1. Scenario ID
An integer code for each simulation scenario that enables them to be identified in the output. There is no requirement that the IDs be sequential.
2. Random number seed
Simulation based power calculation involves generating random numbers. This is done by using a “pseudorandom number generator”. This generates a sequence of numbers that behaves as though it is random, even though it is actually deterministic. Because it is deterministic, once a specific starting “seed” has been specified, it is then possible to generate precisely the same sequence again by using the same seed. If you specify a seed and keep a record of that seed, it means that you can then repeat precisely the same analysis again if, for example, you want to look at the results in more detail, or to check the results if you didn’t record the output correctly. In ESPRESSO you need to specify a seed that is a whole number between 1 and 9999999.
3. The number of simulations
The more simulations that are run, the better reflection the set of simulations will provide of the particular scenario that has been specified. At present, the version of ESPRESSO on the P3G server is limited to running 500 simulations because of limitations on time and computer load. When you first start exploring a study design you may well wish to explore a broad range of scenarios relatively quickly and so you may choose to run 100 or even 50 simulations. But when you come to produce definitive results for a power table, we suggest that you run at least 500 simulations. If you download the ESPRESSO program and run it on your own server the number of simulations is unlimited expect by memory (you may need to reset the amount of memory available to R). In the implemented version of the program, the default number of simulations is set to 100.
4. Number of cases
5. Number of controls
Here, there are two different, but important, issues: (1) The ratio of the number of cases to controls. If you specify 250 cases and 750 controls, part of the output that ESPRESSO will ultimately generate (see below) will be the required size of a case-control study with three times as many controls as cases (750/250) to produce the required power to detect the simulated effect. On the other hand, if you specify 1000 and 5000 it will generate the required size of a study with five times as many controls as cases (5000/1000). (2) The absolute number of cases and controls. The smaller you make the sample size, the faster the program will run, but the more variable the results will be (therefore requiring more simulations) and if you specify a number that is very small, rare combinations may not occur at all in a data set and this might generate misleading results, violate asymptotic assumptions, or it could even make the model fail altogether. As a rule of thumb, and given that for many real problems the required sample size will involve thousands of cases, it is probably wise to use at least 1,000 cases in your simulated sample. Default values are set to 2,000 cases and 8,000 controls (i.e. a design with four times as many controls as cases).
6. Is there an interaction between the genetic determinant and the life-style determinant?
This is a binary indicator variable taking the value 1 if an interaction is to be included and 0 if not.
7. What genetic model?
This is also a binary indicator variable taking the value 1 if the genetic effect is to be modelled as additive (i.e. using a covariate that is “the number of minor alleles”, 0, 1 or 2) and 0 if it is to be modelled as a binary exposure.
8. The population prevalence of disease
This parameter represents the prevalence of the disease in the general population on which the study, for which the power calculations are being undertaken, is to be based. In fact the estimated size requirement for a case-control study seems relatively robust to this parameter and a rough approximation is acceptable (though it appears to become more sensitive in the presence of greater measurement error). If the true prevalence is very low, a very large number of individual subjects will have to be simulated before enough cases are generated and this will make the simulation process very slow. If the prevalence is less than 1 per 1,000 we often choose, therefore, to simulate assuming that the prevalence is 1 per 1,000. The default prevalence is set (completely arbitrarily) to 0.025.
9. The Minor Allele Frequency (MAF)
This parameter represents the population prevalence of the rarer (minor) allele. The default prevalence is set (completely arbitrarily) to 0.3.
10. The population prevalence of 'at risk' level of environmental factor
This parameter represents the prevalence of the ‘at risk’ life-style determinant in the general population on which the study is to be based. The default prevalence is set (completely arbitrarily) to 0.1.
11. The odds ratio (OR) associated with the 'at risk' genetic variant
This is the odds ratio associated with a 1 unit increase in the genetic covariate (the extent to which the odds of disease is multiplied by being ‘at risk’ rather than ‘not at risk’ in a binary genetic model, or the multiplicative effect of each additional minor allele in an additive genetic model. The default OR is set (completely arbitrarily) to 1.5.
12. The OR associated with the 'at risk' level of environmental factor
This is the odds ratio reflecting the ratio of the risk of developing the disease in subjects exposed to the ‘at risk’ level of the environmental determinant compared to those that are not exposed to this ‘at risk’ level. The default OR is set (completely arbitrarily) to 1.5.
13. Interactive OR
In a binary model, this is the ratio of the odds ratio associated with having an ‘at risk’ genotype rather than a ‘not at risk’ genotype in subjects exposed to the ‘at risk’ lifestyle determinant compared to the same odds ratio in subjects not exposed to the ‘at risk’ lifestyle determinant. It should be noted that this is precisely the same as the ratio of the odds ratio associated with the ‘at risk’ lifestyle determinant in subjects exposed to the ‘at risk’ genotype compared to the same odds ratio in subjects not exposed to the ‘at risk’ genotype. If this odds ratio is 1.0 it implies that neither determinant influences the odds ratio associated with the other, and there is therefore ‘no interaction’. In an additive genetic model, it is the equivalent ratio of the odds associated with each additional minor allele. The default OR is set (completely arbitrarily) to 1.5.
