Simulation Study Clause Examples

Simulation Study. In the simulation, we set the numbers of subjects, raters and time points as I = 100, J = 30 and Ti = 5 for any i = 1, . . . , I. We will first demonstrate our approach in Section 3.1 based on one simulated dataset for each setup. We will also present the averages of parameter estimates based on 1000 Monte Carlo replicates. In Section 3.2, we will compare our approach with approaches that do not account for the rater’s effect. The GLMM fitting is implemented by PROC GLIMMIX in SAS 9.4[35].

Simulation Study. The BioCycle Study, conducted from 2005 to 2007, followed premenopausal women from Western New York State for one or two complete menstrual cycles. Regularly menstruating women not currently taking oral contraceptives were eligible for participation. 259 women between the ages of 18 and 44 completed the study. Data collected during the study included age (years) and BMI (kg/m2), as well as serum estrodial, vitamin E, and HDL levels, which were measured on the 22nd day of a participant’s menstrual cycle. Participant BMI was right-skewed, with values ranging from 16.1 to 35.0, with an average body mass index of

Simulation Study. I conducted four sets of real-data based simulation studies to demonstrate advantages of IPBT over existing methods.

Simulation Study. In order to study the performance of the cχ2 and normal distributions as approximations of the null distribution of the score statistic, we performed a simulation study. For sake of simplicity we used the data structure of our example of 33 families (see below). We generated 100,000 data sets of inde- pendently binomially distributed outcomes and 100,000 data sets of indepen- dently normally distributed outcomes. The score statistics were calculated using correlation structure (2.1) based on the coefficients of relationship. We also studied the performance of the distributions in a very small set of nine families. In table 2.1, the actual p-values corresponding to a nominal p-value of 0.05, 0.01, 0.001 and 0.0001 are given. The results were in favour of the cχ2 distri- bution for both binomially and normally distributed outcomes. Even for the set of nine families, the cχ2 distribution performed very well. TABLE 2.1: Type I error rate when using cχ2 distribution and normal distribution as approximation for the distribution of Q under the null hypothesis. The estimates are based on 100,000 simulations. 33 families 9 families nominal cχ2 normal cχ2 normal Binomial (DM2) 0.05 0.0547 0.0606 0.0550 0.0649 0.01 0.0143 0.0194 0.0137 0.0239 0.001 0.0020 0.0041 0.0017 0.0070 0.0001 0.0004 0.0011 0.0002 0.0019 Normal (BMI) 0.05 0.0538* 0.0615* 0.0566 0.0651 0.01 0.0125* 0.0196* 0.0151 0.0233 0.001 0.0016* 0.0047* 0.0027 0.0069 0.0001 0.0002* 0.0011* 0.0004 0.0023 To illustrate the score statistic, we used data from 79 patients with type 2 diabetes mellitus (DM2), their first-degree relatives and spouses (Xxxxxxxxx et al., 2003). These families were derived from the GRIP population (Ge- netic Research in Isolated Populations), an isolated village in the Southwest of the Netherlands. The GRIP population is described in detail elsewhere (Xxxxxxxxx et al., 2003; Xxxxxxx et al., 2002; xxx Xxxxx et al., 2001). Probands are patients with DM2 treated by physicians participating in GRIP. Among the relatives are patients not related to ascertainment namely patients of other physicians and subjects who did not know that they have DM2. In a combined linkage and association study, a genome scan was carried out on these data and Xxxxxxxxx et al. (2003) found a borderline association between marker D3S3681 and DM2 (LOD score of 1.20, P=0.01). For DM2 we analysed 33 families informative for linkage. One of these families was a combination of two nuclear families. Three families had ...

Simulation Study. For each of the simulation scenarios, 5000 simulations were performed in R. Datasets from the first two simulation studies were simulated to resemble actual motivating data described in Section 3.2, with sample size N = 672. Independent predictor variables were generated to mimic age (years), smoking status (yes/no), race (1 = white / 2 = black), and SA status (yes/no), and the outcome variable was generated to resemble the cytokine MCP1 (µg/mL) based on a lognormal regression against those predictors. Age was simulated as a normal random variable with mean 26.6 and standard deviation 6.4, then rounded to the nearest whole number (this permits the formation of x-homogeneous pools when average pool size is small). Smoking status, race, and SA status were simulated as Bernoulli random variables with probabilities 0.47, 0.28, and 0.46, respectively. The outcome, MCP1, was generated under a lognormal distribution such that E[log(MCP1)|X] = —2.48+0.017(Age)+ 0.007(Smoking Status) — 0.388(Race) + 0.132(SA) and V ar[log(MCP1)|X] = 1.

