If you need to brush up on biostatistics, I recommend you buy the little biostatistics book ACCP offers (it’s cheap and it has some good practice problems in it). This is also a really good study guide and here’s a really, really simple sheet. I have more topics in biostatistics (including the “which statistical test to pick” questions). And, while you need to know how to calculate these things in real life, ClincCal has a few of them (NNT, Odds Ratio, Sample Size, etc) if you want to double check your own calculations.
Biostats Definitions:
Here are some basic things in case you have forgotten them:
- Nominal date – data with no order (yes/no, male/female)
- Ordinal data – data with order, but no consistent difference in magnitude change (classes of heart failure, pain scales)
- Interval data – continuous data with consistent interval difference (temperature)
- Ratio data – continuous data with consistent interval difference, but zero is the starting point (HR, BP)
- Mean– “Average.” Only with continuous data (parametric, normally distributed)
- Median – 50th percentile. The data point exactly in the middle of the data points. Usually only used with ordinal data or continuous data that is not normally distributed
- Mode – the most frequently occurring value
- Range – how far apart the data points are
- Interquartile range – related to the median. Most data is in the 25-75 percentile.
- Standard deviation (SD) – only applicable to parametric data. Measures how data points scatter around the mean. Not available for nominal data or ordinal data. 99% of the data should be found in +/-3 SDs, 95% of the data in +/- 2 SDs, 68% in +/- 1 SD.
- Standard error the mean (SEM) – smaller than the standard deviation. Average variability of data.
- Parametric data – continuous data that is normally distributed (like a parabola)
- Nonparametric data – continuous data that does not follow a normal distribution (skewed)
- If mean > median, skewed to the right
- Correlation coefficient (R) – how variables relate. The closer the number is to 1, the stronger the relationship.
- R2 – How much of the relationship is due to Y (ie: 70% of weight gain is due to calories, 30% is unknown).
- Narange Scale – the probability that an adverse effect is related to drug toxicity.
- Lot Proportional Hazard – survival data
Dependant and Independant Variables
The dependent variable is the variable measured in response to the independent variable, which is what the researcher manipulates. So, if you’re looking at how a drug affects blood pressure, the independent variable would be drug or no drug and the dependant variable would be the blood pressure measurement.
Therapeutic Index
- Therapeutic Index = Median Toxic Dose / Medicontinuousive Dose (also Lethal dose 50/effective dose 50)
- The higher the TI, the safer the drug
- IF LD50>ED50 TI is large so the drug is safe
Specificity, Sensitivity, Predictive Values and Accuracy
These variables predict how well a test measures the true status.
- Sensitivity = True Positives / (True Positives + False Negatives) Sensitivity measures true positives. If a highly sensitive test is negative, you can be sure they don’t have the disease (SNOUT Rules Things Out)
- Specificity = True Negatives / (True Negatives + False Positives) Specificity measures true negative. If a highly specific test is positive, you can be sure they have the disease (SPin Rules Things In)
- Bigger Numbers are more significant.
- Positive Predictive Value = True Positives / (True Positives + False Positives) This is the percentage of people who test positive who actually have the disease. *Bigger numbers are more significant*
- Negative Predictive Value = True Negatives / (True Negatives + False Negatives ) This is the percentage of people who test negative who don’t have the disease. *Bigger numbers are more significant*
- Accuracy = (True Positives + True Negatives) / Total
- When you increase sensitivity, you decrease specificity. You get more diagnosis but more false positives.
- Prevalence = the number of cases / total at risk; incidence = new cases/total population at risk
Some people like to set up a table (this is called a “confusion matrix” in the statistics world):
| + | – | ||
| + | TP | FP | TP+FP |
| – | FN | TN | FN+TN |
| TP+FN | TN+FP | TP+FP+FN+TN |
- Sensitivity= TP/(TP+FN) (column 1)
- Specificity = TN/ (TN+FP) (column 2)
- PPV = TP/ (TP+FP) (row 1)
- NPV = TN/(TN+FN) (row 2)
- Accuracy = diagonal down chart : TP+TN/ (TP+FP+FN+TN)
Hypothesis Testing:
The null hypothesis is that there is no difference between groups in a study. In order to find significance, you need to REJECT the null. This can be a little confusing.
| Null is True | Null is False | |
| Accept Null | correct decision | Type II Error (β) |
| Reject Null | Type I error (alpha) | correct decision |
- The P-value (p) is the probability that a particular statistical measure, such as the mean or standard deviation, of an assumed probability distribution will be greater than or equal to (or less than or equal to in some instances) observed results. In other words, the p-value is the probability that the null hypothesis is true. 1 – the p-value, is the probability that the alternative hypothesis is true. A low p-value shows that the results are replicable and predicts a larger effect. P-values are calculated from the deviation between the observed value and a chosen reference value, given the probability distribution of the statistic, with a greater difference between the two values corresponding to a lower p-value.
