05/07/2023
Likelihood Ratio (LR) is applied when we want to assess the diagnostic power of an investigation or laboratory test.
To understand the likelihood ratio, we first need to understand that the tests we use to diagnose a particular disease condition or state are rarely 100% sensitive.
By sensitivity, we mean the ability of a test to ‘detect‘ a disease when there is ‘one‘.
This means sometimes the test may fail to detect a disease when there is ‘one’.
e.g., A 90% sensitivity means the test can correctly detect 90 out of 100 patients with a particular disease.
By Specificity, we mean the ability of a test to ‘exclude‘ a disease when there is ‘none‘.
This means sometimes the test may mistakenly detect a disease when there is ‘none’.
e.g., A 80% specificity means the test can correctly exclude 80 out of 100 persons who don’t actually have the disease.
Suppose a test is 90% sensitive and fails 10% of time to detect the disease when it is positive. What is the likelihood that ‘a particular person’ might have the disease when tested (and the test comes out positive for the specific disease) with this specific investigation?
To calculate this likelihood, we need to use some mathematical formulation.
Let us first consider what the possibilities are when a test is done among a group of persons.
- group a, who are disease positive and test positive;
- group b, who are disease negative but test positive;
- group c, who are disease positive but test negative;
- group d, who are disease negative and test negative.
Check the table in the image.
| Disease Positive | Disease Negative | Total | |
| Test positive | a (True Positive) | b (False Positive) | a+b |
| Test negative | c (False Negative) | d (True Negative) | c+d |
| Total | a+c | b+d | a+b+c+d |
Here,
Sensitivity = a/(a+c)
Specificity = d/(b+d)
Positive predictive value (PPV) = a / (a+b)
Negative predictive value (NPV) = d/(c+d)
Now let us derive the equation for the likelihood ratio for a positive test,
The likelihood that a test will be positive when a disease is present.
= Number of affected persons who are positive / Number of persons who are affected
= a / (a+c)
= sensitivity
The likelihood that a test is falsely positive when the disease is not present.
= Number of unaffected persons who are positive / Number of unaffected persons
= b/ (b+d)
= 1 – d/(b+d)
= 1 – Specificity
So, the likelihood ratio of having a disease when the test is positive is,
(LR+) = sensitivity/ (1 – specificity)
Similarly,
The likelihood that a test will be falsely negative when a disease is present.
= Number of affected persons who tested negative/ Number of persons who are affected
= c / (a+c)
= 1 – a/(a+c)
= 1 – sensitivity
The likelihood that a test is negative when the disease is not present.
= Number of unaffected persons who are negative / Number of unaffected persons
= b/ (b+d)
=Specificity
So, the likelihood ratio of having a disease when the test is negative is,
(LR-) = (1- sensitivity)/ Specificity
Now, the likelihood ratio comes in handy in the calculation of the post-test probability of having the disease after a test is done and, therefore, gives a measure of the diagnostic capability of a test (i.e., investigation).
How?
To calculate the post-test probability of having the disease by a person, you need to know the post-test odds of having the disease (i.e., the post-test probability of having the disease / post-test probability of not having the disease). Post-test odds, on the other hand, depend on pre-test odds. The equations are as follows:
Post-test odds = pre-test odds * LR
Pre-test odds = pre-test probability / (1-pre-test probability)
Post-test probability = post-test odds / (post-test odds+1)
Note that the pre-test probability implies the probability of having the disease before the test was done. This is expressed by the prevalence of the disease (or condition) in the population.
Why does pre-test probability matter?
In the Bayesian approach, we need to know the prior probability of an event to calculate the posterior probability of it. Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a “likelihood function” derived from a statistical model for the observed data.
As the prevalence of disease is not the same for all diseases, taking the prevalence of that disease in question during the calculation of the probability of a person having the disease given a specific test, makes intuitive sense. Also, as the ‘test’ done to detect the disease might not be 100% sensitive and specific, if a test detects a disease in a person, it doesn’t mean the person might be having the disease.
The benefit of calculating the likelihood ratio:
- The Likelihood ratio is not affected by the prevalence of a disease like that of Positive predictive value and negative predictive values of a test.
