Statistics for Non-Statisticians

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Statistics for Non-Statisticians

• Kay M. Larholt, Sc.D.
• Vice President, Biometrics Clinical Operations
• Abt Bio-Pharma Solutions

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Topics

• Basic Statistical Concepts
• 2) Study Design
• 3) Blinding and Randomization
• 4) Hypothesis testing
• 5) Power and Sample Size

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Basic Statistical Concepts
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Statistics

• Per the American Heritage dictionary -
• The mathematics of the collection,
  organization, and interpretation of numerical
  data, especially the analysis of population
  characteristics by inference from sampling.
• Two broad areas
• Descriptive Science of summarizing data
• Inferential Science of interpreting data in
  order to make estimates, hypothesis testing,
  predictions, or decisions from the sample to
  target population.

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Introduction to Clinical Statistics

• Statistics - The science of making decisions in
  the face of uncertainty
• Probability - The mathematics of uncertainty
• The probability of an event is a measure of how
  likely the event is to happen

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Sample versus Population
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Clinical Statistics

• Biostatisticians are statisticians who apply
  statistics to the biological sciences.
• Clinical statistics are statistics that are
  applied to clinical trials

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Basic Statistical Concepts

• Types of data
• Descriptive statistics
• Graphs
• Basic probability concepts
• Type of probability distributions in clinical
  statistics
• Sample vs. population

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Types of Data
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Types of Quantitative Variables
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Continuous Data

• Data should be collected in its rawest form.
  We can always categorize data later. (We can
  never uncategorize data.)
• e.g. If you measure prostate size as part of the
  clinical trial then capture the size in mm on the
  CRF.

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Basic Data Summarization Techniques

• The objective of data summarization is to
  describe the characteristics of a data set.
  Ultimately, we want to make the data set more
  comprehensible and meaningful.
• To put data in a concise form, use
• Summary descriptive statistics
• Graphs
• Tables

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Descriptive Statistics for Continuous Variables

• Measures of central tendency
• Mean, Median, Mode
• Measures of dispersion
• Range, Variance, Standard deviation
• Measures of relative standing
• Lower quartile (Q1)
• Upper quartile (Q3)
• Interquartile range (IQR)
• range (IQR)

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Mean

• Arithmetic average sum of all observations
  divided by of observations.
• Example
• The average age of a group of 10 people is
  24.2 years
• Who are they?

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Mean

• Answer
• They could be ten twenty-somethings who go out
  to dinner together
• Pete aged 24, Jane aged 26, Louise aged 21, Bob
  aged 22, Julie aged 23, Sue aged 22, Jenn aged
  27, John aged 28, Jeff aged 20 and Mark aged 29.
  
• The mean age for these 10 people is
• (24262122232227282029)/10
• 
  24.2 years

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Mean

• Or alternatively
• They could be Mr. Mrs. Smith and their 8
  grandchildren
• Susie aged 3, Abby aged 5, Max aged 8, Laura
  aged 10, Joshua aged 10, Emma aged 12, Jane aged
  13, Sarah aged 18, Mrs. Smith aged 80, Mr. Smith
  aged 83.
• The mean age for these 10 people is
• (35810101213188083)/10
• 
  24.2 years

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Mean

• Presenting the average alone does not give you
  much information about the data you are looking
  at.

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Median

• The midpoint of the values after they have been
  ordered from the smallest to the largest, or the
  largest to the smallest.
• There are as many values above the median as
  below it in the data array.

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Median
Example The age of the people in our data set
is 24, 26, 21, 23, 22, 27, 28, 20, 29 ( I took
out one of the 22 year olds to make this example
easier) Arranging the
data in ascending order gives 20, 21, 22, 23,
24, 26, 27, 28, 29
The median is 24
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There are three kinds of lies lies, damned
lies, and statistics.
This well-known saying is part of a phrase
attributed to Benjamin Disraeli and popularized
in the U.S. by Mark Twain
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Median Home Price

• Connecticut Darien
• Median home price 1,295,000
• Location about 40 miles northeast of midtown
  Manhattan
• Population 20,209, households 6,592

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Properties of Mean and Median

• There are unique means and medians for each
  variable in the data set.
• Median is not affected by extremely large or
  small values and is therefore a valuable measure
  of central tendency when such values occur.
• Mean is a poor measure of central tendency in
  skewed distributions.

