biostatistics

clinical significance

****a measure of statistical significance is NOT the same as "clinical significance"!!!!!! "statistical significance" reflects the influence of chance ON the outcome "clinical significance" reflects the clinical value of the outcome itself I.e.: BP drug lowers BP 3 mmHg may be statistically significant w/ P-value < 0.05 vs placebo, but clinically the drug won't be used because other drugs lower BP much better than that therefore not "clinically significant"

what is relative risk/risk ratio (RR)

*the relative risk (or risk ratio) is the probability of an UNFAVORABLE EVENT occurring in the treatment group versus the control group.

number needed to harm

*used when the treatment or exposure causes harm rather than good effect calculated the same way as number needed to treat BUT you always round DOWN!

observational studies

1. case report or case series: descriptive, no conclusion can be drawn from them BUT can generate hypotheses to be used in larger trials 2. case-control study: compare patients who have disease or outcome of interest and look back retrospectively; good for studying RARE disease or outcomes...can be conducted in less time since condition already happened and useful to establish association...often they generate hypotheses to be studied in other studies 3. cohort study: group of people who share common characteristic/experience within a defined period; this study type follows cohort over time (longitudinal) and the outcomes are compared to a subset of the group who were not exposed to the intervention such as a drug...good for when randomized study UNETHICAL..can be prospective or retrospective 4. cross-sectional study: descriptive, observational trials to estimate relationship between outcome and population variables as they exist in a cross-section; used to determine prevalence of a disease

continuous data

1. interval - measure continuous data that have legitimate mathematical values...the difference between 2 consecutive values is consistent along any point of the scale, but the zero point is arbitrary and doesn't mean anything (aka Celsius) 2. ratio - equal intervals between values and meaningful zero point (weight, time, length, etc)

discrete data types

1. nominal - categories where the order of the category is arbitrary...numbers do not have true numerical or quantitative value (male, female), doesn't matter what order or what value you assign it 2. ordinal - ranked categories where the order of the ranking is important, however, difference between categories cannot be considered to be equal and there is not correlation between the ranking and degree of severity (aka trauma 4 does not mean twice as ill as trauma 2)

experimental studies

1. randomized controlled trial a. parallel - randomized to treatment or placebo group only and stay in there for duration (common for Phase III trial)...large number needed but shorter time b. crossover - randomized to treatment and each receives intervention...in this type the subject serves as the control...washout periods may be needed c. factorial - evaluate multiple interventions in a single experiment (i.e. in 2x2 factorial design patients assigned to 1 or 2 drug doses and 1 of 2 drugs) 2. intent-to-treat vs per protocol analyses a. intent-to-treat - includes data for all patients originally allocated to each treatment group regardless if patient did not complete trial according to protocol (conservative estimate of treatment effect) b. per protocol - subset of the trial population who completed the study according to protocol (may provide optimistic estimate of treatment effect since it is limited to the subset of patient adherent to protocol) 3. non-inferiority trial: another type of RCT where new treatment is not worse than that of an active control by some per-specified margin (generally fewer patient than superiority trials and are appropriate when giving placebo is unethical)

systematic review & meta-analysis

1. systematic review: structured literature review that uses a step-by-step protocol with preset criteria for selecting and evaluating studies. They attempt o identify all studies that meet the pre-defined criteria, evaluate validity of findings and then synthesize results 2. meta-analyses: statistical technique used to combine results from multiple studies to develop a single conclusion that has greater statistical power than the possible in the individual smaller studies; the validity and usefulness of a meta-analysis is largely dependent on the quality of the systematic review that identified which studies to include...they are used for the following purposes: 1. establish statistical significance when studies are conflicting 2. develop more correct estimate of effect magnitude 3. provide more complex analysis of harms, safety data, and/or benefits 4. examine subgroups with individual numbers that are not statistically significant

calculating risk & risk ratio (RR)

1. the risk of developing the event must be calculated for both the treatment group and the control group 2. Then the relative risk is calculated by comparing the risk calculated for the treatment group (numerator) to the risk calculated for the control group (denominator). *The RR is generally expressed as a decimal but can also appear as a percentage. *RR is simply the ratio of risks in the 2 groups. risk = number subjects with unfavorable event / total number of subjects RR = risk in treatment group/risk in control group

