Under this model, case control status are simulated based on logit model of odds ratio and disease prevalence. Power and sample size calculations can be performed using a number of theoretical and empirical methods.

`spower LOGIT -h`

Model specific options are documented in details below. You should find the rest of the options otherwise documented.

These options specify the odds ratios of variants in the region of interest. `-a`

is odds ratio for detrimental rare variants. When used by itself, all detrimental rare variants will be assigned a fixed odds ratio as specified. With the `-A`

option, they together model “variable effects” with `-a`

being the minimum odds ratio and `-A`

being the maximum odds ratio for detrimental rare variants. In variable effects model the maximum odds ratio will be assigned to the variant having smallest MAF, and the minimum odds ratio to the one having largest MAF. Other odds ratios in between are interpolated based on the max. and min. values. Similarly `-b`

and `-B`

are for fixed and variable effects of protective variants. For a protective variant the smaller the OR the larger the protective effect. As a result `-B`

is the minimum OR for protective variants instead. `-c`

and `-d`

are odds ratio for common detrimental and protective variants respectively. No variable effects model for common variants is available for this model.

*Note*

Odds ratios of 1.2 to 3.0 are reasonable choices of detrimental rare variants for complex traits. Protective variants may take an odds ratio if \(1/\gamma\) where \(\gamma\) is effect of detrimental variants. However due to the choice of baseline penetrance the protective effect thus generated is not symmetric to detrimental effect.

Baseline penetrance. For rare variant analysis this can be approximated by disease prevalence.

*Note*

Users should determine this parameter to reflect the particular phenotype of interest for which the power analysis is performed. The default value is 1% which is a valid assumption for common disease in general, but for certain disease e.g. type II diabetes the prevalence can be much higher.

Mode of inheritance. Most aggregated analysis method implicitly assumes an “additive” effect of rare variants, thus simulating and analyzing data under additive model represents a best case scenario for many methods, which is also the default value for both the simulation and the analysis. This option only controls on how the data is simulated. In some `--method`

option there are sub-options to specify the mode of inheritance under which the data will be analyzed.

With the `--resampling`

option, a different implementation of phenotypic simulation is activated. Without this option, input parameters such as odds ratio, prevalence, are used to calculate and update group specific MAF for cases and controls. Analytic power calculation can be performed using the MAFs thus obtained, or for empirical power analysis case control genotype data are simulated from the group specific MAF. With the `--resampling`

option, a sample genotype will be generated first, either from the population MAF or drawn directly from given haplotype pools, depending on the input data being in SEQPower SFS format or SEQPower GDAT format. Then a penetrance value \(f\) for the genotype will be calculated from input parameters, and the sample will be labeled as a *case* with probability \(f\). This is a more computationally cumbersome implementation, since for example with \(f=1\%\) it will require generation of about 100 samples before a *case* can be collected. Also by implementation analytic power analysis cannot be performed with this switch on. The advantage of this model is the potential to sample directly from external haplotype pools given in GDAT file rather than to recover such pools from summary statistics under HWE and no LD assumption, which might be biased.

- Analytic power analysis for case control studies
- Empirical power analysis for case control studies