A conditional probability issue?

There is a question and answer from 'AskMarilyn' at Parade.com. I copy the question and answer here since it is a probability issue.

Question: Four identical sealed envelopes are on a table. One contains a $100 bill. You select an envelope at random and hold it in your hand without opening it. Two of the three remaining envelopes are then removed and set aside, still sealed. You are told that they are empty. You are not given the choice of keeping the envelope you selected or exchanging it for the one on the table. What should you do? A) Keep your envelope; B) switch it; or C) it doesn't matter.

Marilyn said you should switch envelopes. Here's her reason: Imagine playing this game repeatedly. You start with a 25% chance of choosing the envelope with the cash. Then two empty ones are taken away on purpose. (Only someone with knowledge of the contents can inform you that sealed envelopes are empty.) so if the $100 bill is in any of the three unchosen envelopes - which it is 75% of the time - you'll get it by switching.

However, I would choose the answer C) it doesn't matter. This is a conditional probability issue. In the beginning, with all four envelopes sealed, the probability of choosing one envelope with $100 bill is 25%. When two envelopes are revealed not to contain the $100 bill, for the remaining two envelopes, each now has 50% probability with $100 bill in it. It doesn't matter if you keep the envelope on hand or switch it for the one on the table.

Using RevMan to Conduct the Meta Analysis

RevMan (or Review Manager) is designed as a review tool to facilitate the literature review and the meta analyses by the Cochrane Collaboration Group. RevMan can be downloaded from website for free. It can be installed into your system without requiring the system administer privilege. Thousands of systematic reviews and meta analyses published on the Cochrane Library are performed using RevMan. These systemic reviews and meta analyses have been one of the leading resources in evidence-based medicine.

RevMan can be easily used by the medical researchers who are non-statisticians. For statisticians who work in the medical research area, RevMan is an easy tool to perform the meta analyses and generate the graphs (forest plot, funnel plot) in publication standard.

The statistical method and statistical model are described in the document Standard statistical algorithms in Cochrane reviews by Jon Deeks and Julian Higgins and Cochrane Handbook for Systemic Review of Interventions. For statistical models, both fixed model and random model are included in the RevMan. For random models, DerSimonian and Laird random-effects models are used. This is most common random effects model used in Meta Analysis.  

RevMan 5 is extremely easy to use. Various tutorials, tips, webinars are provided in RevMan documentation website and The Cochrane Collaboration Open Learning Material. I find it is extremely useful to watch two webinars (especially the part 2 regarding the data and analyses. For

To perform a Meta analysis, RevMan is just a tool. There are a lot of works to be done prior to enter the information including data into the RevMan. Considerable time needs to be spent on the literature search. Since the data used in Meta analyses relies on the publications, some data needs to be converted first. For example, for outcomes measured in continuous variable, the published article may only provide the Standard Error or just the 95% confidence interval. The SE can be easily converted to the Standard Deviation by multiplying the square root of the sample size. If only the 95% confidence interval is available, the standard deviation can be approximated by normal approximation using upper bound = mean +/- 1.96 * SE.

Good Review Practice

In previous article, 'regulatory science' is discussed. 'Good Review Practice' can be considered one aspect of the regulatory science. Here Good Review Practice is specifically refer to a “documented best practice” within CDER that discusses any aspect related to the process, format, content and/or management of a product review.

On the industry side, the sponsor needs to establish the standard operating procedures (SOP) and the working procedure documents (WPDs) to ensure the compliance of the regulatory guidance and GCP and to improve the efficiency. On the regulatory side, it is important to establish the good review practice to ensure that the same standard procedures are following during the review process for drug approval.

These good review practices could cover the review process in different areas: efficacy, safety, pregnancy, CMC,... They are supposed to be written for FDA reviewers, however, understanding the good review practice is also very helpful for sponsor to prepare the regulatory submission documents in a way that is amenable to the reviewers. The mis-communication between the sponsor and the regulatory could be minimized. All necessary information/analyses required per good review practice are included in the submission documents.

Below are some links related to good review practice:

• Good Review Practices (GRPs)
• Biostatistics New Drug Application Review Template
• Biostatistics Biological Product Application Review Template
• Conducting a Clinical Safety Review of a New Product Application and Preparing a Report on the Review
• Review Guidance: Evaluation of Human Pregnancy Outcome Data
• Reviewer Guidance: Evaluating the Risks of Drug Exposure in Human Pregnancies
• Safety Review and eCTD
• Guidance for Reviewers Instructions and Template for Chemistry, Manufacturing, and Control (CMC) Reviewers of Human Somatic Cell Therapy Investigational New Drug Applications (INDs)