Live cell imaging with high spatiotemporal resolution and high detection sensitivity facilitates the study of the dynamics of cellular structure and function. Of course, how much uncertainty will depend on the situation. If we are slightly conservative in our sample size selection, this will take into account this additional uncertainty. Given that we are never certain about what the parameters should be in the data generation process, this adds an appropriate level of uncertainty that gets reflected in our target estimates.
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One particularly interesting feature of the data generation process used in these simulations is that the effect size parameters are not considered to be fixed, but are themselves drawn from a distribution of parameters. If you do not have access to and HPC, you can run locally using lapply or mclapply rather than Slurm_lapply, but unless you have an extremely powerful desktop or laptop, expect these kinds of simulations to take days rather than hours. The simulations are set up to run on a high performance computing (HPC) environment, so multiple data sets can be generated and analyzed simultaneously.
PROSHOW GOLD 7.0 HIGHEST RESOLUTION 2015 CODE
This code generates repeated data sets under different sample size assumptions and draws samples from the posterior distribution for each of those data sets. To be safe, we might want to set the upper limit for the study to be 600 patients, because we are quite confident that the standard deviation will be low enough to meet our criteria (almost 90% of the standard deviations from the simulations were below 0.135, though at 650 patients that proportion was over 98%). At 550 subjects, the mean standard deviation (represented by the curve) is starting to get close to 0.135, but there is still quite a bit of uncertainty. The plot below shows the estimated standard deviations for a single log-odds ratio (in this case \(\lambda_4\)), with a point for each of the 1,500 simulate data sets. We have estimated seven log-odds ratios (see here for an explanation of why there are seven), and the simulation returns a summary of the posterior distribution for each: selected quantiles and the standard deviation. The structure is similar to what I have described in the past on how one might do these types of explorations with simulated data and Bayesian modelling.)īelow is the output for a single data set to provide an example of the data being generated by the simulations. (I am including the code in the addendum below. In total, this took about 2 hours to run. Given that each model estimation is quite resource intensive, I generated all the data and estimated the models using a high performance computing environment that provided me with 90 nodes and 4 processors on each node so that the Bayesian MCMC process could all run in parallel - so parallelization of parallel processes. For each sample size, I generated 250 data sets, for a total of 1,500 data sets and model estimates. I evaluated sample sizes ranging from 400 to 650 individuals, increasing in increments of 50. The final step was to repeatedly simulate data sets using different sample size assumptions, fitting models, and estimating the posterior distribution standard deviations for associated with each data set (and sample size). Using simulation to establish sample size It looks like the target standard deviation should be close to 0.135, which is also apparent from the plot of the 95% intervals centered at 0.22: Assuming that the target posterior distribution will be approximately normal with a mean of 0.22, I used the qnorm function to find the 95% thresholds for range of standard deviations between 0.10 and 0.15. That is, 95% of the distribution should lie to the right of 0. I did a quick search for the standard deviation that would yield a 95% threshold at or very close to 0.
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The target OR is somewhat arbitrary, but seemed like a meaningful effect size based on discussions with my collaborators. In particular, I identified the posterior probabilities with a mean OR = 1.25 \((log(OR) = 0.22)\) where \(P(log(OR) > 0) \ge 0.95\). To determine the target level of precision, I assessed the width of the posterior distributions under different standard deviations.