PBAT Power Calculations

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23.3.1 Summary

The PBAT capabilities for power calculations are software implementation of the approaches to analytical power calculations for FBATs by [Lange 2002a, Lange 2002b, Lange 2002c] . They allow the user to assess the power of family-based association tests (FBATs) for a large variety of different designs:

  • Dichotomous/binary and continuous traits.
  • Missing parental information.
  • Multiple offspring per family.
  • Combinations of different family-types.
  • Different genetic models.
  • Different ascertainment conditions for the first and second proband.
  • Marker and disease locus are not identical.
  • Combination of different family-types and different ascertainment conditions.
  • Verification of all power calculations by Monte-Carlo simulations.

They also allow the user to assess the power of non-family-based association test designs for both case/control studies and studies based on quantitative traits.

23.3.2 Using The Power Calculations Option

23.3.2.1 Getting Started

The first step is to open an existing project or create a new project where you want to store the calculation results. See 3.1.2 for details about creating a new project. See 3.4.1 for details about opening an existing project.

Now that we have a project open we can begin the analysis process.

The power calculation dialog can be started in two different ways:

  • Begin with the standard default parameters. Select Tools->PBAT Power Calculations->Use Default Parameters from the main menu bar.
  • Begin with the set of parameters used in a previous calculation. Highlight the navigator node of the power calculations results whose parameters you wish to have as new “defaults”, then select Tools->PBAT Power Calculations->Use Parameters From Selected Node. See below.

[Picture]
Figure 23.1: PBAT power calculations can be performed by opening the power calculation options dialog.
23.3.2.2 Power Calculation Types

Four types of power calculations are supported:

  • Family-based using a binary trait
  • Family-based using a continuous trait
  • Case/Control (“Non-family-based using a binary trait”)
  • Quantitative (“Non-family-based using a continuous trait”)

Parameters for these are organized within four tabs, three of which are used at any given time:

  • Methods
  • Family Design
  • Genetic Model
  • Computational

See the subsection below for the type of power calculation you wish to perform. See the glossary 23.6 for definitions of terms. Once you have set the parameters for the type of power calculation you wish to perform, click Calculate to begin.

Upon starting calculations, progress bar will show. Press Cancel if you wish to interrupt the calculations.

When the calculations are finished, a text viewer will show. This viewer will be associated with a new Navigator Node. This node may later be highlighted to extract the power calculation parameters used for this run as new “default parameters” for another power calculation.

23.3.3 Family-Based Power Calculations Using a Binary Trait

23.3.3.1 The Methods Tab

In the Methods tab you can set the type of calculation to be used, the statistical parameters and select the type of computation to be used in calculating the power.

[Picture]
Figure 23.2: The initial tab of the Power Calculation Options dialog.
23.3.3.2 Type of Calculation

Select the calculation type (Power Calculations for Binary traits). Other fields which apply will be made accessible.

23.3.3.3 Statistical Parameters
  • Significance Level. The Significance Level is the probability of wrongly rejecting the null hypothesis when in fact it is true (probability of type one error). Ideally the Significance Level should be as small as possible. The default is 0.01.
  • Offset. The Offset parameter is used to balance or counter-balance the disease factor. An offset choice of 0 means that only affected offspring are included in the computation of FBAT statistic while the unaffected are ignored. When the offset is set to one the test statistic is computed based on unaffected offspring but not affected. A good rule of thumb is to choose the offset close to the disease prevalence. Guidelines for the choice of the Offset parameter are discussed in [Whittaker & Lewis (1998)] and [Lange 2002a].

23.3.3.4 Computation Method

Three radio buttons apply to family-based studies, and may be used with either binary or continuous traits. PBAT will use the selected method to compute the power of the FBAT statistic. These radio buttons are:

  • Numerical Integration. When the power of the FBAT statistic is computed based on numerical integration, the numerical precision is 0.01. This method can take several minutes depending on the complexity of the study design and the computer speed.
  • Approximation. The analytical power of the FBAT statistic will be computed based on a second order Taylor expansion. The precision is good for sample sizes of at least 100 families, and it is the fastest approach. Computation time is usually one second or less. This method is described in [Knapp (1998)] and [Lange 2002a].
  • Simulation. The power will be estimated based on one million Monte-Carlo simulations and can take up to several minutes.

