Statistics

Evidence in Medial Resources

key differences and details regarding systematic reviews and meta-analyses:

Systematic Review:

• Definition: A systematic review aims to identify, appraise, and synthesize all relevant empirical evidence to answer a specific research question.
• Purpose: Provides the most relevant, adequate, and current information on a topic.
• Position in Evidence Hierarchy: Systematic reviews rank just below meta-analyses in the levels of evidence pyramid.
• Key Components for Conducting:
  • Specific Research Question: Often formulated as a PICO (Population, Intervention, Comparison, Outcome) question.
  • Pre-Specified Eligibility Criteria: Determines which articles are included or excluded.
  • Systematic Methodology: Minimizes bias by adhering to a consistent process.
  • Protocols and Guidance: Resources such as Cochrane and the Equator Network offer guidance for performing systematic reviews.
• Function: Synthesizes available evidence systematically, making it a comprehensive and detailed evaluation of the literature on a specific topic.

Meta-Analysis:

• Definition: A meta-analysis is a quantitative, epidemiological study design used to combine and assess the results of multiple previous studies mathematically.
• Focus: Often based on data from randomized controlled trials but can include other study types.
• Conditions for Conducting:
  • Studies included should be of good quality.
  • Similar designs and outcome measures among studies improve the reliability of meta-analyses.
• Importance:
  • Provides more precise estimates of an effect by combining data from multiple studies.
  • Presents results using statistical tools like forest plots (to visualize combined effect estimates) and funnel plots (to detect publication bias).
• Function: Provides a summary estimate of an effect size by combining data from the included studies, enhancing the power and accuracy of conclusions.

Key Differences:

• Systematic Review:
  • Synthesizes available evidence on a topic using a systematic, structured method.
  • Can exist without a meta-analysis.
• Meta-Analysis:
  • Quantitative component that assesses and combines the data from studies included in a systematic review.
  • Relies on systematic reviews for source data.

	Systematic Review	Meta-Analysis
DEFINITION	Synthesis of empirical evidence regarding a specific research question .	Statistical tool used with quantitative outcomes of various  studies regarding a specific topic.
RESULTS	Synthesizes relevant and current   information regarding a specific   research question (qualitative).	Merges multiple outcomes from   different researches and provides   an average result (quantitative).

Conclusion:

• A systematic review synthesizes evidence using a specific, structured approach.
• A meta-analysis quantitatively combines data from the studies within a systematic review to produce an overall effect estimate.

Definitions of Allocation and Blinding in Clinical Trials

Allocation Concealment

• Allocation Concealed:
  • Adequate measures were taken to conceal allocation to study group assignments from those responsible for assessing patients for entry in the trial.
  • Examples:
    • Central randomization
    • Sequentially numbered, opaque, sealed envelopes
    • Numbered or coded bottles and containers
    • Drugs prepared by the pharmacy
    • Other descriptions with convincing elements of concealment
• Allocation Not Concealed:
  • Inadequate measures were taken to conceal allocation to study group assignments.
  • Examples:
    • No concealment procedures
    • Sealed envelopes that were not opaque
    • Other descriptions not convincing of concealment
• Unclear Allocation Concealment:
  • The article did not report or provide a description of the allocation concealment sufficient to classify as concealed or not concealed.

Blinding

• Blinded:
  • Any or all of the following groups were unaware of who received which study intervention:
    • Clinicians
    • Patients
    • Participants
    • Outcome assessors
    • Statisticians
  • If “initially” is indicated (e.g., “blinded [patients and outcome assessor initially]”), it means the code was broken during the trial, possibly due to adverse effects.
• Blinded (Unclear):
  • The authors did not report or provide an indication of who, if anyone, was unaware of who received which study intervention.
• Unblinded:
  • All participants in the trial, including clinicians, patients, participants, outcome assessors, and statisticians, were aware of who received which study intervention.