- Usually p-values are set to P < 0.05.
- Some studies are set to different p-values. The U.S. Census Bureau stipulates that any analysis with a p-value greater than 0.10 must be accompanied by a statement that the difference is not statistically different from zero.
- If you have two similar studies, one with a p-value of 0.03 and one with a p-value of 0.04, the result with a p-value of 0.03 will be considered more statistically significant than the p-value of 0.04 (this isn’t taking clinical significance into account). You could compare a 0.04 p-value to a 0.001 p-value. Both are statistically significant, but the 0.001 example provides an even stronger case against the null hypothesis than the 0.04.
- P-values don’t say anything about study applicability or clinical significance. I could have a p-value of 0.001 in a study about Seizereduce preventing seizures with just one dose, but if the study is in dogs, it doesn’t matter to people. You should always look at the methods to see dosing, patient population, etc. before deciding something has clinical significance.
- Type 1 error: Rejecting the null hypothesis when it is true. A difference is found where none exists. The maximum acceptable alpha error is usually 0.05 (think of alpha as the p-value you are designing the study to obtain).
- Type 2 Errors: Accepting the null hypothesis when it is not true. No difference found when one exists. The maximum acceptable probability of a Type II error should be 20% (β = 0.2).
- Beta errors are usually due to sample size or a poorly powered study. The easiest way to decrease Beta is to increase the sample size. Alpha and sample size have the greatest impact on study power.
- You’ll always have the risk of making either a Type 1 or Type 2 error, but never have the risk of making both. If the p-value is significant, you have the risk of making a Type 1 error. If it is not, you have the risk of making a Type 2. For example, a p-value of 0.01 would mean there is a chance of committing a Type I error (i.e.: you found the p was significant, rejected the null and stated there was a different between the groups. In real life, there was no difference between the two groups).
- “If the p-value is low, the null must go.” If the p-value is less than alpha, the null is rejected.
- P VALUES DO NOT SUGGEST CLINICAL SIGNIFICANCE, just statistical significance. Clinical significance can only be assessed by reading the study and finding the methods, inclusion criteria, etc.
Confidence intervals:
- The confidence interval shows the range of values you expect the true estimate to fall between if you redo the study many times.
- The confidence interval tells you more than just the possible range around the estimate. It also tells you about how stable the estimate is. A stable estimate is one that would be close to the same value if the survey were repeated. An unstable estimate is one that would vary from one sample to another. Wider confidence intervals in relation to the estimate itself indicate instability. Narrow confidence intervals in relation to the point estimate tell you that the estimated value is relatively stable; that repeated polls would give approximately the same results. This can be important information, especially when a p-value is borderline (i.e., it is equal to the critical p-value).
- Statisticians often use confidence intervals that contain either 95% or 99% of expected observations. Thus, if a point estimate is generated from a statistical model of 10.00 with a 95% confidence interval of 9.50 – 10.50, it means we are 95% confident that the true value falls within that range.
- When the 95% CI spans 1 (the null) the results are likely not significant.
- The closer a data point lies to the 95% confidence interval, the more likely it represents the population.
- For a ratio confidence interval, if it includes 1, it’s not significant (think 1/1 = 1, no difference)
- For a continuous confidence interval, if it includes 0, it’s not significant (think 1-1 = 0, no difference)The confidence interval shows the range of values you expect the true estimate to fall between if you redo the study many times.
- Sometimes studies only include the confidence interval, and not the p-value. Sometimes that’s because the p-value is borderline and sometimes it’s because the confidence intervals are tight and clearly significant.
Measures of Risk and Hazard
Risk in statistical terms refers simply to the probability that an event will occur.
Relative Risk (RR):
- Relative risk is a comparison between two groups of people, or in the same group of people over time, not the entire population.
- Relative Risk = incidence in exposed patients / incidence in non-exposed patients or, to say it in another way, the risk in one group divided by the risk in another
- >1 incidence in the exposed group is higher (R=1.5 = 50% greater risk, 3.0=200% risk)
- <1 incidence in the exposed group is lower (0.5=50% less risk, 0.8=20% less risk)
- Relative risk can be stated as X times as likely or X times the risk where X is the relative risk, but it could also be illustrated as a relative risk reduction and stated as a (1-X)*100% risk reduction or (1-X)*100% lower risk by implementing the intervention. Relative risk is a proportion so remember it’s “times as likely” when interpreting results.
- If the relative risk is greater than 1, it’s a risk increase.
If you’re reading a study instead of calculating your own work, it’s often easier to calculate relative risk using the event rate than using a table.
