The CaTS Power Calculator
CaTS is a friendly tool that can carry out power calculations for genetic
association studies. CaTS can be used to estimate power for any genetic association study, but
is especially designed to
facilitate the design of twostage genetic
association studies. This page describes in detail the parameters that CaTS requires
as input and the output it generates.
Sample Size
In this section, you should specify the total number of cases and controls available
for the study. In a onestage design, all the cases and controls would be genotyped; in
a more costeffective design only a fraction of the cases and controls would be genotyped initially and
the results from this preliminary analysis would be used to select markers to genotype in the remaining individuals.
Cases: The number of cases available for the study. This will include both
cases to be genotyped in stage 1 and stage 2.
Controls: The number of controls available for the study. This will include
both controls to be genotyped in stage 1 and stage 2.
Two Stage Design
This section allows you to specify design parameters for a twostage study. In a
twostage study, all the markers are examined in a fraction of the sample. Then, results of
this initial analysis are use to select a fraction of markers to be followed up in the
remainder of the sample.
Samples Genotyped in Stage 1 (%): The proportion of samples genotyped in stage 1.
The number of cases and controls genotyped in stage 1 will be a function of the total
number of samples available (specified in the sample size section). For example, if you
have 1000 cases and 1000 controls and set this proportion to 30%, you should plan to
genotyped 300 cases and 300 controls in the stage 1. Using the notation developed in
Skol et al. (2006), this value is π_{samples}.
Markers Genotyped in Stage 2 (%): The percentage of markers that you plan to
followup in Stage 2. Using the notation developed in Skol et al., this value is
π_{markers}. The power calculation assumes that you will test each marker for
association at the end of stage 1, and followup markers whose corresponding pvalue is <
π_{markers} by genotyping them in the remaining cases and controls.
Significance level: The desired false positive rate per marker. If all M markers
are independent and you wish to maintain a genomewide false postive rate of .05,
the per marker false positive rate should be .05/M. In the Skol et al. paper this value
is denoted α_{marker}.
Disease Model
Prevalence: The disease prevalence. This is the probability that a randomly
sampled individual is affected by the disease.
Disease Allele Frequency : The frequency of the risk allele in the general
population. Usually, the allele will be a little more common in cases, and a little
rarer in contros.
Genotype Relative Risk: The definition of genotype relative risk (GRR) is depends on
the disease model. If f_{0}, f_{1}, f_{2}
are the probabilities of being affected for individuals with 0, 1, or 2 copies of the
risk allele, then GRR is defined as follows:
 Multiplicative
 GRR = f_{1} / f_{0} = f_{2} / f_{1}
 Additive
 GRR = f_{1} / f_{0}
 Dominant
 GRR = f_{1} / f_{0} = f_{2} / f_{0}
 Recessive
 GRR = f_{2} / f_{0} = f_{2} / f_{1}
CaTS output
Power Tab
This section displays estimated power for different analysis and genotyping strategies.
One Stage Design: Power attained when all samples are genotyped on all markers in a single stage
Replication Analysis: Power attained when stage 2 data is analyzed independently of the strength of
association in stage 1. Replication is deemed successful when the the two stages provide evidence for an effect in
same direction
Joint Analysis: Power attained when test statistics from stage 1 and stage 2 are combined.
Thresholds Tab
This section displays suggested thresholds for association tests. These thresholds will ensure the user specified
type I error rate. At each stage, a zstatistic should be calculated to compare allele frequencies in cases and controls
(for example, as defined in Skol et al.). If desired, the statistic can be adjusted for population stratification using
Genomic Control or another appropriate strategy.
One Stage Design: Critical value for twosided test of association using a zstatistic and the markerwise
false positive rate specified by Significance Level.
Stage One Threshold: This is the critical value that should be used when selecting markers for followup
genotyping in stage 2
Replication Threshold: Critical value to be used for stage 2 when using replicationbased analysis.
Joint Analysis Threshold: Critical value to be use when test statistics from stage 1 and stage 2 are
combined.
Penetrances Tab
This tab displays the probability that an individual will be affected for each marker genotype. It also displays the
Attributable fraction, which is the proportion of cases due to the effect of the disease predisposing locus, and
Recurrance risk to siblings, which is a factor summarizing the increase in risk to siblings of affected
individuals due to this locus.
Information Tab
Reduction in total genotyping required: Number of genotypes saved when using the specified twostage design
/ Number of genotyped performed in a onestage design
Case and Control allele frequency: Risk allele frequency in cases and controls given the disease model
Probability marker is followed up: Probabillity a disease predisposing variant with the specified disease
model and parameters is selected for genotyping in stage 2
given the specified twostage design
Optimization Tab
Genotyping Cost Ratio: Specifies the relative cost of genotypes generate in Stage 2 (typically, Stage 1 uses a massive
throughput platform with very low per genotype costs, whereas Stage 2 uses more customizable and expensive assays). If it costs
one penny to generate a genotype in stage 1 and 5 pennies to generate a genotype in stage 2, the cost ratio is $0.05 / $0.01 = 5.
Target Power (%): This is the power you want to achieve for the two stage design, using joint analysis. It must be less
than the power of the onestage design, since two stage designs always lose a little power. After pressing the Optimize! button,
the twostage design that achieves Target Power at the lowest cost will be reported.
Target Cost (%): This is the amount of funds available for genotyping, as a proportion of the cost for a one stage design.
For example, if the one stage design would cost $1 million, but you only have $400,000 available, set the target cost to 40%.
Pressing the Optimize! button will report the twostage design that costs achieves the highest possible power for the target cost.
Optimize! button: When you click this button, the most cost effective design (for a Target Power) or the most power (for a
Target Cost) is reported. Optimization may take a few seconds, depending on the speed of your computer, so please be patient.
