interest Multiple study visits

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DataCamp Designing and Analyzing Clinical Trials in R

Multiple testing

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DataCamp Designing and Analyzing Clinical Trials in R

Bonferroni correction

Divide the overall significance level by the number of tests to generate new significance levels, or Multiply the p-value from the tests by the number of tests to generate the adjusted p-value

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DataCamp Designing and Analyzing Clinical Trials in R

Bonferroni correction

Divide the overall significance level by the number of tests to generate new significance levels, or Multiply the p-value from the tests by the number of tests to generate the adjusted p-value

0.05/4

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DataCamp Designing and Analyzing Clinical Trials in R

Bonferroni correction

Divide the overall significance level by the number of tests to generate new significance levels, or Multiply the p-value from the tests by the number of tests to generate the adjusted p-value May be conservative Alternatives include Holm–Bonferroni method and false discovery rate

0.05/4

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DataCamp Designing and Analyzing Clinical Trials in R

Subgroup analysis

asthma.u65<-lm( fev.change ~group , asthma.trial, subset = age<65) summary(asthma.u65) asthma.o65<-lm( fev.change ~group , asthma.trial, subset = age>=65) summary(asthma.o65)

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Subgroup analysis

Large number of subgroups can be derived

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DataCamp Designing and Analyzing Clinical Trials in R

Subgroup analysis

Large number of subgroups can be derived Increase chance of observing a Type I error

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DataCamp Designing and Analyzing Clinical Trials in R

Subgroup analysis

Large number of subgroups can be derived Increase chance of observing a Type I error Lack of power within subgroups

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DataCamp Designing and Analyzing Clinical Trials in R

Subgroup analysis

Large number of subgroups can be derived Increase chance of observing a Type I error Lack of power within subgroups Imbalance of other patient characteristics within subgroups

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DataCamp Designing and Analyzing Clinical Trials in R

Subgroup analysis

Large number of subgroups can be derived Increase chance of observing a Type I error Lack of power within subgroups Imbalance of other patient characteristics within subgroups Recommendations: Limit number of subgroups Use external evidence Correct p-values Use interaction tests

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Interim analysis

Multiple looks at the data can increase overall Type I error Trial may stop too early

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DataCamp Designing and Analyzing Clinical Trials in R

Interim analysis

Multiple looks at the data can increase overall Type I error Trial may stop too early Recommendations: Limit the number of looks at the efficacy data Use an appropriate stopping rule, e.g. Pocock or O'Brien-Fleming

library(gsDesign) Pocock <- gsDesign(k=3, test.type=2, sfu="Pocock") 2*(1-pnorm(Pocock$upper$bound))

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Multiple endpoints

Multiple endpoints of interest e.g. different assessments of lung function, occurrence of an asthma attack Recommendations: Prioritize endpoints Correction for multiple testing, e.g. Bonferroni

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Composite endpoints

Can combine certain endpoints May increase statistical power

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DataCamp Designing and Analyzing Clinical Trials in R

Composite endpoints

Can combine certain endpoints May increase statistical power

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DataCamp Designing and Analyzing Clinical Trials in R

Composite endpoints

Can combine certain endpoints May increase statistical power Check results for each endpoint

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Repeated measurements

Outcome collected for participants at several time-points

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DataCamp Designing and Analyzing Clinical Trials in R

Repeated measurements

Outcome collected for participants at several time-points Should not ignore collected data

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DataCamp Designing and Analyzing Clinical Trials in R

Repeated measurements

Outcome collected for participants at several time-points Should not ignore collected data Testing at each time-point increases chance of observing a Type I error Within-patient assessments are likely correlated and not independent

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Repeated measurements

Outcome collected for participants at several time-points Should not ignore collected data Testing at each time-point increases chance of observing a Type I error Within-patient assessments are likely correlated and not independent Recommendations: Summary statistic approach: area under the curve, mean, maximum value, etc More advanced statistical methods, such as mixed models

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Let's look at some examples

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

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DataCamp Designing and Analyzing Clinical Trials in R

Conclusion

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

Tamuno Alfred, PhD

Biostatistician

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DataCamp Designing and Analyzing Clinical Trials in R

Clinical trials

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DataCamp Designing and Analyzing Clinical Trials in R

Guidelines

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Randomization

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Trial designs

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Sample size determination

power.prop.test(p1=0.3, p2=0.15, power=0.8)

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Statistical analyses

Continuous outcomes Two-sample t-tests Linear regression Wilcoxon Rank Sum test Binary outcomes Test for equal proportions Logistic regression

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Further topics

Adverse events Survival analysis Longitudinal data Count data Missing data Meta-analysis

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DataCamp Designing and Analyzing Clinical Trials in R

Thank you

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

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