Importance of type I & type II error

False positive (type I) for a disease marker = may make patient anxious and seek unnecessary treatment False negative (type II) is worse because the patient will not seek medical care that they need which could prevent or heal disease

odds

NOT the same as risk - it is the probability of the event occurring compared with probability that it will not occur

interpreting RR

RR = 1: no difference in risk b/n 2 groups RR < 1: fewer events are occurring in the treatment group compared to the control group RR > 1: more events are occurring in the treatment group compared to control group

type I error

alpha is type I error type I error occurs when the null hypothesis is TRUE but REJECTED in error - AKA they said there was a difference between the two groups when there was not...it is a FALSE POSITIVE *chosen by researcher before study starts to be acceptable threshold of statistical significance (p-value) - generally it is <0.05 (which means <5% of the time this error will occur) Remember - in relation to CI: CI = 1- alpha

mean

average value of a data set mean = sum of all values/number of values *means can be used when the data are NOT skewed; will be sensitive (reflect) the extremes of values - may be inflated/not reflect

normal distribution

bell-shaped curve of Gaussian curve *when sample is large, the distribution approximates a normal, bell shaped curve *u = mean *o thing = standard deviation (SD) *in normal distribution, the mean, mode & median would all have same value and would look symmetric around the mean and skew is zero *the test may not say "it is normally distributed"..may need to look for words like bell-shaped curve, etc. to know whether you will use the mean (non-skewed data, bell-shaped) or median (skewed data) *EXAMPLE: new drug for weight lost, mean is 10 pounds, you find out standard deviation is -1, +1...that means 68% of people lost between 9-11 pounds...then if it's 2 standard deviations 95% of people lost between 8-12 pounds...NOT SHOWING STATISTICAL SIGNIFICANCE! JUST a description

type II error

beta is type II error generally set at 0.1 or 0.2 (accept a type II error 10 or 20 times in 100 comparisons) *type II error occurs when null hypothesis is false yet it is accepted in error AKA they said there was no difference when there was actually a difference...FALSE NEGATIVE statistical power = 1 - beta

skewed data curves

data WITHOUT an normal distribution (asymmetrical curve) *data has extremes/outliers *can be a positive skew (data skewed to the right, curve to the left) *can be a negative skew (data skewed to the left, curve to the right) *the DIRECTION (positive or negative) refers to the direction of the longer TAIL, NOT the bulk of the data points/curve hump *DO NOT USE THE MEAN!!!!!!!!! USE THE MEDIAN!!!!!!!!!!!

correlation

describes relationship between two or more variables which is then plotted on a linear scale; direction & magnitude of linear correlation can be quantified with a correlation coefficient *MOST WIDELY USED CORRELATION COEFFICIENT: Pearson Correlation Coefficient (r), between -1 to 1 if coefficient 0 = no correlation if coefficient is negative = inversely related if coefficient is 1 or -1 exactly = perfect correlation (straight line)

absolute risk reduction (ARR) or attributable risk

difference between control group event rate & treatment group event rate ARR = % risk in control - % risk in treatment group

range

difference between the highest and lowest value

study design

expert opinion --> case series/reports-->case-controlled trials-->cohort studies -->randomized controlled trials --> systematic reviews & meta-analysis

P-value

likelihood (probability) that chance would produce a difference as large or larger than the one found in the study (if null hypothesis is true) *AKA: probability that the result obtained was due to chance (alpha level) *generally, p-value <0.05 indicates STATISTICAL SIGNIFICANCE saying that there is <5% probability that the result occurred by chance *when the p-value is smaller than the predetermined significance level (alpha level) the difference found between groups is statistically significant and the study failed to accept (rejected) the null hypothesis (aka there was a difference)

null hypothesis (H0)

means NO DIFFERENCE OR RELATIONSHIP "null, nada, none) *study is designed to disprove this assertion by testing for a statistically significant difference between Drug A and Drug B (AKA alternate hypothesis"...if there is a difference the null hypothesis is rejected *ALL STUDIES start with null that drug A = drug B and they are working to disprove that through statistical significance

