Department of Biostatistics Faculty Research Seminar Series

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Department of Biostatistics Faculty Research
Seminar Series
Abdus S Wahed, Ph.D. Assistant Professor

• What am I doing?
• (Besides teaching BIOST 2083 Linear Models)

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Department of Biostatistics Faculty Research
Seminar Series
Topics

• Survival Analysis Related to Multi-Stage
• Randomization Designs in Clinical Trials
• Skew-Symmetric Distributions
• Statistical Modeling of Hepatitis C Viral Dynamics

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Multi-stage Randomization Designs In Clinical
Trials
Department of Biostatistics Faculty Research
Seminar Series

• Patients randomized to two or more treatments in
  the first stage (upon entry into the trial)
• Those who respond to initial treatment are
  randomized to two or more available treatments in
  the second stage
• Those who respond to the second-stage treatment,
  they are randomized to two or more available
  treatments in the third stage
• And so on..

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Department of Biostatistics Faculty Research
Seminar Series
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Question of Interest and Available Answers
Department of Biostatistics Faculty Research
Seminar Series

• Which combination of therapies results in the
  longest survival?
• Usual Analysis
• Separates out two stages
• Lunceford et al. (Biometrics, 2002)
• Defined treatment strategies such as
• Treat with X followed by Y if respond to X and
  consents to Y-randomization
• Consistent estimators for mean survival time
  under each strategy

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Question of Interest and Available Answers
Department of Biostatistics Faculty Research
Seminar Series

• Wahed and Tsiatis (Biometrics, 2004)
• Consistent and efficient estimators for mean
  survival time (and survival probability) under
  each strategy when there is no censoring
• Wahed and Tsiatis (Submitted, 2004)
• Consistent and efficient estimators for mean
  survival time (and survival probability) under
  each strategy for independent right censoring

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Question of Interest and Current Research
Department of Biostatistics Faculty Research
Seminar Series

• Recent work
• How do you efficiently estimate quantiles of
  survival distribution for each treatment
  strategy?
• A clinical question of interest is what is the
  estimated mean survival for a population treated
  according to the policy
• Treat with X followed by Y if respond to X and
  consents to Y-randomization

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Question of Interest and Current Research
Department of Biostatistics Faculty Research
Seminar Series

• Work in progress
• Probability of randomization at any stage was
  assumed to be independent of previous outcome but
  can be generalized to depend on the data
  collected prior to the randomization
• Sample size determination (thanks to Dr.
  Majumder)
• Other Issues
• Where censoring can depend on the observed data
• Log-rank-type tests for comparing treatment
  strategies

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Statistical techniques I frequently employ
Department of Biostatistics Faculty Research
Seminar Series

• Martingles (related to censoring)
• Semiparametric methods
• Inverse-probability-weighting
• Counterfactual random variables (even when I am
  not interested in causal inference)
• Formal theory of monotone coarsening (missingness)

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Skew-Symmetric Distributions
Department of Biostatistics Faculty Research
Seminar Series

• Main result (Derived distributions, Wahed, 2004
  )
• If f(x) is a density with CDF F(x), and g(y) is
  a density with support 0, 1, then
• h(z)gF(z)f(z) (1)
• defines a probability density function.

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Skew-Symmetric Distributions
Department of Biostatistics Faculty Research
Seminar Series

• Observation
• h(z)f(z), if g(.) is uniform
• If f and g are symmetric, so is h.
• If g is skewed and f is symmetric (or
  asymmetric), then h is skewed.

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Skew-Symmetric Distributions
Department of Biostatistics Faculty Research
Seminar Series

• Innovation
• Betak-normal distribution
• Take f in (1) to be a standard normal
  distribution and g to be a beta distribution
  call the corresponding derived distribution from
  (1) h1
• Take f to be h1 and g to be a beta distribution
  and call the derived distribution h2
• Repeat k-times.

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Beta-normal Distributions
Department of Biostatistics Faculty Research
Seminar Series
BetaN(10,8,0,1)
BetaN(10,3,0,1)
BetaN(5,1,0,1)
BetaN(5,3,0,1)
N(0,1)
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Skew-Symmetric Distributions
Department of Biostatistics Faculty Research
Seminar Series

• Innovation
• Triangular-normal distribution
• Beta-Gamma distribution

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Skew-Symmetric Distributions
Department of Biostatistics Faculty Research
Seminar Series

• Application
• Distributions that are close to normal but have
  one tail extended (or squeezed ) can be modeled
  by skew-normal distributions
• Mixed effect modeling with non-normal error
  distributions

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Statistical Modeling of Hepatitis C Viral Dynamics
Department of Biostatistics Faculty Research
Seminar Series

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Statistical Modeling of Hepatitis C Viral Dynamics
Department of Biostatistics Faculty Research
Seminar Series
V(t ) V0 A exp -?1(t t0)
(1- A) exp-?2 (t t0) t gt t0 ---
(4) where ?1 ½ ( c ? ) ( c- ?
)2 4 ( 1 - ?) c ? ½ ?2 ½ ( c ? )
- ( c- ? )2 4 ( 1 - ?) c ? ½ A
(? c - ?2 ) / (?1 - ?2 )
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Statistical Modeling of Hepatitis C Viral Dynamics
Department of Biostatistics Faculty Research
Seminar Series

• Assumes ? being constant over time, which is
  not the case with PEG-Interferon alpha-2a
  (Pegasys?).
• Only works with the biphasic viral level
  declines. (Herrmann et al., 2003 Hepatology)
• Ignores the possible correlations in viral levels
  over time.

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Statistical Modeling of Hepatitis C Viral Dynamics
Department of Biostatistics Faculty Research
Seminar Series
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Statistical Modeling of Hepatitis C Viral Dynamics
Department of Biostatistics Faculty Research
Seminar Series

• ?( ?(t) ) ? max ?(t) / (? ?(t) )
• ?(t) any function that describes the pattern
  of drug concentration over time

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Statistical Modeling of Hepatitis C Viral Dynamics
Department of Biostatistics Faculty Research
Seminar Series