lga 972 : a cross-platform application for optimizing LD studies using a genetic algorithm

Summary: lga972 is a user-friendly cross-platform application with a graphical interface for determining the design features of two-stage genetic linkage disequilibrium studies that minimize the genotyping burden. Availability: lga972 is freely available at http://www.vipbg. vcu.edu/∼edwin. Contact: jrobles@vcu.edu Supplementary information: Program instructions and more detailed technical information can be found in the manual that can also be downloaded from the aforementioned website. A challenge faced by geneticists is to find a limited number of causal mutations among a large set of possible ‘candidates’ or markers. This brings along a considerable risk of false discoveries and makes genetic studies expensive because many markers will need to be typed. To address these problems, we have proposed a method for designing linkage disequilibrium (LD) studies (van den Oord and Sullivan, 2003a,b) that controls the false discovery rate (Benjamini and Hochberg, 1995) and can reduce the amount of genotyping by 50–75% using a two-stage instead of one-stage design. The method can be applied when markers are independent or in LD with each other (see van den Oord and Sullivan, 2003a). From a practical point of view this previous work suffered from three limitations: only tests for specific case–control designs were considered, a primitive search algorithm was used that did not guarantee the optimal design parameters, and the program used for the calculations was not user-friendly and essentially for personal use only. In this note, we describe the program lga972 that remedies these shortcomings. Detailed program instructions and technical information can be found in the manual. Here we confine ourselves to a general description. The user is required to specify (1) the desired false discovery rate (FDR) for the study; (2) the desired Proportion of markers with True effects that she/he wants to Detect (PTD), which corresponds with the average power of the tests; (3) whether there are 1 or 2 stages; (4) information ∗To whom correspondence should be addressed. needed to compute the power of tests (e.g. size and nature of genetic effects such as the amount of dominance); and (5) the proportion of tests for which the null hypothesis is true (p0). Parameters such as p0 may be difficult to know but, similar to what one would do in power calculations, this can be dealt with by performing the calculations for a range of values. The goal of the program is to compute the two-stage study design ensuring that the desired FDR and PTD are achieved with the smallest possible amount of genotyping/genotyping burden (GB). To be able to examine how much this optimal two-stage design reduces the amount of genotyping, the program can also compute the GB for one-stage designs. The GB is defined as the average number of genotypes needed per marker. For an one-stage design, the genotype burden is simply the number of individuals screened. For a two-stage design, the GB is the stage 1 sample size plus the proportion of markers selected for stage 2 times the sample size of stage 2. The GB is useful to compute the total costs of the study given that a fixed number of markers will be typed, or the number of markers that can be typed given a certain budget. For example, if 10 markers will be typed the total number of genotypes needed equals 10 times the GB. Alternatively, if the total budget for the study is $ 10 000, 1 genotype costs 50 cents, and the GB is 500, then the total number of markers that can be typed equals 10 000/(0.5 × 500) = 40. All other design features such as sample size and critical P value/FDR are a ‘byproduct’ of the optimization and required to achieve the desired FDR and PTD. For example, the statistical tests should be performed with the reported critical P -value as the significance level or using a procedure (e.g. Storey and Tibshirani, 2003) that controls the FDR at the calculated level. Using the FDR as a goal allows the use of a procedure that is independent of the number of test performed. The user can choose among a variety of tests assuming that the outcome is dichotomous (present–absent) or continuous, and that the sample consists of cases and control or caseparents triads. A special class of categorical tests is based on the ‘liability-threshold model’ (Falconer, 1989). This model will be helpful to study different kind of selection schemes 3244 Bioinformatics vol. 20 issue 17 © Oxford University Press 2004; all rights reserved. A cross-platform application for optimizing LD studies for cases and controls. Computational details for this class of tests can be found elsewhere (van den Oord, 1999). Once the FDRs and PTDs at each stage are fixed, all other design parameters are determined. The task is therefore to find the FDR and PTD at each stage that minimizes the GB. This optimization is subject to a set of theoretical constraints (van denOordandSullivan,2003a). Ageneticalgorithm(Goldberg, 1989) was used to find the optimal FDR and PTD at each stage. Section 3.2 of the manual gives detailed information about the optimization. In comparison to other optimization procedures, the genetic algorithm can be computationally intensive, and in consequence slow. However, we found that genetic algorithm was robust to changes in initial study configurations (e.g. FDR–PTD goals, p0 value, type of design). Furthermore, it has great flexibility with respect to the optimization function definition, allowing further extensions of the program, (Pelikan et al., 2003). To compute the sample sizes required to achieve the desired PTD, non-central χ2-square and F -distributions are needed. Different numerical approximations of these distributions may yield somewhat different answers (Chattanvelli, 1995; Ding, 1999; Richter and Schumacher, 2000). The avoid discrepancies with standard statistical packages, we chose the most commonly used algorithms. Standard numerical methods, such as bisection-based root-finders were used to solve the sample size needed for a given PTD as well as for some of the computations involving the liability-threshold model (Marsaglia and Zaman, 1991 and Robles, 1996). The lga972 program has a user-friendly graphical interface and its text-based output that can easily be exported to other programs, such as word-processors and spreadsheets. lga972 requires JRE 1.3. 1 or better, and may run in most Java-compatible systems. JRE is available for several platforms at http:/java.sun.com. lga972 has been successfully tested in FreeBSD 4.9, Linux (kernel 2.4.19) and Microsoft Windows XP.