Prognostic Factor Analyses

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Prognostic Factor Analyses

• ? ? ? (Yue-Cune Chang)
• ???????????
• ? ? ? ? ? ? ?

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Introduction

• Prognostic factor analyses (PFAs) are studies
  that attempt to assess the relative importance of
  several predictor variables simultaneously. The
  need to prognosticate is basic to clinical
  reasoning, but most of us are unable to account
  quantitatively for the effects of more than one
  or two variables at a time. Using the formality
  of a PFA, the additional structure provided by a
  statistical model, and thoughtful displays of
  data and effect estimates, one can extend
  quantitative accounting to many predictor
  variables.
• PFAs are usually based on data in which
  investigators did not control the predictor
  variables or confounders as in experimental
  designs.
• The validity of PFAs depend on the absence of
  strong selection bias, on the correctness of the
  statistical models employed, and on having
  observed, recorded, and analyzed appropriately
  the important predictor variables.

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Why do we need prognostic factor analyses

• To learn the relative importance of several
  variables that are associated with disease
  outcome simultaneously. This is especially
  important for diseases that are treated
  imperfectly such as AIDS, cardiovascular disease,
  and cancer.
• To improve the design of clinical trial, e.g.
  adjusting the severity of the disease and
  treating the severity as a prognostic factor.
• To detect the possible interaction effects
  between treatment and covariates or between
  prognostic factors themselves.
• To assess clinical landmarks during the course of
  an illness and to decide if changes in treatment
  strategy are warranted. For example, when
  monitoring the time course of CD4 lymphocyte
  count in HIV positive patients, when the count
  drops below some threshold, a change in treatment
  may be indicated. A threshold such as this could
  be determined by an appropriate PFA.

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Types of Prognostic Factors

• Prognostic factors can be continuous measures,
  ordinal, binary, or categorical. Most often,
  prognostic factors are recorded at study entry
  or time 0 (baseline) with respect to follow-up
  time and remain constant, e.g. sex, treatment.
• Some prognostic factors may change their value
  over time, named time dependent covariates
  (TDC).
• There are two types of time dependent covariates
  
• intrinsic or internal (i.e. those that exist
  within study subject), and extrinsic or external
  (i.e. those that exist independently of the study
  subject, e.g. in cancer study, the environmental
  levels of toxins).

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Model-Based Methods

• One of the most powerful and flexible methods for
  assessing the effects of more than one prognostic
  factor simultaneously is a statistical model.
• Statistical models can be used to describe a
  plausible mathematical relationship between the
  predictors and the observed endpoint in terms of
  one or more model parameters which have handy
  clinical interpretations.

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Using statistical models, the investigator must

• be knowledgeable about the subject matter and
  interpretation
• collect and verify complete data
• consult an experienced statistical expert to
  guide/do the analysis
• make a plan for dealing with decision points
  during the analysis.

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• Models combine theory and data
• A model is any construct which combines
  theoretical knowledge, represented by
  equation(s), with empirical knowledge,
  represented by data.
• The scale of measurements (coding) may be
  important
• The first step in a PFA is to code the
  measurements (variable values) in a numerically
  appropriate way. Even qualitative variables can
  be represented by the proper choice of numerical
  coding. Ordinal and qualitative variables often
  need to be re-coded as binary indicator or
  dummy variables that facilitate group
  comparisons. A variable with N levels requires
  N-1 binary dummy variables to compare levels in a
  regression model. Each dummy variable implies a
  comparison between a specific level and the
  reference level (which is omitted from the
  model).

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Some widely used statistical models in clinical
trials The appropriate statistical models to
employ in PFAs are dictated by the specific
type of data and biological questions.