14. Baseline OR for subject on 95% population centile v 5% centile
This parameter reflects the heterogeneity in baseline disease risk (i.e. the heterogeneity in disease risk arising from determinants that have not been measured or have not been included in the model. Under the model currently implemented, it is assumed that the variation in baseline disease risk is normally distributed on the logistic scale. If this parameter is set to 10, the implication is that a ‘high risk’ subject (someone at the upper 95% centile of population risk) is, all else being equal, at 10 times the odds of developing disease compared to someone else who is at ‘low risk’ (at the lower 5% centile of population risk). This implies a log(10) = 2.3026 difference on the log(odds) scale. But the 5% and 95% centiles of a standard normal distribution occur at -1.645 and + 1.645 standard deviations. This means that, on the log(odds) scale, 2.3026 corresponds to (21.645 = 3.29 standard deviations) and that the normal distribution that provides the correct baseline heterogeneity in disease risk has a standard deviation of 2.3026/3.29 = 0.6999. In essence, when parameter #14 is specified, a normally distributed random effect with a mean of 0 and a standard deviation of log(parameter #14)/3.29 is generated.
The default value for this parameter is 10. In much of our earlier work we used 12.355 as the default setting. Although this may appear to be a surprising choice it corresponds to an approximate 20 fold ratio of risks between a very high risk subject on the 97.5% population centile and a very low risk subject on the 2.5% centile.
15. P value defining statistical significance
This is totally up to the user, but it must take appropriate account of the related concepts of ‘there being a very low prior probability that any one SNP will truly be associated with disease’ and/or ‘multiple testing’. We typically use p<10-4 for testing ‘vague’ candidate genes (candidature defined by vague biology, or location under a linkage peak), p<10-7 for genome wide association scans (GWASs), and we have tried using 10 10 for gene-gene interactions in a GWAS. For lifestyle determinants we typically use p<0.01.
16. Statistical Power
This is again up to the user. We prefer to design studies with a power of 80% to detect effects of true interest, but in the field of genetic epidemiology, 50% power is sometimes used.
17. Sensitivity of genotype
18. Specificity of genotype
The principal benefit of the ESPRESSO power calculator is that it enables power calculations to be carried out, taking appropriate account of measurement/ assessment error in both outcome and explanatory variables. One of the important explanatory variables is the genotype.
A fundamental issue in constructing ESPRESSO was how best to define assessment error in a way that was meaningful to the user. For the purposes of the genetic determinant we felt that the most meaningful way was to relate it to the concept of r2 - i.e. a measure of linkage disequilibrium (LD) that is, in effect, the squared Pearson correlation coefficient between the variables reflecting the alleles of two linked SNPs coded as 1s and 0s. That said, however, it is important to note that choosing to set the genotypic assessment error as being equivalent to, say, r2 = 0.8 does not imply that we believe that genotypic measurement error is consequent solely on incomplete LD. Rather we choose to represent genotypic assessment error as if it were incomplete LD, because that representation may well be meaningful to users.
In practice, in order to keep the means of generating measurement error consistent across genetic and lifestyle explanatory variables, as well as outcome variables, the extent of measurement error is actually controlled by fixing the sensitivity and specificity of each variable (see supplementary materials, and the R code for ESPRESSO). So, r2 is not specified directly: rather, one specifies the sensitivity and specificity that are required to generate an r2 of the value desired for a SNP with a MAF that has been specified. There are therefore hyperlinks beside input parameters #17 and #18 leading to a program that generates the appropriate sensitivities and specificities that are required to generate the r2 specified (given the specified MAF). The default values that are specified correspond to r2 = 0.8, for a MAF of 0.3 (the default value for the MAF).
The sensitivity of a binary [1,0] variable is the proportion of true positives (which should therefore be coded 1) that are actually coded 1. Specificity is the proportion of true negatives (which should therefore be coded 0) that are actually coded 0.
21. Sensitivity of disease
22. Specificity of disease
These are the sensitivity and specificity of the assessment of disease. Sometimes these are known directly. For example, the default values used in ESPRESSO correspond to the reported sensitivity and specificity of diagnosis of diabetes mellitus as diagnosed on the basis of a measured value of HbA1C (glycosylated haemoglobin) falling at or above the population 97.5% centile (Rohlfing CL, Little RR, Wiedmeyer HM, England JD, Madsen R, Harris MI, et al. Use of GHb (HbA1c) in screening for undiagnosed diabetes in the U.S. population. Diabetes Care 2000;23(2):187-91)