Global Data Science Forum

Combining Effectiveness of Drugs

By Moloy De posted Thu August 06, 2020 09:34 PM


CLINICAL TRIALS: A fundamental distinction in evidence-based practice is between observational studies and randomized controlled trials. Types of observational studies in epidemiology, such as the cohort study and the case-control study, provide less compelling evidence than the randomized controlled trial. In observational studies, the investigators retrospectively assess associations between the treatments given to participants and their health status, with potential for considerable errors in design and interpretation.

A randomized controlled trial can provide compelling evidence that the study treatment causes an effect on human health.

Randomized: Each study subject is randomly assigned to receive either the study treatment or a placebo.

Blind: The subjects involved in the study do not know which study treatment they receive. If the study is double-blind, the researchers also do not know which treatment a subject receives. This intent is to prevent researchers from treating the two groups differently. A form of double-blind study called a "double-dummy" design allows additional insurance against bias. In this kind of study, all patients are given both placebo and active doses in alternating periods.

Placebo-controlled: The use of a placebo (fake treatment) allows the researchers to isolate the effect of the study treatment from the placebo effect.

Clinical studies having small numbers of subjects may be "sponsored" by single researchers or a small group of researchers and are designed to test simple questions or feasibility to expand the research for a more comprehensive randomized controlled trial.


HOW TO MEASURE THE EFFECTIVENESS OF DRUGS: It’s a part of Statistical Design of Experiments. There is standard literature in Clinical Trials to measure the effectiveness of drugs.

One way could be developing a two by two table as follows and perform a Chi Square Test of independence with the null hypothesis that the drug has no effect. The p-value of the test will measure the effectiveness of drug. P-value is a number between 0 and 1 and lower is the p-value higher is the effectiveness of the drug in curing illness.


Not Cured

Drug Applied



Placebo Applied




For an easier method one can use p = (a+d)/(a+b+c+d) as the effectiveness of the drug which is a number between 0 and 1. More is the value of p higher is the effectiveness of drug. 


HOW TO MEASURE THE EFFECTIVENESS OF A COMBINATION OF DRUGS: As per this article QASES is a weighted combination of the efficacy and toxicity effect sizes based on differences in efficacy and toxicity using the ½ standard deviation method.

Following this approach, we may set the effectiveness of a combination of drugs as a weighted mean of individual effectiveness where weights are set as another measure, say inverse of the variances of individual effectiveness.

p = (a+d)/(a+b+c+d)

Variance = p(1-p)/(a+b+c+d)


A SANITY CHECK OF THIS METHOD USING COOKED DATA: Consider four drugs, Drug 1, Drug 2, Drug 3 and Drug 4 are tested on each of 4 samples of 10 patients. Let the effectiveness are found out to be 0.34, 0.46. 0.73 and 0.91.

p1 = 0.34

p2 = 0.46

p3 = 0.73

p4 = 0.91

v1 = p1 * (1-p1) / 10

v2 = p2 * (1-p2) / 10

v3 = p3 * (1-p3) / 10

v4 = p4 * (1-p4) / 10

v1Inverse = 1 / v1

v2Inverse = 1 / v2

v3Inverse = 1 / v3

v4Inverse = 1 / v4

p = ((p1 * v1Inverse) + (p2 * v2Inverse) + (p3 * v3Inverse) + (p4 * v4Inverse)) / (v1Inverse + v2Inverse + v3Inverse + v4Inverse)

Then the effectiveness of combined drugs is 0.7056.

QUESTION I: Can the effectiveness of the combined drugs exceed all the individual effectiveness?

QUESTION II: Which area of Statistics include clinical trials?



Wed August 19, 2020 02:31 AM


Tue August 18, 2020 03:04 PM

Thank you very much for this valuable information