 Adverse Outcomes

• These are the potential side effects or bad things that could happen because of a treatment or test.
• Adverse outcomes are the risks or side effects that can happen with a treatment or test. We always weigh the benefits against these risks to make the best decision for your care.
• example
  • Adverse Outcome of a Blood Thinner (e.g., Warfarin):
    Blood thinners are used to prevent blood clots, but an adverse outcome could be bleeding. For instance, a person taking blood thinners may experience bleeding gums, easy bruising, or, in serious cases, internal bleeding, which could be dangerous.
  • So while the medication helps reduce the risk of clots (the benefit), the adverse outcome (the risk) is that it could also make you more likely to bleed.

Key Domains of Risk of Bias Assessment

Bias due to Randomization:

• Occurs when participant allocation is not truly random or is not concealed.
• Can lead to systematic differences between groups, causing selection bias.
• Example: Unconcealed allocation may lead sicker patients to one group.

Bias due to Deviations from Intended Interventions:

• Arises when participants do not adhere to the treatment protocol or significant deviations occur.
• If not accounted for, it can distort the intervention’s true effect.
• Example: Participants in a diabetes trial using previous insulin therapy instead of the intervention.

Bias due to Missing Outcome Data:

• Results from incomplete data, such as participant dropouts.
• If not properly addressed, it can skew study outcomes.
• Example: High dropout rates due to adverse effects in an antidepressant trial may introduce attrition bias.

Bias in Measurement of the Outcome:

• Occurs when outcomes are measured inconsistently or with systematic errors.
• Can lead to inaccurate comparisons between groups.
• Example: Different methods used to assess pain (e.g., interviews vs. questionnaires) in a pain relief study.

Bias in Selection of the Reported Result:

• Arises when only statistically significant or favorable outcomes are reported.
• Skews the perception of an intervention’s efficacy or safety.
• Example: Reporting only significant weight loss in a drug trial while ignoring non-significant effects on cholesterol or blood pressure.

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Definitions Relating to Data Presentation in Therapeutics (Treatment Calculations)

Control Event Rate (CER):

The proportion of events occurring in the control group.

Experimental Event Rate (EER):

The proportion of events occurring in the experimental group.

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The Experimental Treatment Reduces the Risk for a Bad Event

Relative Risk (RR):

• Relative risk (RR) is a statistical measure used to compare the risk of a certain event (like developing a disease) happening in two different groups.
• Relative risk tells us how much more or less likely something is to happen in one group compared to another.
  • RR = 1: No difference in risk between the groups.
  • RR > 1:  Increased risk in the exposed group (e.g., a risk factor increases the chance of disease).
  • RR < 1: Decreased risk in the exposed group (e.g., a treatment reduces the chance of disease)
• Is accompanied by 95% Confidence Interval (CI)
  • The 95% CI shows the range within which we are 95% confident that the true RR lies.
  • If the CI includes 1, it indicates that the difference may not be statistically significant.
  • Narrow CIs indicate more precise estimates, while wider CIs suggest greater uncertainty.

example:

Relative Risk Reduction (RRR)

is a measure used in clinical studies to compare the risk of a certain outcome between two groups—typically one receiving an experimental treatment and the other receiving a placebo or standard treatment. It helps to understand how much a treatment reduces the risk of a negative outcome in relative terms.

• CER (Control Event Rate): The rate of the outcome in the control group (i.e., those receiving the placebo or standard treatment)
• EER (Experimental Event Rate): The rate of the outcome in the experimental group (i.e., those receiving the new treatment).

Alternatively, it can also be expressed as:

Absolute Risk Reduction (ARR):

Absolute difference in bad event rates between control (CER) and experimental (EER) groups.

Number Needed to Treat (NNT):

• Number of patients needed to be treated to prevent one additional bad outcome.
• Focuses on preventing negative events, such as preventing a heart attack, stroke, or death.
• Example:
  • If a medication is given to prevent heart attacks, the NNT tells us how many people need to take that medication for one person to avoid a heart attack.
  • Lower NNT: example NNT = 2 – means you only need to treat 2 people to prevent 1 heart attack.) indicates that the treatment is more beneficial, meaning fewer patients need to be treated to prevent one adverse event.
  • Higher NNT: example NNT = 25 – you need to treat 25 people to prevent 1 heart attack.) means that the treatment is less effective, and many more patients need to be treated to achieve the same benefit.
  • NNT should always be reported with a 95% confidence interval (CI) to express the range within which the true NNT might lie.
  • Example:
    • If NNT = 25 with a 95% CI of 20–30, it means that the true NNT might be as low as 20 or as high as 30, depending on the population variability or study design. (ie : with 95% confidence that the true number lies within somewhere between 20 and 30)

example: Scenario: A clinical trial is conducted to evaluate the effectiveness of an experimental cardiac drug in preventing heart attacks. Participants in the study are divided into two groups:

1. Control Group: Receives standard care (without the experimental drug).
2. Treatment Group: Receives the experimental cardiac drug in addition to standard care.