23.3.3.5 The Family Design Tab

[Picture]
Figure 23.3: The Family Design tab of the Power Calculation Options dialog for binary traits.

The Family Design tab contains the options which allow the specification of multiple family types which will be included in in the calculations. These options include:

  • Number of families
  • Number of offspring per family
  • Number of missing parents
  • Whether additional offspring are phenotyped
  • Ascertainment conditions for the probands (these may be set to unaffected, affected, or unavailable)

Each of these options can be specified for a given family design, and multiple family designs can be included in a set of calculations (e.g. one set of calculations could be run with 100 families with 2 offspring and 1 missing parent, and 50 families with 3 offspring and 0 missing parents, etc.). Usually more families will increase the power of the study while missing parents will decrease the power of the study.

To add a family type, enter the appropriate values for the options contained in the Change Family Design group, and click the Add Design button. The family design will appear in the list of Family Designs Currently Used, and will be included in the calculation.

Similarly, to remove a family type from the calculations, highlight the corresponding entry in the list of included family designs by clicking on it, then click the Remove Design button.

23.3.3.6 The Genetic Model Tab

[Picture]
Figure 23.4: The Genetic Model tab of the Power Calculation Options dialog.

Under the Genetic Model tab you can specify the genetic model (see 23.6) underlying the power calculations. Note the disease gene (see 23.6) is specified by allele "A".

The basis for defining the genetic model may be specified (within the Specify Basis box) as follows:

  • Mode of inheritance (MOI),p,K and attributable fraction (AF) (see 23.6)
  • Penetrance Values and Allele Frequency
  • Mode of inheritance (MOI),p,K and Odds Ratio
  • Mode of inheritance (MOI),p,K and Allelic Odds Ratio

Selecting the basis selects the parameters that are used to define the genetic model.

NOTE: The mode of inheritance is the manner in which a particular genetic trait or disorder is passed from one generation to the next. Examples of MOI are autosomal dominant, autosomal recessive, X-linked dominant, X-linked recessive, multifactoral and mitochondrial, etc. Penetrance indicates the likelihood that a given gene will actually result in the disease. Odds ratio is a way of comparing whether the probability of a certain event is the same for two groups. Attributable fraction is the proportion of disease occurance that can be potentially eliminated if the exposure was prevented.

NOTE: One of the parameters will always be the conditional probability of observing the disease allele given the marker allele A and the value of D’ between the disease locus and marker locus. If the values of the conditional probability of observing the disease allele given the marker allele and of D’ are both one, this is equivalent to the disease locus and the marker locus being identical.

The parameters for the respective bases are as follows:

  • MOI,p,K,AF

    If you choose MOI,p,K,AF as your basis you will be able to specify the following parameters.

    • mode of inheritance
      1. Additive
      2. Multifactoral
      3. Recessive
      4. Dominance
    • allele frequency (see 23.6) of the disease gene (default 0.2)
    • increment in allele frequency (see 23.6) per iteration (default 0.1)
    • population prevalence of disease (default 0.3)
    • genetic attributable fraction (see 23.6) of the gene (default 0.1)
    • whether the disease locus is equal to the marker locus (default false)
    • allele frequency of the marker gene–specify when the disease locus is not equal to the marker locus (default 1.0)

    The following parameters will be calculated for you according to the inputs to the above parameters.

    • penetrance for AA
    • penetrance for AB
    • penetrance for BB
    • relative risk for carrying one allele (RR1)
    • relative risk for carrying two alleles (RR2)
    • odds ratio for one carrying allele (OR1)
    • odds ratio for two carrying alleles (OR2)
    • allele frequency (see 23.6) of the marker gene (see 23.6)
    • probability of disease allele A equal to marker allele A
    • linkage disequilibrium denoted by D’
  • Penetrance Values and Allele Frequency

    If you select Penetrance Values and Allele Frequency you will be able to specify the following parameters.

