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Basic Statistics
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Sensitivity & Specificity
Test Positive Test Negative
Disease TP FN Sn = TP / (TP +FN)
No Disease FP TN Sp = TN / (TN + FP)
PPV = TP / (TP + FP)
NPV = TN/ (TN+FN)
Sensitivity rules out disease (SNOUT)
Specificity Rules in disease (SPIN)
PPV is probability of having a disease if the test is positive
NPV is probability of not having a disease if the test is negative
PVs are affected by Prevalence
Trues are always on TOP
Likelihood Ratios Likelihood Ratios are very great tool for assessing diagnostic accuracy of a
symptom or sign or tests
Positive Likelihood Ratio (LR+) = Sn / (1 – Sp)
Negative Likelihood Ratio (LR-) = Sp / (1 – Sn)
Likelihood Ratio >1 is showing test is associated with diseases and <1 is showing test is not associated with diseases
Likelihood ratio of 1 is useless
However, LR+ >5 and LR- < 0.2 are very useful
Incidence & Prevalence Number of New Cases / Population at risk = Incidence Total Number of Cases/ Population at Risk = Prevalence Prevalence = Incidence x Duration (P = ID) ~ PID If duration of Illness is short, Prevalence ~ Incidence Similarly, If Duration of Illness is Longer (Chronic Conditions),
Prevalence > Incidence Note: Prevalence affects Predictive Value If Prevalence Increases, PPV Increases and NPV Decreases Sn & Sp are not affected by Prevalence
Types of Study Retrospective Studies: Will see control group and case group and see if the
risk factor was present. ODD Ratio = Case: Control
Prospective: Cohort study. Relative Risk
Cross Sectional Study: Looks at disease prevalence
ProspectiveRetrospective
Simple Normal Distribution Curve ( Gaussian Curve)
Mean = Algebraic average
Mode = Maximum appearing variable
Median = Middle Term
In a Simple Normal Bell Shaped Curve: Mean = Mode = Median = Peak of Curve
Data is equally distributed (symmetrical)
1 SD each side is 34 % (Total both sides 68 %)
2 SD = 95 %
3 SD = 99.7%
Absolute Risk Reduction Consider we have 2 groups of patients with pain, we divide them equally in
Control group and Experimental Group.
Control Group Event Rate (CER) = 30/100 (30%)
Experimental Group Event Rate (EER) = 80/100 (80%)
ARR = EER – CER = 50% = 0.5
NNT = 1/ARR = 1/0.5 = 2
Drug Given Benefit + No Benefit
Experimental Drug 80 20
Placebo Drug 30 70
Numbers Needed to Treat Number of patients needed to treat to benefit 1 patient (prevent 1 bad
outcome)
Ideal or perfect NNT is 1 (5 – 20 is much more than useful and still represents good therapeutic benefit)
NNT = 1/ARR
Aspiring in AMI has NNT of 40
NNT should be as low as possible but not “0”, and Numbers needed to harm should be as high as possible
Types of Data Can be Qualitative or Quantitative
Nominal Ordinal Interval Ratios
NOn Parametric (Nominal, Ordinal)
Parametric
Central Measure
Median (Skewed Data) Mean (Normally Distributed Data)
Correlation Test
Spearman Pearson
Other Tests Mann Whitney, Wilcoxon, Friedmann
T Test, ANOVA
Types of BiasSelection Bias Randomization
Recall Bias
Measurement Bias
Procedure Bias
Observer Expectancy Bias
Cofounding Bias
Lead Time Bias
P Value & Types of Errors Whenever you see a study, they run stats and say the P Value (alpha) was
found to be < 0.05 and therefore results are significant.
What do you understand by that?
What is a hypothesis?
What is alpha error or type 1 error
What is beta error or type 2 error
Which one is BAD?
What you can do about it?
Hypothesis is any statement which we want to prove
Ex PCOD Patients are prone to be diabetic
Then we make an opposite hypothesis. We call it null hypothesis
We collect data and analyze it using one of the test.
The test says that, P Value is less than 0.05, which means that the null hypothesis is false, that is there is less than 5 % chance that the things has happened by chance
Type 1 error (alpha error) is rejecting Null hypothesis when it is true
Type 2 error (Beta error) is accepting Null hypothesis when it is actually not true
Type 1 is worse than type 2
We reduce errors by increasing sample size (More people = More POWER)
Power = 1 - beta
Blinding in Clinical Trials In Double Blind Study, Neither the investigator nor the subjects are aware of
which intervention they are being given. Ideally those analyzing data are also unaware of the interventions, but it is not possible always. Those interpreting data may know the intervention without affecting the results.
Blinding helps to reduce BIASES
Publication Biases are bias by the researchers, pharma and journals that are biased to produce positive results