Study Results:

• In the Control Group, 15 out of 100 participants had a heart attack (i.e., 15% or 0.15).
• In the Treatment Group, 9 out of 100 participants had a heart attack (i.e., 9% or 0.09).

Step-by-Step Calculation of RRR:

• Calculate the Risk in Each Group:
  • Risk in Control Group (without experimental drug): 15% = 0.15
  • Risk in Treatment Group (with experimental drug): 9% = 0.09
• Calculate the Absolute Risk Reduction (ARR):
  • ARR is the difference in risk between the control group and the treatment group:
  • 𝐴𝑅𝑅 = Risk in Control Group −Risk in Treatment Group
  • ARR = 0.15 – 0.09 = 0.06 (or 6%)}
• Calculate the Relative Risk Reduction (RRR):
  • RRR represents the proportional reduction in risk due to the experimental cardiac drug compared to the control group:
  • 𝑅𝑅𝑅 = (Risk in Control Group − Risk in Treatment Group)/ Risk in Control Group
  • RRR = {0.15 – 0.09}/{0.15} = 0.40 (or 40%)}

Interpretation of RRR:

• The Relative Risk Reduction (RRR) of 40% means that the experimental cardiac drug reduces the risk of having a heart attack by 40% compared to those who do not receive the drug.
• In other words, patients taking the experimental drug have a 40% lower relative risk of experiencing a heart attack compared to those in the control group.

Practical Meaning of RRR in This Scenario:

• RRR provides a sense of how much the experimental cardiac drug is helping reduce the relative risk of heart attacks.
• For example, if a patient has an initial 15% risk of having a heart attack without treatment, using the experimental drug reduces that risk to 9%, which means 40% relative reduction compared to not taking the drug.

Consider the Absolute Risk:

While RRR shows an impressive reduction in relative risk, it’s also important to consider the Absolute Risk Reduction (ARR) and Number Needed to Treat (NNT) for a complete understanding of the drug’s effectiveness:

• ARR in this scenario is 6%, meaning that 6 fewer heart attacks per 100 patients occur when using the drug compared to not using it.
• NNT can be calculated as: NNT=1/ARR= 1/0.06 ≈17
• This means that 17 patients need to be treated with the experimental drug to prevent one additional heart attack.

Summary:

• The Relative Risk Reduction (RRR) of 40% shows that the experimental cardiac drug is effective in reducing the risk of heart attacks relative to the control group.
• However, looking at ARR (6%) and NNT (17) also gives insight into how many patients actually benefit, helping balance expectations and provide a clear understanding of the overall impact of the treatment.

Using both RRR and other measures like ARR and NNT provides a comprehensive view of the effectiveness of the experimental cardiac drug, guiding clinical decision-making.

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The Experimental Treatment Increases the Probability of a Good Event

Relative Benefit Increase (RBI):

Increase in rates of good events between experimental (EER) and control (CER) groups.

Absolute Benefit Increase (ABI):

Absolute difference in good event rates between experimental (EER) and control (CER) groups.

Number Needed to Treat (NNT):

• Number of patients needed to receive the experimental treatment to create one additional improved outcome.
• achieving a positive outcome, such as recovery from an illness, improved quality of life, or remission of a disease.
• Example:
  • If a new drug is being tested to improve recovery rates from an infection, the NNT tells us how many people need to receive the drug for one additional person to recover compared to a control group
  • Lower NNT: example NNT = 12 – every 12 patients treated with the new drug, 1 additional person recovers compared to placebo, This means the drug is more effective
  • Higher NNT: example NNT = 56 – every 56 patients treated with the new drug, 1 additional person recovers compared to placebo. This indicates that the drug is less effective, as more patients need to be treated to see the same benefit.
• NNT should always be reported with a 95% confidence interval (CI) to express the range within which the true NNT might lie.