    • mode of inheritance
      1. Additive
      2. Multifactoral
      3. Recessive
      4. Dominance
    • allele frequency (see 23.6) of the disease gene (default 0.2)
    • increment in allele frequency (see 23.6) per iteration (default 0.1)
    • penetrance for AA (default 0.8)
    • penetrance for AB (default 0.5)
    • penetrance for BB (default 0.3)
    • whether the disease locus is equal to the marker locus (default false)
    • allele frequency of the marker gene–specify when the disease locus is not equal to the marker locus (default 1.0)

    The following parameters will be calculated for you according to the inputs to the above parameters.

    • population prevalence of disease
    • genetic attributable fraction (see 23.6) of the gene
    • whether the disease locus is equal to the marker locus
    • relative risk for carrying one allele (RR1)
    • relative risk for carrying two alleles (RR2)
    • odds ratio for one carrying allele (OR1)
    • odds ratio for two carrying alleles (OR2)
    • allele frequency (see 23.6) of the marker gene (see 23.6)
    • probability of disease allele A equal to marker allele A
    • linkage disequilibrium denoted by D’
  • MOI,p,K and Odds Ratio

    The parameters that you will be able to set using this basis (for family-based studies with binary traits) are as follows:

    • mode of inheritance
      1. Additive
      2. Multifactoral
      3. Recessive
      4. Dominance
    • allele frequency (see 23.6) of the disease gene (default 0.2)
    • increment in allele frequency (see 23.6) per iteration (default 0.1)
    • population prevalence of disease (default 0.3)
    • odds ratio (default 2.333)
    • whether the disease locus is equal to the marker locus (default false)
    • allele frequency of the marker gene–specify when the disease locus is not equal to the marker locus (default 1.0)
  • MOI,p,K and Allelic Odds Ratio Model

    The parameters that you will be able to set using this basis (for family-based studies with binary traits) are as follows:

    • mode of inheritance
      1. Additive
      2. Multifactoral
      3. Recessive
      4. Dominance
    • allele frequency (see 23.6) of the disease gene (default 0.2)
    • increment in allele frequency (see 23.6) per iteration (default 0.1)
    • population prevalence of disease (default 0.3)
    • allelic odds ratio (default 2.471)
    • whether the disease locus is equal to the marker locus (default false)
    • allele frequency of the marker gene–specify when the disease locus is not equal to the marker locus (default 1.0)
23.3.3.7 The Computational Model Tab

(This tab is not used with family-based power calculations.)

23.3.4 Family-Based Power Calculations Using a Continuous Trait

23.3.4.1 The Methods Tab

In the Methods tab you can set the type of calculation to be used, the statistical parameters and select the type of computation to be used in calculating the power.

[Picture]
Figure 23.5: The initial tab of the Power Calculation Options dialog.

Select the calculation type (Power Calculations for Continuous traits). Other fields which apply will be made accessible.

The statistical parameters are as follows:

  • Significance Level. See 23.3.3.3 for more information.
  • Offset. See 23.3.3.3 for more information.

Three Computation Method radio buttons apply to family-based studies, and may be used with either binary or continuous traits. PBAT will use the selected method to compute the power of the FBAT statistic. See 23.3.3.4 for description of these options.

23.3.4.2 The Family Design Tab

[Picture]
Figure 23.6: The Family Design tab of the Power Calculation Options dialog for continuous traits.

The Family Design tab contains the options which allow the specification of multiple family types which will be included in in the calculations. These options include:

  • Number of families
  • Number of offspring per family
  • Number of missing parents
  • Whether additional offspring are phenotyped
  • Ascertainment conditions for the probands (see below)

Each of these options can be specified for a given family design, and multiple family designs can be included in a set of calculations (e.g. one set of calculations could be run with 100 families with 2 offspring and 1 missing parent, and 50 families with 3 offspring and 0 missing parents, etc.). Usually more families will increase the power of the study while missing parents will decrease the power of the study.

Any of ten ascertainment conditions may be specified. The numbers in the ascertainment conditions refer to sampling conditions for the phenotypes of the first and second probands (see 23.6). These are specified by the corresponding probabilities of the phenotypic distributions of the traits.