- It gives an idea about the diagnostic capacity of a test.
05/07/2023
The probability of finding ‘no’ difference (in the variable of interest) between two study groups when there is ‘none’ (in the original population) is known as confidence.
The opposite of confidence is the type I error. I mean, the probability of finding ‘a’ difference when there is ‘none’ is the type I error.
When we are 95% confident, we mean that in 95 out of 100 cases, our study procedure will find ‘no’ difference, when there is ‘none’.
Remember the NULL hypothesis! We assume that there is no difference.
Based on the type I error, we set the level of significance. When we set the level of significance (p) at <0.05. We allow the probability of finding a difference when there is none in less than 5 out of 100 cases.
The probability of finding ‘a’ difference when there is ‘one’ between two study groups (in the original population) is known as power.
The opposite of power is the type II error. This means the probability of finding a ‘no’ difference when there is ‘one’.
When we say we have 80% power, we mean that in 80 out of 100 cases, our procedure will find ‘a’ difference when there is one.
Usually in study designs, researchers prefer 95% confidence. But they are often more flexible with power. The usual practice is to set the power at 80%.
Can anyone tell me why is this the case? I mean, why do we allow flexibility in power, but not in confidence?
০২/০৩/২০২৩
নিপাহ ভাইরাস প্রতিরোধে ChAdOx1 NiV ভ্যাক্সিন
বাংলাদেশের নিপাহ ভাইরাসের স্ট্রেইন-এর বিরুদ্ধে ধেড়ে ইঁদুরের ন্যায় প্রাণি হ্যাম্সটার (1) এবং গ্রিন মানকি (2) প্রজাতিতে ChAdOx1 NiV ভ্যাক্সিন প্রয়োগ করে দেখা গেছে যে ভ্যাক্সিনটি নিপাহ ভাইরাসের বিপরীতে সম্পূর্ণ প্রতিরোধ গড়ে তুলতে সক্ষম।
বিজ্ঞানী Doremalen এবং তার সহযোগীরা নিপাহ ভাইরাসের বাংলাদেশে স্ট্রেইন থেকে গ্লাইকোপ্রোটিন জি জিন নিয়ে থার্মো ফিসার সায়েন্টিফিক -এর জিনআর্ট এর সাহায্যে প্রথম জি জিন তৈরী করেন। এরপর এর সাথে মানুষের সাইটোম্যাগালোভাইরাসের মোডিফাইড ভার্শন থেকে টেট্রাসাইক্লিন অপারেটর সহ প্রমোটার এবং বোভাইন গ্রোথ হরমোনের পলি এডিনাইলেশন সিগনাল নিয়ে একটি জিন ক্যাসেট তৈরী করেন । উক্ত জিন ক্যাসেটকে T-Rex-293 (ইনভাইট্রোজেন)- সেল লাইনে প্রবেশ করিয়ে তার থেকে পরবর্তীতে এডেনোভাইরাস ভেক্টরকে আইসোলেট করা হয় (1)।
এরপর, হ্যামস্টার এবং গ্রিন মানকিতে ভ্যাক্সিন প্রয়োগ করে নির্দিষ্ট প্রক্রিয়ায় নিপাহ ইনফেকশন করার পর দেখা হয় যে তা নিপাহ প্রতিরোধ করতে পারে কি না। দু’ধরনের প্রানীর ক্ষেত্রেই উক্ত ভ্যাক্সিনের সাফল্য পাওয়া গিয়েছে, যা খুবই আনন্দের খবর।
আমরা জানি, মানুষের প্রয়োগের আগে মানুষের কাছাকাছি জিন সম্বলিত প্রাণীতের ভ্যাক্সিনের ট্রায়াল করে তার কার্যকরিতা এবং নিরাপদ কি না তা দেখা হয়। সে হিসেবে এ ধাপে উক্ত ভ্যাক্সিনটি সফল। তবে সামনে আরও কয়েক ধাপে ট্রায়াল হয়ে ভলানটির মানব দেহে পরীক্ষা করার পর সফল হলেই আমরা বলতে পারবো যে নিপাহ ভাইরাস প্রতিরোধ আমাদের হাত থেকে কত দূরে।
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