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The Experimental Treatment Increases the Probability of a Bad Event

Relative Risk Increase (RRI):

Increase in rates of bad events between experimental (EER) and control (CER) groups.

Absolute Risk Increase (ARI):

• Absolute difference in bad event rates between experimental (EER) and control (CER) groups.

Number Needed to Harm (NNH)

• Number of patients needed to receive the experimental treatment for one additional person to be harmed compared with control treatment.

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Statistical Significance vs. Clinical Significance

• Statistical Significance tells us whether the observed effect or difference in a study is likely to be real and not due to random chance, usually determined through a p-value (e.g., p < 0.05).
• Clinical Significance focuses on the practical or meaningful impact of a treatment or intervention on patient outcomes. A result can be statistically significant but may not necessarily have a meaningful or important impact on patient health or well-being.

P-Value

• Definition: The p-value quantifies the likelihood that the observed results occurred by chance.
• A small p-value (typically <0.05) indicates it is unlikely the result is due to random chance, suggesting a real effect.
• Example: A p-value of 0.03 means there is a 3% chance that the observed result happened by random chance, implying 97% confidence that the effect is real.

Confidence Interval (CI)

• Definition: A confidence interval provides a range within which the true effect is expected to lie and indicates the precision of the estimate.
• A narrow CI suggests a precise estimate; a wide CI indicates more uncertainty.
• Example: If a study shows a drug reduces blood pressure by 5 points with a CI of 4 to 6, it means the true effect likely lies within this range with a 95% confidence level. A wider CI (e.g., 1 to 9) implies less certainty about the effect’s magnitude.

Summary:

• Statistical Significance: Confirms that an observed effect is likely genuine, not random.
• P-Value: A small p-value (<0.05) suggests the observed effect is unlikely to be due to chance.
• Confidence Interval: Shows the range of possible values for the true effect, with a narrow interval indicating more certainty.

Scenario: Evaluating a New Antihypertensive Drug (Drug A)

Study Design:

• Participants with hypertension were randomized into two groups: Drug A (treatment) and placebo (control).
• Primary outcomes measured: reduction in systolic blood pressure (BP), proportion reaching target BP (<140/90 mmHg), and occurrence of cardiovascular events.

Step-by-Step Data Analysis:

1. Descriptive Statistics:
   • Systolic BP Reduction:
     • Drug A Group: Mean reduction = 15 mmHg, Median = 14 mmHg.
     • Placebo Group: Mean reduction = 7 mmHg, Median = 7 mmHg.
     • Close mean and median values suggest symmetrical distribution.
2. Statistical Significance:
   • Outcome: Proportion of patients reaching target BP (<140/90 mmHg).
   • Results:
     • Drug A Group: 60 out of 100 patients (60%) reached target BP.
     • Placebo Group: 40 out of 100 patients (40%) reached target BP.
   • Analysis: Chi-square test yielded a p-value of 0.02 (0.02 < 0.05), indicating a statistically significant difference unlikely due to chance.
3. Clinical Significance:
   • Control Event Rate (CER): 40% (placebo group).
   • Experimental Event Rate (EER): 60% (Drug A group).
   • Relative Risk (RR): EER/CER = 0.60/0.40 = 1.5. Interpretation: Patients on Drug A are 1.5 times more likely to reach target BP compared to placebo.
   • Relative Risk Reduction (RRR): (CER – EER)/CER = (0.40 – 0.60)/0.40 = 50%. Interpretation: Drug A reduces the risk of not reaching target BP by 50% compared to placebo.
   • Absolute Risk Reduction (ARR): EER – CER = 0.60 – 0.40 = 0.20 (20%). Interpretation: 20% absolute increase in patients reaching target BP with Drug A compared to placebo.
   • Number Needed to Treat (NNT): 1/ARR = 1/0.20 = 5. Interpretation: 5 patients need to be treated with Drug A for one additional patient to reach target BP.
4. Conclusion:
   • Statistical Significance: The p-value of 0.02 indicates a significant difference between Drug A and placebo.
   • Clinical Significance: The ARR of 20% and NNT of 5 demonstrate meaningful clinical benefit. Drug A shows a 15 mmHg mean reduction in systolic BP, which is clinically impactful.