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Mode
3-14

• The value of the observation that appears most
  frequently.
• Example
• The exam scores for ten students are
• 81, 93, 84, 75, 68, 87, 81, 75, 81, 87.
• Since the score of 81 occurs the most, the
  modal score is 81.

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Averages and What Else?

• As we have seen, just knowing the mean or even
  the median of a data set does not tell us enough
  about the data. We need more information to
  really describe the data.

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Measures of Dispersion

• Once we know something about the centre of the
  data we need to understand how the data are
  dispersed around this centre.
• How variable are the data?

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Range

• Maximum value in the data set minus Minimum value
  in the data set
• The age of the patients in our data set is
• 21, 25, 19, 20, 22
• Range 25 19 6
• 2. The age of the patients in our data set is
• 21, 45, 19, 20, 22.
• Range 45 19 26
• When max and min are unusual values, range may be
  a misleading measure of dispersion. The range
  only uses the 2 extreme values in the data.

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Variance and Standard Deviation

• The variance of a data set measures how far each
  data point is from the mean of the data set.
• It provides a measure of how spread out the data
  points are
• The Standard Deviation is the square root of the
  variance

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Variance and Standard Deviation
Variance Measure of dispersion, the square of
the deviations of the data from the mean Standard
deviation positive square root of the
variance Small std dev observations are
clustered tightly around the mean Large std dev
observations are scattered widely about the mean
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Standard Deviation
Take each observation and subtract it from the
mean of the observations Square the answer Sum up
all the results Divide by n-1 Take the square root
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Example Standard Deviation

• The age of the patients in our data set is
• 21, 25, 19, 20, 22
• Mean 21.4, Median 21, StdDev 2.302
• 2. The age of the patients in our data set is
• 21, 45, 19, 20, 22.
• Mean 25.4, Median 21, StdDev 11.014

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Choosing an Appropriate Method of Central Tendency

• The mean is ordinarily the preferred measure of
  central tendency. The mean should always be
  presented along with the variance or the standard
  deviation
• There are situations when a median might be more
  appropriate
• - a skewed distribution
• - a small number of subjects

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Measures of Relative Standing

• Descriptive measures that locate the relative
  position of an observation in relation to the
  other observations.

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Measures of Relative Standing

• The pth percentile is a number such that p of
  the observations of the data set fall below and
  (100-p) of the observations fall above it.
• Lower quartile 25th percentile (Q1)
• Mid-quartile 50th percentile (median or Q2)
• Upper quartile 75th percentile (Q3)
• Interquartile range (IQR Q3-Q1)

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Measures of Relative Standing an Example
The age of the patients in our data set is 21,
25, 19, 20, 22 Q1 20, Q2 21, Q3 22, IQR
2 The age of the patients in our data set is
21, 45, 19, 20, 22 Q1 20, Q2 21, Q3
22, IQR 2
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Definitions

• Statistics - The science of making decisions in
  the face of uncertainty
• Probability - The mathematics of uncertainty
• The probability of an event is a measure of how
  likely the event is to happen

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Basic Probability Concepts

• Sample spaces and events
• Simple probability
• Joint probability

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Sample Spaces

• Collection of all possible outcomes
• Example All six faces of a die
• Example All 52 cards in a deck

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Sample Space

• Gumballs in a gumball machine

60 red 50 green 40 yellow 30 white 25 pink 20
blue 16 purple
Total 241 gumballs
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Events

• Simple event
• Outcome from a sample space with one
  characteristic
• Examples A red card from a deck of cards
• A purple gumball from the
  gumball machine
• Joint event
• Involves two outcomes simultaneously
• Example An ace that is also red from a deck of
  cards

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Events

• Mutually exclusive events
• Two events cannot occur together
• Example Drawing one card from a deck
• A Drawing a queen of diamonds
• B Drawing a queen of clubs
• As only one of these can happen
• Events A and B are mutually exclusive

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Probability
Certain
1

• Probability is the numerical measure of the
  likelihood that an event will occur
• Value is between 0 and 1

.5
0
Impossible
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Computing Probabilities

• The probability of an event E
• Assumes each of the outcomes in the sample space
  is equally likely to occur

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Computing Probabilities

• Example
• What is the probability of rolling a 4 when you
  roll a die?
• of possible outcomes in the sample space 6
• of 4s in the sample space 1
• Prob (rolling a 4 when you roll a die) 1/6

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Computing Probabilities

• Example
• What is the probability of rolling a six and a
  four when you roll 2 dice?
• of possible outcomes in the sample space 36
• of ways to roll one 6 and one 4 2