- RR: Take the event rate in the experimental group and divide by the event rate in the control group.
- For example, if the experimental group (A) had 17 events out of 1513 patients and the control or comparator group (B) had 57 events out of 1473 patients, the relative risk would be 0.2903 = (17/1513)/(57.1473)
- Relative Risk Reduction (RRR): Is 1-relative risk * 100.
- In the above case, it’s 0.71 or 71%
Absolute Risk:
- Absolute risk (AR) is the number of people experiencing an event in relation to the total population at risk or the likelihood that a person who is free of a specific thing in a certain patient population will develop an outcome. It’s sometimes called Risk Difference (RD).
- AR (absolute risk) = the number of events (good or bad) in treated or control groups divided by the number of people in that group.
- ARC = the AR of events in the control group.
- ART = the AR of events in the treatment group.
- ARR (absolute risk reduction) = ARC – ART.
- RR (relative risk) = ART / ARC.
Number Needed to Treat/Harm:
- Everyone likes to have some kind of measure they can relate to. Number needed to treat (or harm) is the number of patient’s you’d need to treat to prevent (or cause) one bad outcome. It’s very relatable to most practitioners. The lower number needed to treat (NNT) the better. For example, if a study looking at myocardial infarctions(MI) and DrugX reports a NNT of 4, that means only 4 patients need to be treated to prevent one MI. That’s better than a NNT of 400. Number needed to harm (NNH) is the inverse. A NNH of 400 is better than a NNH of 4. If the value is a decimal, you always round up (4.1 would be 5, there’s no 0.1 person) for NNT and down for NNH (4.1 would be 4, we want to be more cautious for harm).
- Usually, you have to account for study duration. If the MI study followed these patients for 5 years, the NNT of 4 means you’d have to treat 4 patients for 5 years.
- The number needed to treat is the reciprocal (or inverse) of the absolute risk reduction. It is calculated by dividing 1 by the absolute risk reduction. As the absolute risk reduction is usually expressed as a percentage, we need to multiply the answer by 100.
- NNT=1/ARR
Calculating These With a Table:
| Treatment | Disease | No Disease |
| Exposed | A | B |
| Unexposed | C | D |
- Relative Risk = A/(A+B)
- Absolute Risk Reduction (ARR) = C/(C+D)
- Odd Ratio = AD/CB
- Only used in retrospective studies
- If used in a prospective study, odds ratio overestimates the risks. They may try to trip you up on this.
- The further the OR is from 1, the more the OR overestimates the RR
- Number needed to treat or Number Needed to Harm: 1/ARR (it’s a decimal, not a percentage)
- Include duration of study = must treat 10 patients for 5 years
Odds Ratios:
- Odds ratio (OR) = (exposed cases / unexposed cases) / (exposed non-cases / unexposed non-cases)
- Risk ratio = rate
- An odds ratio means the exposure was associated with an event X% of the time. For example, an odds ratio 0.33 means the exposure was associated with the even 33% of the time (compared to 100% of the time).
- Odds ratio = 1: Exposure does not affect odds of outcome
- Odds ratio > 1: Exposure is associated with higher odds of outcome
- Odds ratio < 1: Exposure is associated with a lower odds of outcome
- The odds reduction is 1-OR. In the above example, the odds reduction is 67%. That means exposure to whatever the intervention was (could be a drug) was associated with a 67% reduction in risk.
Hazard Ratio:
- A hazard ratio is a type of relative risk that can be used to compare time-to-event data between 2 groups. The hazard ratio describes the relative risk of the complication based on comparison of event rates.
- Hazard ratios have also been used to describe the outcome of therapeutic trials where the question is to what extent treatment can shorten the duration of the illness. It does not always accurately portray the degree of abbreviation of the illness that occurred. In these circumstances, time-based parameters available from the time-to-event curve, such as the ratio of the median times of the placebo and drug groups, should be used to describe the magnitude of the benefit to the patient.
- The difference between hazard-based and time-based measures is analogous to the odds of winning a race and the margin of victory. The hazard ratio is the odds of a patient’s healing faster under treatment but does not convey any information about how much faster this event may occur.
- .For example, a hazard ratio (HR) of 0.75 over 10 years that the intervention patients were 0.75 times likely to have the outcome at any time during the 10 years. This means that intervention had a 25% reduction in the outcome.
Epidemiology Stats
These are not as commonly calculated in pharmacy, but you may need them for public health initiatives.
- Prevalence = Cases in a population in a given time period / total population at that time
- Incidence proportion = New reported cases / initial population at risk
- Incidence rate = New reported cases / summed person-years of observation (avg population during time interval)
- Mortality rate = deaths during specified time interval / population size at risk for death