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Diagnostic Test Calculations

Diagnostic Standard

• Diagnostic Standard: The method used to confirm the presence or absence of the target disorder, often referred to as the “gold” or “reference” standard.

Definitions and Formulas

1. True Positive (a): Individuals who have the target disorder and a positive test result.
2. False Positive (b): Individuals who do not have the target disorder but have a positive test result.
3. True Negative (d): Individuals who do not have the target disorder and have a negative test result.
4. False Negative (c): Individuals who have the target disorder but have a negative test result

Sensitivity

• Sensitivity tells us how good a test is at correctly identifying people who actually have the condition.
• Sensitivity is how well a test finds people who really have the condition.
• If the sensitivity is high, it means the test is good at catching almost everyone who is sick, so very few people with the disease will be missed
• Example:
  • If a test for flu has 90% sensitivity, it means that out of 100 people who have the flu, the test will correctly identify 90 of them as positive. However, it will miss 10 people who actually have the flu, giving them a false negative result.
• High Sensitivity:
  • Best for catching people with the condition, so it’s useful for screening tests, where missing someone with the disease could have serious consequences. For example, high sensitivity is important in tests for serious conditions like HIV, where you want to make sure almost no one with the disease is missed.

Specificity

• Specificity is the ability of a test to correctly identify people who do not have the condition. In other words, it tells us how well a test avoids false positives.
• If a test has high specificity, it means it correctly identifies most people without the disease, resulting in very few false positive results.
• High specificity is important when it is critical to minimize false positives, so most people without the disease are correctly identified as disease-free.
• This is important when the diagnostic confirmation of a disease is associated with serious consequences, like invasive testing or heavy social stigma.
• Example of Specificity:
  • If a flu test has 90% specificity, it means that out of 100 people who do not have the flu, the test will correctly identify 90 as negative. However, it may falsely identify 10 people as having the flu when they actually do not (false positives).

High Sensitivity and High Specificity:

• When to prioritize: In situations where both false positives and false negatives can have significant consequences, a balance of high sensitivity and high specificity is ideal. This often applies to confirmatory diagnostic tests or tests guiding major medical interventions.
• Example: Diagnostic Test for Tuberculosis (TB) Before Initiating Treatment
  When diagnosing TB, both high sensitivity and high specificity are desirable. Missing TB (false negative) could lead to untreated disease and public health risks, while false positives might expose the patient to unnecessary and potentially toxic medications. Therefore, a balance is necessary to accurately diagnose the disease while minimizing the chance of over- or under-treatment.

Summary Table:

Situation	Priority	Example
High Sensitivity	When it’s crucial to catch almost all cases, even if some false positives occur	HIV screening tests
High Specificity	When avoiding false positives is critical to prevent unnecessary treatments or interventions	Confirmatory cancer tests
High Sensitivity and High Specificity	When both accurate detection and minimizing false results are necessary	Tuberculosis diagnostic testing

Pre-Test Probability (Prevalence)

the proportion of individuals who have the target disorder before the test is carried out.

• What it means: This is how likely it is that a person has a condition before any test results are known.
• How to explain:
  “Before we do any tests, we already have an idea of how likely it is that you have a condition. This likelihood is based on things like your symptoms and medical history. That’s the pre-test probability.”
• High Pre-test Probability:
  • What it means: This indicates a strong likelihood that the patient already has the condition, even before testing.
  • Example: If a patient has multiple risk factors for heart disease (like chest pain, high cholesterol, and a family history of heart disease), the pre-test probability of them having heart disease would be high.
  • Why it matters: If the pre-test probability is high, a positive test result is more likely to confirm the diagnosis, and even a negative test might not fully rule it out because the initial suspicion was strong.
• Low Pre-test Probability:
  • What it means: This suggests a low likelihood that the patient has the condition before any testing is done.
  • Example: If a healthy young patient with no symptoms or risk factors comes in worried about heart disease, their pre-test probability of having it is low.
  • Why it matters: If the pre-test probability is low, a positive test result might not be as convincing, as it could be a false positive. Similarly, a negative test might be more reassuring in ruling out the condition.
• Summary:
  • High Pre-test Probability: There’s a strong chance the patient has the condition, so tests are used to confirm or further clarify the diagnosis.
  • Low Pre-test Probability: There’s a low chance the patient has the condition, so tests are more likely to rule it out or catch an unexpected diagnosis.
  • In short, high pre-test probability means you already think the condition is likely, while low pre-test probability means the condition is unlikely, and the test is more of a precaution.