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Computing Joint Probability

• The probability of a joint event, A and B

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Computing Joint Probability
P (Red Card and an Ace) 2 Red Aces Total
Cards 2/52 1/26
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Type of Probability Distributions in Clinical
Statistics

• Bernoulli
• Binomial
• Normal

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Bernoulli Distribution

• The bernoulli distribution is the coin flip
  distribution.
• X is bernoulli if its probability function is

Examples X1 for heads in coin toss
X1 for male in survey
X1 for defective in a test of product
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Binomial Distribution

• The binomial distribution is just n independent
  bernoullis added up.
• It is the number of successes in n trials.
• Probability of success is usually denoted by p,
  and therefore probability of failure is 1-p.
• Example Number of heads when we flip a coin 10
  times. Here n 10, p0.5 (the probability of
  getting a head when we toss the coin once).

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Binomial Distribution

• The binomial probability function

Example X Number of heads when we flip a coin
10 times. Here X Binomial (n 10, p0.5) n!
n factorial n.n-1.n-2..1 10!10.9.8.7.6.5.4.3.2
.13,628,800
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Binomial Distribution

• Expectation
• Variance

X Number of heads when we flip a coin 10 times.
Here X Binomial (n 10, p0.5). Then E(X)5
(on average we expect to get 5 heads) and Var(X)
2.5.
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Gaussian or Normal Distribution aka Bell Curve

• Most important probability distribution in the
  statistical analysis of experimental data.
• Data from many different types of processes
  follow a normal distribution
• Heights of American women
• Returns from a diversified asset portfolio
• Even when the data do not follow a normal
  distribution, the normal distribution provides a
  good approximation

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Gaussian or Normal Distribution aka Bell Curve

• The Normal Distribution is specified by two
  parameters
• The mean, ?
• The standard deviation, ?

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Standard Normal Distribution
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Characteristics of the Standard Normal
Distribution

• Mean µ of 0 and standard deviation s of 1.
• It is symmetric about 0 (the mean, median and the
  mode are the same).
• The total area under the curve is equal to one.
  One half of the total area under the curve is on
  either side of zero.

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Area in the Tails of Distribution

• The total area under the curve that is more than
  1.96 units away from zero is equal to 5.
  Because the curve is symmetrical, there is 2.5
  in each tail.

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Normal Distribution

• 68 of observations lie within 1 std dev of
  mean
• 95 of observations lie within 2 std dev of
  mean
• 99 of observations lie within 3 std dev of mean

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Study Design
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Sample versus Population

• A population is a whole, and a sample is a
  fraction of the whole.
• A population is a collection of all the elements
  we are studying and about which we are trying to
  draw conclusions.
• A sample is a collection of some, but not all, of
  the elements of the population

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Sample versus Population
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Sample versus Population

• To make generalizations from a sample, it needs
  to be representative of the larger population
  from which it is taken.
• In the ideal scientific world, the individuals
  for the sample would be randomly selected. This
  requires that each member of the population has
  an equal chance of being selected each time a
  selection is made.

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Type of Studies and Study Design

• Phase I IV
• Controlled vs. non-controlled studies
• Single arm, parallel groups, cross-over designs,
  and stratified designs
• Selecting an appropriate study design
• Analysis population Intent-to-treat vs.
  per-protocol

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Phases of Clinical Trials

• Clinical trials are generally categorized into
  four phases.
• An investigational medicine or product may be
  evaluated in two or more phases simultaneously in
  different trials, and some trials may overlap two
  different phases.

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Phase 1 Studies Safety and Dosing

• Initial safety trials in which investigators
  attempt to establish the dose range tolerated by
  20-80 healthy volunteers.
• Although usually conducted on healthy volunteers,
  Phase 1 trials are sometimes conducted with
  severely ill patients, for example those with
  cancer or AIDS.

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Phase 2 Studies Safety and Limited Efficacy

• Pilot clinical trials to evaluate safety and
  efficacy in selected populations of about 100-300
  patients who have the disease or condition to be
  treated, diagnosed, or prevented. Often referred
  to as feasibility studies
• Used as dose finding studies as different doses
  and regimens are investigated

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Phase 3 studies - efficacy

• Large definitive studies that are carried out
  once safety has been established and doses that
  are likely to be effective have been found
• Often called pivotal studies
• FDA usually requires 2 Phase III studies for
  registration

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Phase 4 studies post marketing surveillance

• After the product is marketed, Phase 4 studies
  provide additional details about the products
  safety and efficacy.
• May be used to evaluate formulations, dosages,
  durations of the treatment, medicine
  interactions, and other factors.
• Patients from various demographic groups may be
  studied.