Simulation Study. Acute antinociception paradigm Chronic analgesia paradigm

Simulation Study. Simulation studies enable the systematic exploration of inferences made in our study with respect to anticipated norketamine effect size. Here we performed simulations to estimate the effect of the large change in norketamine concentration and relatively modest change in ketamine concentration that we observed after rifampicin treatment on pain relief. Two sets of simulations were performed, one set on pain relief induced by short‐term ketamine infusion and another set on pain relief induced by chronic ketamine administration. To that end we made a priori assumptions with respect to the norketamine contributions to ketamine effect: simulations with 0, 10 and 25% norketamine contribution were made. The difference in effect observed in the simulated pain relief with and without rifampicin treatment will give an indication of the norketamine contribution to effect. Using the pharmacokinetic model parameters the effect of rifampicin treatment on acute antinociception was simulated for different norketamine contributions to effect. To that end, analgesic effect during and following a 2 hour S‐ketamine infusion of 40 mg/h was simulated using the current pharmacokinetic data set linked to pharmacodynamic data previously obtained and modeled in a similar subject population in our laboratory.4 Analgesia was simulated using a sigmoid EMAX model assuming an additive effect of S‐ketamine and S‐norketamine as follows: BLN 1+⎜ ⎟ ⎛ Cket (t)+Cnkt (t)⎞ ⎜ C C ⎟ ⎝ 50,ket 50,nkt ⎠ where VAS is visual analogue score (ranging from 0 cm = no pain to 10 cm = severe pain), BLN is baseline (or predrug) VAS, γ a shape parameter, Cket and Cnkt the plasma concentrations of S‐ketamine and S‐norketamine, respectively; C50,ket the plasma concentration S‐ketamine causing 50% effect, C50,nkt the concentration S‐norketamine causing 50% effect. The following model parameters where used (reference 4: BLN = 6.7 cm, γ = 2.5, and C50,ket = 375 ng/ml. The C50,nkt was varied in such a way that it contributed 0, 10 and 25% to total analgesic effect. We assumed no delay between blood concentration and acute antinociceptive effect (i.e., pain relief in response to an experimental heat pain stimulus) for both S‐ketamine and S‐norketamine.4,5 Using pharmacokinetic model parameters (from references 6 and 7 on a study on the effect of ketamine on spontaneous chronic pain relief in complex regional pain syndrome type 1 patients), the effect of rifampicin treatment on chronic analgesia was simulated for di...

Simulation Study. I conducted two sets of data based simulation studies to illustrate the consistency of gene panels and its applications to DE gene detection.

Simulation Study. The aim of the simulation study is to evaluate empirically the power of the score test Sˆp in comparison with the Pearson’s χ2, Zˆmax and Zˆclump tests. We generated at least 1000 replicates from the multinomial distributions ac- cording to the models described previously. Without loss of generality we assumed that the first or first two haplotypes are associated with the disease. The remaining haplotypes were equally frequent. We varied the number of variants m from 3 to 20. The p-values of the test statistics were calculated em- pirically by means of 0000 Xxxxx-Xxxxx permutations using a program based on the program Clump (Sham and Xxxxxx, 1995). We used a nominal p-value of 0.05. To verify whether Monte-Carlo yields the right type I error rate of these test statistics, data sets were generated under the null model (λ = 0) each time for markers with 5, 7, 9, 11, 16 and 20 alleles. The frequency of the first allele was set to 0.5, whereas the remaining alleles were equally frequent. The results are shown in Table 4.1. The type I error rate is approximately equal to the nominal rate for the score Sˆp, Xxxxxxx’x χ2, and Zˆclump tests, regardless of the number of alleles m at the marker locus, whereas the Zˆmax becomes somewhat conservative as the number of marker alleles m increases (Sham and Xxxxxx, 1995). TABLE 4.1: The type I error rates based on 10000 simulated m-by-2 tables for λ = 0 and p1 = 0.5. α m χ2 Zˆclump Zˆmax Sˆp m χ2 Zˆclump Zˆmax Sˆp 0.05 5 0.053 0.053 0.047 0.054 11 0.047 0.046 0.039 0.046 0.01 0.011 0.011 0.009 0.011 0.010 0.010 0.008 0.010 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.000 0.001 0.05 7 0.051 0.048 0.045 0.052 16 0.049 0.049 0.040 0.047 0.01 0.011 0.010 0.009 0.010 0.011 0.011 0.007 0.010 0.001 0.001 0.001 0.000 0.001 0.001 0.001 0.000 0.001 0.05 9 0.051 0.052 0.044 0.052 20 0.052 0.052 0.035 0.053 0.01 0.001 0.011 0.008 0.010 0.011 0.011 0.008 0.010 0.001 0.002 0.002 0.001 0.001 0.001 0.002 0.001 0.002 To study the power of the statistics we first considered the model used by Terwilliger (1995) for one positively associated common haplotype. The fre- quency p1 of this haplotype was 0.5 in controls. The parameter λ was fixed to 0.5, which corresponds to a haplotype frequency of 0.75 in the cases and a relative risk γ of 3. We considered 100 case chromosomes (n1) and 100 con- trol chromosomes (n2). The results are shown in Table 4.2. For m 5 all test statistics performed well; however Sˆp had slightly higher power than other t...