For example, suppose ascertainment condition 2 is set as follows:

  • Proband 1 Lower: 0.0
  • Proband 1 Upper: .25
  • Proband 2 Lower: .85
  • Proband 2 Upper: 1.0

For this condition, the trait of the first proband must be in the lower 25% of the phenotypic distribution, while the trait of the second proband must be in the upper 15% of the phenotypic distribution.

Condition 1, which is predefined and may not be changed, is always equivalent to a total population sample.

You may specify ascertainment conditions 2 through 10.

To add a family type, enter the appropriate values for the options contained in the Change Family Design group, and click the Add Design button. The family design will appear in the list of Family Designs Currently Used, and will be included in the calculation. The currently highlighted ascertainment condition will be associated with the new family design.

Similarly, to remove a family type from the calculations, highlight the corresponding entry in the list of included family designs by clicking on it, then click the Remove Design button.

23.3.4.3 The Genetic Model Tab

[Picture]
Figure 23.7: The Genetic Model tab of the Power Calculation Options dialog.

Under the Genetic Model tab you can specify the genetic model (see 23.6) underlying the power calculations. Note the disease gene (see 23.6) is specified by allele "A".

The following parameters may be used to specify a model for family-based calculations with continuous traits:

  • mode of inheritance
    1. Additive
    2. Recessive
    3. Dominance
  • allele frequency (see 23.6) of the disease gene (default 0.1)
  • increment in allele frequency (see 23.6) per iteration (default 0.1)
  • Heritability (default 0.1)
  • whether the disease locus is equal to the marker locus (default false)
  • allele frequency of the marker gene–specify when the disease locus is not equal to the marker locus (default 1.0)

NOTE: One of the parameters is the conditional probability of observing the disease allele given the marker allele A and the value of D’ between the disease locus and marker locus. If the values of the conditional probability of observing the disease allele given the marker allele and of D’ are both one, this is equivalent to the disease locus and the marker locus being identical.

23.3.4.4 The Computational Model Tab

(This tab is not used with family-based power calculations.)

23.3.5 Case/Control Power Calculations

23.3.5.1 The Methods Tab

In the Methods tab you can set the type of calculation to be used, the statistical parameters and select the type of computation to be used in calculating the power.

[Picture]
Figure 23.8: The initial tab of the Power Calculation Options dialog.

Select the calculation type (Power and Sample Size Calculations for Case/Control). Other fields which apply will be made accessible.

The statistical parameters are as follows:

  • Significance Level. See 23.3.3.3 for more information.

Two Computation Method radio buttons apply for power calculations for case/control or quantitative trait studies of unrelated individuals. You may:

  • Create a table of predicted powers based on sample size information. Select Compute Power For Given Sample Size.
  • Create a table of sample sizes required to achieve a given power under various tests. Select Compute Required Sample Size For Given Power and Significance Level.
23.3.5.2 The Family Design Tab

(This tab is not used with power calculations for studies of unrelated individuals.)

23.3.5.3 The Genetic Model Tab

[Picture]
Figure 23.9: The Genetic Model tab of the Power Calculation Options dialog.

Under the Genetic Model tab you can specify the genetic model (see 23.6) underlying the power calculations. Note the disease gene (see 23.6) is specified by allele "A".

The basis for defining the genetic model may be specified (within the Specify Basis box) as follows:

  • Mode of inheritance (MOI),p,K and Odds Ratio
  • Mode of inheritance (MOI),p,K and Allelic Odds Ratio

Selecting the basis selects the parameters that are used to define the genetic model.

NOTE: The mode of inheritance is the manner in which a particular genetic trait or disorder is passed from one generation to the next. Examples of MOI are autosomal dominant, autosomal recessive, X-linked dominant, X-linked recessive, multifactoral and mitochondrial, etc. Penetrance indicates the likelihood that a given gene will actually result in the disease. Odds ratio is a way of comparing whether the probability of a certain event is the same for two groups. Attributable fraction is the proportion of disease occurance that can be potentially eliminated if the exposure was prevented.