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Phase 4 studies post marketing surveillance

• Important part of many Phase 4 studies detecting
  and defining previously unknown or inadequately
  quantified adverse reactions and related risk
  factors.
• Phase 4 studies are often observational studies
  rather than experimental.

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Hierarchy of medical evidence

• From weakest to strongest evidence
• Case reports
• Case series
• Database studies
• Observational studies
• Controlled clinical trials
• Randomized controlled trial
• 
  Byar, 1978

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Clarke MJ Ovarian Oblation in breast cancer, 1896
to 1998 milestones along hierarchy of evidence
from case report to Cochrane review BMJ 1998 317
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Controlled studies

• Studies in which a test article is compared with
  a treatment that has known effects.
• The control group may receive no treatment,
  standard treatment or placebo.

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What is a randomized clinical trial?

• A prospective study in humans
• Randomization
• Comparable control group
• Complete accounting of all cases
• Carefully monitored for safety and efficacy
• Adheres to regulatory requirements GCP,FDA, ICH
  guidelines

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Blinded studies

• Blinded study one in which subject or the
  investigator (or both) are unaware of what trial
  product a subject is receiving.
• Single-blind study subjects do not know what
  treatment they are receiving (active or control)
• Double-blind study neither the subjects nor the
  investigators know what treatment a subject is
  receiving

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• Analysis Populations

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Intent-to-Treat Principle

• Primary analysis in most randomized clinical
  trials testing new therapies or devices.
• Requires that any comparison among treatment
  groups in a randomized clinical trials is based
  on the results for all subjects in the treatment
  group to which they were randomly assigned.
• Full analysis includes compliers and
  non-compliers

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Intent-to-Treat

• ITT Population includes the following
• All Randomized patients Preserve initial
  randomization
• - Prevents biased comparison
• - Basis for statistical tests and inference

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Intent-to-Treat

• Problems Predictable or Unpredictable
• Ineligible Patients allowed in the trial
• Non-compliance, ie. not following the assigned
  treatment
• Patients refusing a trial procedure
• Prohibited medication
• Early withdrawal/termination
• Invalid data

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Intent-to-Treat
FDA guideline related to regulatory submission
states As a general rule, even if the sponsors
preferred analysis is based on a reduced subset
of the patients with data, there should be an
additional intent-to-treat analysis using all
randomized patients. Ref ICH E3 Structure and
Content of Clinical Study Reports
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Intent-to-Treat

• When can we exclude randomized patients?
• Failure to satisfy major entry criteria
• Failure to take at least one dose of medication
• Failure to complete procedure
• Lack of any data post-randomization
• Lost to follow up
• Missing data randomly, not related to treatment
  assignment

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Intent-to-Treat
Problem In a 6-Month study, what should be done
with the patient who drops out and provides no
further data after 2 months ?
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Intent-to-Treat
Last Observation Carried Forward (LOCF) Use last
available valid observation post-baseline on a
particular variable for the missing visit through
the end of study
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LOCF last observation carried forward

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Last Observation Carried Forward (LOCF) Biased
if the early withdrawal is treatment related
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Example
The primary analysis sample will be based on the
principle of intention-to-treat. All patients
who sign the written Informed Consent form, meet
the study entry criteria, and undergo
randomization will be included in the analysis,
regardless of whether or not the assigned
treatment device was implanted.
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Intent-to-Treat Principle

• Using the complete analysis data set
• Preserves the randomization at the time of
  analysis which helps prevent bias
• Provides the foundation for statistical testing.
• Provides estimates of treatment effects which are
  more likely to mirror those observed in clinical
  practice.

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Argument against ITT

• An ITT, by including subjects, randomized to the
  drug but who received little or no drug will
  dilute the treatment effect when compared to the
  placebo group

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How can we improve the ITT analysis?