example: DVT and PE

pre-test probability to the example of a D-dimer test, which is commonly used to help rule out blood clots like deep vein thrombosis (DVT) or pulmonary embolism (PE).

High Pre-test Probability for Blood Clots:

• What it means: The patient has a lot of signs or risk factors that suggest they may have a blood clot before the D-dimer test is done.
• Example: If a patient has swelling in one leg, pain, recent surgery, and a history of blood clots, their pre-test probability of having a blood clot is high.
  • How the D-dimer test works in this case:
    • If the D-dimer test is positive, it supports the idea that the patient likely has a blood clot, and further imaging (like an ultrasound or CT scan) is usually needed to confirm the diagnosis.
    • If the D-dimer test is negative, it might not be enough to rule out a clot completely, because the patient’s risk is already high, so further testing might still be necessary.

Low Pre-test Probability for Blood Clots:

• What it means: The patient doesn’t have many signs, symptoms, or risk factors for a blood clot.
• Example: A young, healthy person with mild calf pain but no swelling, no recent surgery, and no history of blood clots would have a low pre-test probability of having a clot.
  • How the D-dimer test works in this case:
    • If the D-dimer test is negative, it’s very reassuring, and it’s likely that the patient does not have a blood clot, so no further testing is usually needed.
    • If the D-dimer test is positive, it might be a false positive because the pre-test probability was low to begin with. In this case, more tests may still be required to confirm or rule out the diagnosis.

Summary:

• High pre-test probability (lots of risk factors or symptoms): A positive D-dimer result is more meaningful, but a negative result might not be enough to rule out a clot.
• Low pre-test probability (few risk factors or symptoms): A negative D-dimer result is very reliable in ruling out a clot, but a positive result might not be as convincing, and further testing is needed to confirm.

Post-test Probability

• What it means: This is how likely it is that a person has a condition after getting the test results.
• How to explain:
  “Once we have the test results, we can be more certain about whether you have the condition or not. The post-test probability tells us how likely it is that you actually have the condition after the test.

Pre-Test Odds

• Pre-Test Odds: The odds that an individual has the target disorder before the test is carried out

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screening and diagnostic tests

Aspect	Screening Test	Diagnostic Test
Purpose	To identify potential disease or condition in asymptomatic individuals.	To confirm the presence or absence of a disease in symptomatic individuals or those with a positive screening test.
Population Targeted	Generally applied to large groups of asymptomatic individuals.	Applied to individuals with symptoms, signs, or a positive screening test result.
Test Characteristics	– Often less invasive and lower cost – Designed for high sensitivity (ability to correctly identify those with the disease; minimizes false negatives to avoid missing cases)	– Typically more precise and may be more invasive and higher cost – Designed for high specificity (ability to correctly identify those without the disease; minimizes false positives for accurate diagnosis)
Example Goals	Early detection to enable timely intervention and management of a disease.	Definitive diagnosis of a suspected disease or condition.
Sensitivity and Specificity	High Sensitivity: Emphasizes catching as many true positives as possible, even at the risk of some false positives.	High Specificity: Focuses on accurately confirming a diagnosis and minimizing false positives, even if some true positives are missed.
Example Use Cases	– Mammography for breast cancer screening – Blood pressure screening for hypertension – Pap smear for cervical cancer	– Biopsy to diagnose cancer following an abnormal mammogram – Angiography for suspected coronary artery disease – Genetic testing for confirmed symptoms of a genetic disorder
Follow-Up Requirement	Positive results typically require further diagnostic testing for confirmation.	Results often lead to specific management or treatment plans.