• Generalized Linear Models
• General Linear Models
• Regression, ANOVA, ANCOVA
• Logistic Regression
• Log-linear Model
• Proportional Hazards Model (PH Models)
• Coxs regression models (Coxs PH Model)

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No
No
Y ?Normal, Binomial, or Poisson ??
????????
??????
Yes
Yes
Y ?Normal, Binomial, or Poisson??
GEE Methods of Generalized Linear Model
Yes
No
???????? ? Wilcoxon Ranks Sum test, Kruskal
Wallis Test
Generalized Linear Model
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Use Appropriate Statistical Model

• Depends on the specific type of data and
  biological questions (study purposes)
• General Linear Model
• Logistic Regression
• Log-linear Model

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Coxs Proportional Hazards Model

• In the Coxs PH model, the logarithm of the
  hazard rates ratio is assumed to be a constant
  related to a linear combination of the predictor
  variables
• Hazard rate Instantaneous failure (death) rate
• Age specific death rate

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Coding of Variables for Brain Tumor Clinical Trail

• Treat 0 placebo 1 polymer
• Resect75 0 lt75 resection 1 gt75 resection
• Age Age in years
• Interval Years from diagnosis
• Karn (PS) 0 lt70 1 ?70
• Race 1 White 0 other
• Local 1 Local 0 Whole Brain Irradiation
• Sex 1 Male 0 Female
• Nitro 1 Previous Nitrosurea 0 None
• Weeks Survival time in weeks
• Event 1 Death 0 Alive
• Path 1 Glioblastoma 2 Anaplastic Astrocytoma
• 3 Oligodendroglioma 4 other
• Grade 1 Active 0 Quiescent

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Coxs Proportional Hazards Model Using SPSS V.10.0
Age/10
P-values
Hazard Rates Ratio
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Logistic Regression Models Using STATA V8.0
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General Linear Models (ANCOVA) Using STATA V8.0

• Example Effect of Three Teaching Methods
• on Students Score after adjusting
  IQ.
• Method 1 Uses the standard lecture format
• Method 2 Uses short movie clips at the
• beginning of each period.
• Method 3 Use a short interactive computer
• module at the end of the
  period.

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Building parsimonious models

• Quantitative prognostic factor assessment can be
  thought of as the process of constructing
  parsimonious statistical model. These models are
  most useful when
• (1) they contain a few clinically relevant and
  interpretable predictors,
• (2) the parameters or coefficients are
  estimated with a reasonable
• high degree of precision,
• (3) the predictive factors each carry
  independent information about
• prognosis,
• (4) the model is consistent with other
  clinical and biological data.
• Constructing models that meet these criteria is
  usually not a simple or automatic process. We can
  use information in the data themselves
  (data-based variable selection), clinical
  knowledge (clinically based variable selection),
  or both.

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• Dont use automated procedures.
• Resolve missing data
• Screen factors for importance in univariable
  regressions
• Build multiple regressions
• Correlated predictors may be a problem (Depends)
• The only reasonable way for the methodologist to
  solve these difficulties is to work with
  clinicians who have expert knowledge of the
  predictor variables, based on either other
  studies or pre-clinical data. Their opinion, when
  guided by statistical evidence, is necessary for
  building a good model. Even when a particular set
  of predictors appears to offer slight statistical
  improvement in fit over another, one should
  generally prefer the set with the most clear
  clinical interpretation. Of course, if the
  statistical evidence concerning a particular
  predictor or set of predictors is very strong,
  then these models should be preferred or studied
  very carefully to understand the mechanisms,
  which may lead to new biological findings.

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• Adjusted Analyses of Comparative Trials
• Investigators might consider adjusting
  estimated treatment effects for prognostic
  factors that meet one of the following criteria
• (1) Factors that (by chance) are
  statistically significantly
• unbalanced between the treatment
  groups,
• (2) Factors that are strongly associated with
  the outcome,
• whether (significantly) unbalanced or
  not,
• (3) To demonstrate that a particular
  prognostic factor
• does not artificially create the
  treatment effects,
• (4) To illustrate and quantify the effects of
  factors of
• known clinical importance.

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Thanks for Your Attention