• Careful identification of inclusion/exclusion
  criteria
• Careful review of reasons for failure, missing
  data, and exclusions
• Adherence to Good Clinical Practices
• Better monitoring practices to reduce the
  protocol deviations and non compliance
• Appropriate and detailed statistical plan and
  analysis

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Per-Protocol aka Evaluable patient population

• Subset of ITT who are compliant with the protocol
  and excluding patients who
• Major protocol violation/deviation
• Use prohibited medication as per protocol
• Technical or procedural failure
• Lost to follow up, lack of efficacy/response
• Wrong treatment assignment

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Per-Protocol Population

• Advantages and disadvantages
• Analysis in its pure form, completely as per the
  protocol
• Maximize the efficacy from new treatment
• Not a conservative approach, results in bias
• due to exclusion

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Per-Protocol Population

• Advantages and disadvantages
• May not have enough power and sample size
• Both analyses are done in confirmatory trials
• If the results and conclusions are the same from
• two analyses, the confidence is higher.

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Blinding and Randomization
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Randomisation

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History

• The concept of randomisation was introduced by
  R.A. Fisher in 1926 in the area of agricultural
  research.
• Previous to that clinical trials in the 18th and
  19th centuries had used controls from the
  literature, other historical controls and
  concurrent controls.

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Randomisation

• To guard against any use of judgement or
  systematic arrangements i.e to avoid bias
• To provide a basis for the standard methods of
  statistical analysis such as significance tests
• Assures that treatment groups are balanced (on
  average) in all regards.
• i.e. balance occurs for known prognostic
  variables and for unknown or unrecorded variables

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• Inferential statistics calculated from a clinical
  trial make an allowance for differences between
  patients and that this allowance will be correct
  on average if randomisation has been employed.

96

• Randomisation promotes confidence that we have
  acted in utmost good faith. It is not to be used
  as an excuse for ignoring the distribution of
  known prognostic factors.
• Randomisation is essential for the effective
  blinding of a clinical trial.

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Non-Randomised Trials

• It is difficult to obtain a reliable assessment
  of treatment effect from non-randomised studies.

98
Uncontrolled Trials

• Medical Practice implies that a doctor prescribes
  a treatment for a patient that in his/her
  judgement, based on past experience, offers the
  best prognosis.
• Clinicians are always looking for new therapies,
  improvements in therapies and alternative
  therapies.

99

• When a new treatment is proposed some clinicians
  might try it on a few patients in an uncontrolled
  trial.
• The new treatment is studied without any direct
  comparison with a similar group of patients on
  more standard therapy.

100

• Uncontrolled trials have the potential to provide
  a very distorted view of therapy.
• Why?

101
Laetrile

• In the 1970s in the US Laetrile achieved
  widespread popular support for treating advanced
  cancer of all types without any formal testing in
  clinical trials.
• NCI tried to collect documented cases of tumour
  response after Laetrile therapy. Although an
  estimated 70,000 cancer patients had tried
  Laetrile only 93 cases were submitted for
  evaluation and 6 were judged to have a response.

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Laetrile

• An uncontrolled trial of 178 patients found no
  benefit and evidence of cyanide toxicity
• The final conclusion of NCI was that Laetrile is
  a toxic drug that is not effective as a cancer
  treatment

103

• Uncontrolled trials are much more likely to lead
  to enthusiastic recommendation of the treatment
  as compared with properly controlled trials.

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Historical Controls

• Instead of randomising groups studies compare the
  current patients on the new treatment with
  previous patients who had received the standard
  treatment.
• This is a Historical Control group.

105

• Major flaw - How can we be sure that the
  comparison is fair. How do we know whether the 2
  groups differ with respect to any feature other
  than the treatment itself.

106
Patient Selection

• Historical control group is less likely to have
  clearly defined criteria for patient inclusion
  because the patients on the standard treatment
  were not known to be in the clinical trial when
  their treatment began.
• Historical controls were recruited earlier and
  possibly from a different source and therefore
  might be a different type of patients.
• Investigator might be more restrictive in choice
  of patients for new treatment

107
Concurrent Non-randomised Controls

• Use some pre-determined systematic method or
  investigator judgement to assign patients to
  groups

108
Non-Randomised controls

• Date of Birth odd/even day of birth
  new/standard treatment
• Date of presentation odd/even days
  new/standard treatment
• Alternate assignment odd/even patients
  new/standard treatment

109
Example

• Trial of anticoagulant therapy for MI
• Patients admitted on odd days of the month
  received anticoagulant and patients admitted on
  even days did not.
• Treated Control
• N 589 442

110

• Is it ethical to randomise?
• Assuming we have sufficient supply of the new
  treatment why shouldnt every new patient be
  given the new treatment?

111

• Tendency is to do non-randomised trial first and
  then follow up with RCT.
• However it is difficult to do the RCT if the
  results from the non-randomised trial are too
  good.