The parameters for the respective bases are as follows:

  • MOI,p,K and Odds Ratio You may specify the following parameters with power calculations for case/control studies.
    • mode of inheritance
      1. Additive
      2. Multifactoral
      3. Recessive
      4. Dominance
    • Min allele frequency of the disease allele (default 0.05)
    • increment in allele frequency (see 23.6) per iteration (default 0.1)
    • population prevalence of disease (default 0.1)
    • Odds ratio OR1 (AB versus BB) (default 1.25)
  • MOI,p,K and Allelic Odds Ratio Model You may specify the following parameters with power calculations for case/control studies.
    • mode of inheritance
      1. Additive
      2. Multifactoral
      3. Recessive
      4. Dominance
    • Min allele frequency of the disease allele (default 0.05)
    • increment in allele frequency (see 23.6) per iteration (default 0.1)
    • population prevalence of disease (default 0.1)
    • Allelic odds ratio (default 1.248)
23.3.5.4 The Computational Model Tab

[Picture]
Figure 23.10: The Computational tab of the Power Calculation Options dialog.

The options available for case/control calculations are as follows, depending on on the computation method (see 23.3.5.1 above):

  • Create a table of predicted powers based on sample size information.
    • Number of simulations
    • Number of cases
    • Number of controls
  • Create a table of sample sizes required to achieve a given power under various tests.
    • Number of simulations
    • Achieved power for sample size calculations powers based on sample size information.
    • Ratio: cases vs. controls

23.3.6 Quantitative Trait Power Calculations

23.3.6.1 The Methods Tab

In the Methods tab you can set the type of calculation to be used, the statistical parameters and select the type of computation to be used in calculating the power.

[Picture]
Figure 23.11: The initial tab of the Power Calculation Options dialog.

Select the calculation type (Power and Sample Size Calculations for Quantitative traits). Other fields which apply will be made accessible.

The statistical Parameters are as follows:

  • Significance Level. See 23.3.3.3 for more information.

Two Computation Methodradio buttons apply for power calculations for case/control or quantitative trait studies of unrelated individuals. See 23.3.5.1 for further description.

23.3.6.2 The Family Design Tab

(This tab is not used with power calculations for studies of unrelated individuals.)

23.3.6.3 The Genetic Model Tab

[Picture]
Figure 23.12: The Genetic Model tab of the Power Calculation Options dialog.

Under the Genetic Model tab you can specify the genetic model (see 23.6) underlying the power calculations. Note the disease gene (see 23.6) is specified by allele "A".

The basis for defining the genetic model for quantitative traits is always:

  • Mode of inheritance (MOI),p,K and Heritability

NOTE: The mode of inheritance is the manner in which a particular genetic trait or disorder is passed from one generation to the next. Examples of MOI are autosomal dominant, autosomal recessive, X-linked dominant, X-linked recessive, multifactoral and mitochondrial, etc. Penetrance indicates the likelihood that a given gene will actually result in the disease.

You may specify the following parameters for quantitative power calculations:

  • Mode of inheritance
    1. Additive
    2. Recessive
    3. Dominance
  • Min. allele frequency of the disease allele (default 0.02)
  • Allele frequency increment (default 0.1)
  • Heritability (default 0.001)

The following parameters will be calculated for you according to the inputs to the above parameters.

  • genetic attributable fraction (see 23.6) of the gene
  • whether the disease locus is equal to the marker locus
  • relative risk for carrying one allele (RR1)
  • relative risk for carrying two alleles (RR2)
  • odds ratio for one carrying allele (OR1)
  • odds ratio for two carrying alleles (OR2)
  • allele frequency (see 23.6) of the marker gene (see 23.6)
  • probability of disease allele A equal to marker allele A
  • linkage disequilibrium denoted by D’
23.3.6.4 The Computational Model Tab

[Picture]
Figure 23.13: The Computational tab of the Power Calculation Options dialog.

The options available for quantitative traits are:

  • Number of simulations
  • Achieved power for sample size calculations (for creating a table of sample sizes required to achieve a given power under various tests)
  • Number of probands (for creating a table of predicted powers based on sample size information)

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