Statistics

import matplotlib.pyplot as plt import pymc3 as pm import aesara.tensor as at import arviz as az import scipy.stats as st import numpy as np az.style.use(‘arviz-whitegrid’) Multivariate bernoulli distribution Sources https://doi.org/10.1016/0047-259X(90)90084-U https://arxiv.org/pdf/1206.1874 Motivation I have recently been introduced to Bayesian framework for statistical analysis with PyMC3 package for Probabilistic Programming in Python 3. I came across to a data given to me by my friend, which had multiple columns of binary data (responses to various questions with answers in binary format, yes or no).

Introduction Sample size calculation is an integral part in the inferential statistics, in which we are estimating a population parameter (our interest) from a sample statistic (data available to us). We carry out experiment on a finite numbered sample and calculate a summary measure out of it (sample statistic, lets say, sample mean) with an intent to estimate the unknown population parameter (population mean). The basic premise of statistical estimation is that as the sample size increases, the sample statistic will be reflecting the population parameter more accurately (its variation will be less around the population parameter).

Introduction Practicing Evidence Based Medicine (EBM) has become the norm in Clinical Medicine for past few decades. Generating evidences by carrying out and publishing clinical research of various types (clinical trials, observational studies) have become a norm. It has been observed that around 80% of the clinical research findings and interpretations are not replicable, implicating that wrong clinical decisions are made based on the false findings. Major factors contributing to false results are biases created by researcher, editorial boards of journals and mis-interpretation of statistical terminologies.

Study The study in question is the ALCYONE Trial, published in NEJM in 12 December 2017 by María-Victoria Mateos, Meletios A Dimopoulos, et al. The investigators studied the effect of adding Daratumumab with Bortezomib, Melphalan and Prednisolone in patients with freshly detected Myeloma ineligible for Autologous Bone Marrow Transplantation. The study arms were Arm 1: Daratumumab + Bortezomib + Melphalan + Prednisolone and Arm 2: Bortezomib + Melphalan + Prednisolone