112

• We assume that the new treatment has a reasonable
  chance of being an improvement.
• Before agreeing to enter patients into a
  randomised trial the investigator must be
  prepared to stay objective about the treatments
  involved.
• Randomised trials often produce scientific
  evidence that contradicts prior beliefs.

113
Equipoise

• What is equipoise and why is it important?
• A state of being equally balanced
• Clinical equipoise provides the ethical basis for
  medical research involving randomly assigning
  patients to different treatment arms.

114
Clinical Equipoise

• Term was first used by B. Freedman in 1987, in
  the article 'Equipoise and the ethics of clinical
  research NEJM 1987 317(3) .
• The ethics of clinical research requires
  equipoise - a state of genuine uncertainty on the
  part of the clinical investigator regarding the
  comparative therapeutic merits of each arm in a
  trial. Should the investigator discover that one
  treatment is of superior therapeutic merit, he or
  she is ethically obliged to offer that treatment.
  

115
Clinical Equipoise
Freeman suggests that as long as there is genuine
uncertainty within the expert medical
community about the preferred treatment then
there can be clinical equipoise, even if a
specific investigator has a preference.
116
Randomisation
117
Randomisation

• Randomised trial with two treatments, A or B
• How do we assign treatments
• Toss a coin each time Heads A, Tails B
• Random Numbers Table
• Random Permuted Blocks

118
Flip a coin

• Could flip coin for each participantcalled
  complete randomisation or simple randomisation
• Problem can get imbalance in groups, especially
  in smaller trials
• Imbalance in prognostic factors more likely
• Inefficient for estimating treatment effect

119
Probability of 5 Treated and 5 Controls in 10
patients

• What is the probability of getting 5 Treated
  patients out of 10?
• Remember the binomial distribution

120
Binomial Distribution

• The binomial probability function

X Binomial (n 10, p0.5) In this case, we
want x5
121
Imbalance with 10 Participants

• (T, C) Probability Efficiency
• (5,5) .246
  1
• (4,6) or (6,4) .410 .96
• (3,7) or (7,3) .234 .84
• (2,8) or (8,2) .088 .64
• (1,9) or (9,1) .020 .36
• (0,10) or (10,0) .002 0

122

• Even if treatment balanced at end of trial, may
  be unbalanced at some time
• E.g., may be balanced at end with 400
  participants, but first 10 might be
• CCCCTCTCTC

123
Random Permuted Blocks

• To balance over time, could randomize in blocks
  (called random permuted blocks)
• Conceptually, for blocks of size 4 put 2 T
  labels 2 C labels in hat for next 4
  participants, draw labels at random without
  replacement from hat
• TTCC TCTC TCCT CTTC CTCT CCTT all equally
  likely

124
Forces balance after every 4

• TCTC CCTT C T C T
• 1 2 3 4 5 6 7 8 9 10 11 12

T TC C
T TC C
T TC C
125
Randomisation by blocks 5 sites, 6 patients per
site
126
Incomplete Blocks

• What happens if a site does not enroll all the
  patients in a block?
• What happens if multiple sites do not enroll all
  the patients in a block?

127

• The smaller the block size, the more often
  balance is forced e.g., in trial of 100,
• blocks of size 2 force balance after every 2
• A block of size 100 forces balance only at end

128

• With blocks of size 2 in an unblinded trial, we
  know every second participants assignment in
  advance
• I can veto potential participants until I find
  one I like (sick one if next assignment is
  control, healthy one if next patient is
  treatment)
• Schulz KF Subverting Randomization in Controlled
  Trials, JAMA 1995 Vol. 274

129

• Even with larger blocks, in unblinded trial you
  know some assignments in advance
• With blocks of size 8 if first 6 are TCTTCT, we
  know next 2 are C
• Using a variable block size in a study makes it
  harder to guess
• Never include the block size in a protocol

130
Subgroup balance

• Sometimes want to balance treatment assignments
  within subgroups
• Especially important if subgroup size is small
• E.g., with 6 diabetics in a trial, with a
  complete randomisation, there is 22 chance of
  5-1 or 6-0 split!