relative risk reduction (RRR)

measures how much the risk is reduced in the treatment group compared to control group RRR = (% risk in control grp - % risk in trmt grp)/ % risk in control group OR 1-RR *expressing result as relative risk reduction is more intuitively understandable *RR and RRR are limited in that these data do not reflect how important or how large the treatment effect is in the population at large

sensitivity and specificity

often applied to diagnostic testing for diseases 1. sensitivity: proportion of time a test is POSITIVE in patients who have the disease (ability of the test to correctly identify people who have the disease)...percentage of "true-positive" results sensitivity = 1- beta (type II error) 2. specificity: proportion of time a test is NEGATIVE in patients who do not have the disease....ability of test to correctly identify patients known NOT to have the disease...a percentage of "true-negative" results specificity = 1 - alpha (type I error)

dependent variables

outcome of interest, which should change in response to some intervention

statistical power

power of a statistical test is the probability that the test will REJECT NULL when the null hypothesis is ACTUALLY FALSE (avoiding type II error) *as power increases, chance of type II error decreases power = 1- beta (type II error) *higher statistical power means that we can be more certain that the null hypothesis was correctly rejected

Confidence Interval

range of values derived from sample data that has given probability of encompassing the "true" value; CI states that there is a given probability that the populations true value is contained within this interval *reflects margin of error that inherently goes along when a sample statistic is used to estimate true value of population *help determine validty of sample statistic by attempting to capture true population parameter *generally 95% is used in studies; 95% CI would also be said as a 5% degree of uncertainty *CI = 1-alpha (type I error) OR CI = 1 - type I error *can be used DESCRIPTIVELY or INFERENTIALLY - descriptive: study reports mean weight of newborns @ hospital was 7.5 pounds with 95% confidence interval (6.6-8.8 pounds) = researcher 95% confident that the CI contains the sample statistic - inferential: looks @ values as a way of comparing groups & determine level of significance...a few rules for that 1. when 95% CI for estimated DIFFERENCE b/n groups (or in group over time) does NOT include zero..the results are significant at the 0.05 level 2. when 95% CI for ODDS RATIO, RISK RATIO, HAZARD RATIO that compares 2 groups does not include ONE, the results are significant @ 0.05 level

number needed to treat

represents number of people who would need to be treated with intervention for certain period of time in order to achieve the desired outcome NNT = 1 / (risk in control)-(risk in trmt) OR NNT = 1 /ARR (in decimal) ALWAYS ROUND UP!!!!!!!!!

standard deviation (S)

shows how much variation (dispersion) from the mean *the closer the numbers cluster around the mean, the SMALLER the standard deviation...if the SD is small one would conclude that the drug being studied had a similar effect on most subjects *same units as the data *used for data under normal distribution *always a positive number and can be used for continuous data only *roughly 68% of values within 1 standard deviation from mean and 95% are within 2 standard deviations from mean

alternative hypothesis (HA)

states that there IS a treatment difference or relationship between groups..if you fail to accept (rejected) the null hypothesis

hazard ratio

the chance of an unfavorable event occurring by a given point in time. A hazard ratio is the hazard or chance of an event occurring at any given time during the study in the treatment group as compared to a comparator group *used in clinical trials with time-to-event (or survival) analysis *assumes ratio is constant over time...they are a specific type of RR with distinction that HR ratios are the relative likelihood of an event in the treated vs comparison group AT ANY GIVEN POINT IN TIME during the trial versus RR where it is the likelihood of an event in the treated vs comparison group AT THE END of the trial HR = hazard rate in the treatment group/ hazard rate in the control group interpreting: HR = 1: event rates are the same in both arms over time HR < 1: at any time, fewer patients in TREATMENT group have had an event HR > 1: at any time, MORE patients in TREATMENT group have had an event

independent variables

the intervention or what is being manipulated

median

the value in the middle of a ranked list *rank in order of lowest to highest and pick middle value...if even number, select to middle values and average *ANOTHER way to say median: 50th percentile *median values should be used when data IS skewed; it is less sensitive to outliers

mode

value that occurs most frequently in set of data *some sets MAY NOT have a mode