131
Stratified Randomisation

• To avoid this problem could stratify the
  randomisation (use blocked randomisation
  separately for factors such as diabetics
  nondiabetics)
• E.g., for blocks of size 6,
• Diabetics Nondiabetics
• CTTCCT TTCTCC TCCTTC

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Stratified Block randomisation

• Typical examples of such factors are age group,
  severity of condition, and treatment centre.
  Stratification simply means having separate block
  randomisation schemes for each combination of
  characteristics (stratum)

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Stratified Block randomisation

• For example, in a study where you expect
  treatment effect to differ with age and sex you
  may have four strata
• male over 65,
• male under 65,
• female over 65
• female under 65

134
Stratification

• If we believe that gender is a prognostic factor,
  that is, the treatment effect for males may be
  different than the treatment effect for females
  then we should stratify the randomisation (and
  the analysis) on gender
• This does not mean that we need identical numbers
  of males and females in the trial, but rather
  that the males be equally distributed between
  treatment and control and the females also be
  equally distributed between treatment and control

135
Stratification

• Example
• In RA trials there are usually about 70 females
  and 30 males.
• Stratification at randomisation would help ensure
  that each treatment group had about 70 females
  and 30 males.
• If we believe that males and females may have
  different responses to treatment this would be
  important.

136
Blinding
137
Blinding

• Many potential problems can be avoided if
  everyone involved in the study is blinded to the
  actual treatment the patient is receiving.
• Blinding (also called masking or concealment of
  treatment) is intended to avoid bias caused by
  subjective judgment in reporting, evaluation,
  data processing, and analysis due to knowledge of
  treatment.

138
Hierarchy of Blinding

• open label no blinding
• single blind patient blinded to treatment
• double blind patient and assessors blinded to
  treatment
• complete blind everyone involved in the study
  blinded to treatment

139
Open Label Studies

• These may be useful for
• pilot studies
• dose ranging studies
• However knowledge of treatment can lead to
• over or under reporting of toxicity
• over estimation of efficacy
• Even a small fraction of patients assigned at
  random to placebo will reduce these potential
  problems substantially.

140
Single Blind Studies

• Usually justified when it is practically
  infeasible to blind the investigator
• Patients should be blinded if the endpoints are
  patient reported outcomes and for safety
• Where possible use blinded assessor to elicit
  adverse events or patient outcomes

141
Double Blind Studies

• When both the subjects and the investigators are
  kept from knowing who is assigned to which
  treatment, the experiment is called double
  blind"
• Serve as a standard by which all studies are
  judged, since it minimizes both potential patient
  biases and potential assessor biases

142
Double BlindingTechniques

• Coded treatment groups
• Sham treatments
• If impossible try to use a blinded assessor for
  assessing endpoints.

143
Double Blind Studies issues

• Side effects
• Side effects (observable by patient or assessor)
  are much harder to blind and are one of the major
  ways in which blinding is broken
• Efficacy
• A truly effective treatment can be recognized by
  its efficacy in patients

144
Hypothesis Testing
145
Hypothesis Testing

• Steps in hypothesis testing state problem,
  define endpoint, formulating hypothesis, - choice
  of statistical test, decision rule, calculation,
  decision, and interpretation
• Statistical significance types of errors,
  p-value, one-tail vs. two-tail tests, confidence
  intervals
• Significance vs. non-significance
• Equivalence vs. superiority tests

146
Descriptive and inferential statistics

• Descriptive statistics is devoted to the
  summarization and description of data (population
  or sample) .
• Inferential statistics uses sample data to make
  an inference about a population .

147
Objectives and Hypotheses

• Objectives are questions that the trial was
  designed to answer
• Hypotheses are more specific than objectives and
  are amenable to explicit statistical evaluation

148
Examples of Objectives

• To determine the efficacy and safety of Product
  ABC in diabetic patients
• To evaluate the efficacy of Product DEF in the
  prevention of disease XYZ
• To demonstrate that images acquired with product
  GHI are comparable to images acquired with
  product JKL for the diagnosis of cancer

149
How do you measure the objectives?

• Endpoints need to be defined in order to measure
  the objectives of a study.

150
Endpoints Examples

• Primary Effectiveness Endpoint
• Percentage of patients requiring intervention due
  to pain, where an intervention is defined as
• Change in pain medication
• Early device removal

151
Endpoints Examples

• Primary Endpoint
• Percentage of patients with a reduction in pain
  
• Reduction in the Brief Pain Inventory (BPI) worst
  pain scores of 2 points at 4 weeks over
  baseline.

152
Endpoints Examples

• Patient Survival
• Proportion of patients surviving two years
  post-treatment
• Average length of survival of patients
  post-treatment

153
Objectives and Hypotheses

• Primary outcome measure
• greatest importance in the study
• used for sample size
• More than one primary outcome measure -
  multiplicity issues

154
Hypothesis Testing

• Null Hypothesis (H0)
• Status Quo
• Usually Hypothesis of no difference
• Hypothesis to be questioned/disproved
• Alternate Hypothesis (HA)
• Ultimate goal
• Usually Hypothesis of difference
• Hypothesis of interest

155
Hypothesis Testing
Type I Error Societys Risk Type II Error
Sponsors Risk
156
Hypothesis testing

• Null Hypothesis
• No difference between Treatment and Control
• Type I error aka alpha, ?, p-value
• The probability of declaring a difference between
  treatment and control groups even though one does
  not exist (ie treatment is not statistically
  different from control in this experiment)
• As this is societys risk it is conventionally
  set at 0.05 (5)

157
Hypothesis testing

• Type II error aka beta, ?
• The probability of not declaring a difference
  between treatment and control groups even though
  one does exist (ie treatment is statistically
  different from control in this experiment)
• 1 - ? is the power of the study
• Often set at 0.8 (80 power) however many
  companies use 0.9
• Underpowered studies have less probability of
  showing a difference if one exists

158
Steps in Hypothesis Testing

• Choose the null hypothesis (H0) that is to be
  tested
• Choose an alternative hypothesis (HA) that is of
  interest
• Select a test statistic, define the rejection
  region for decision making about when to reject
  H0
• Draw a random sample by conducting a clinical
  trial

159
Steps in Hypothesis Testing

• Calculate the test statistic and its
  corresponding p-value
• Make conclusion according to the pre-determined
  rule specified in step 3

160
Hypothesis Testing Normal Distribution
161
Test of Significance and p-value

• Statistically significant
• Conclusion that the results of a study are not
  likely to be due to chance alone.
• Clinical significance is unrelated to statistical
  significance

162
Test of Significance and p-value

• p-value
• Probability that the observed relationship (e.g.,
  between variables) or a difference (e.g., between
  means) in a sample occurred by pure chance and
  that in the population from which the sample was
  drawn, no such relationship or differences exist.
• It is not the probability that given result is
  wrong.

163
Test of Significance and p-value

• p-value
• The smaller the p-value, the more likely that the
  observed relation between variables in the sample
  is a reliable indicator of the relation between
  the respective variables in the population.

164
Test of Significance and p-value

• The p-level of .05 (i.e.,1/20) indicates that
  there is a 5 probability that the relation
  between the variables found in our sample is by
  chance alone.
• In other words, assuming that in the population
  there was no relation between those variables
  whatsoever, and we were repeating experiments
  like ours one after another, we could expect that
  approximately in every 20 replications of the
  experiment there would be one in which the
  relation between the variables in question would
  be equal or stronger than in ours.

165
Sample versus population
166
Estimation

• We use results from our sample to make inference
  about the population
• How reliable are the sample data at representing
  the population data?
• Is the sample mean a good estimation of the
  population mean?

167
Confidence Intervals

• The results of the analysis are estimates of the
  truth in the population.
• The average reduction in pain score is an
  estimate based on the sample in the study.
• Confidence Intervals indicate the precision of
  the estimate. The wider the confidence interval,
  the less precise the estimate

168
Confidence Intervals

• Example
• Average reduction in pain score from baseline to
  month 6 was 9.7 (95 Confidence Interval 8.3 to
  11.1)
• This does not mean that we are 95 sure that the
  true result lies between 8.3 and 11.1, rather
  if we were to repeat the study 100 times with the
  same sample size and characteristics, 95 of the
  studies would probably show a mean reduction in
  pain score between 8.3 and 11.1

169
What have we learnt?

• Statistics doesnt have to be frightening.
• Statistics is all about a way of thinking
• If you dont have uncertainty you dont need
  statistics
• p-values are probability statements that tell you
  something about your experiment

170
What havent we learnt?

• All the detailed theory and formulae that back up
  everything we have discussed
• How to be a statistician (for that you do have to
  go to graduate school)
• How to get the perfect answer each time we run a
  clinical trial
• We are working with patients not widgets and
  human beings are incredibly complex

171
References

• ICH Guidelines E9, E3 and others
• Statistical Issues in Drug Development Stephen
  Senn 1997 John Wiley Sons
• Freeman B. Equipoise and the ethics of clinical
  research NEJM 1987 317(3)
• Schulz KF. Subverting Randomization in Controlled
  Trials, JAMA 1995 Vol. 274

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Thank You !kay.larholt_at_abtbiopharma.com