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# Biostatistics

### BCPP Recertification

Term | Definition |
---|---|

Descriptive Statistics | Tendency = mean, median, mode. Variaibility = variance, standard deviation, interquartile range. |

Inferential Statistics | Conclusions based on rules of probability. Used to compare investigational medication to control treatment. Minimizes investigator bias. |

Variables | Dependent - outcome of interest. Independent - variable used to predict the value of the dependent variable. Ex. Independent variable new medication, Dependendent variable HAM-D score |

Continuous Data | Defined units, equal distance between increments. Interval zero point arbitrary (deg F. ) Ratio absolute zero - blood pressure, blood glucose, triglycerides. |

Discrete Data | Nominal names, categories (eye color, religion, sex blood type presence of absence of disease) Ordinal order of rank - cancer staging, heart failure class |

Mean | sum of all data points divided by the number of data points. Continuous data. Extremely sensitive to outliers |

Median | Value above or below which half of the data points fall. 50th percentile. Not sensitive to outliers. Useful when outliers present of continuous data not nl distribution. Cont or Ordinal data |

Mode | Most commonly observed value in distribution. Describes nominal, ordinal or continuous data. May be more than one - bimodal |

Variance | Measure of degree to which data are scattered around the mean/median. Mean of the squared differences of the observed values from their mean. |

Standard Deviation (SD) | Most common, measures spread, meaningful only in nl or near nl continuous distribution. Computed by square root of variance. 68% within 1 SD, 95% within 2SD, 99.7% within 3SD. |

Standard Error of the Mean (SEM) | Quantifies the uncertainty in the estimate of the mean.Computed from SD SEM= SD divided by the square root of n (n=number of subjects) Always smaller than SD unless = 1. Decreases as sample size increases, increases as SD increases. |

SEM vs. SD | Some report findings as a point estimate +/_ SEM, rather than +/_ SD. makes data appear to have less variation. |

Range and Interquartile range. | Range-difference between largest and smallest value. outliers big impact. Interquartile range measure of variability related to median between 25th and 75th %ile. Describes variability for ordinal data. Defines where 50% of measures occur, spread |

Distributions | Demonstrates # of times particular measurement obtained. Nl = Gaussian (bell shaped) mean=median=mode |

Skewness | Mean and median pulled in direction of longer tail. Mean is pulled farther than median. Tail may contain outliers. |

Kurtosis | Measure of whether data are flat or peaked. Normal (mesokurtic) dist = 3.High peak (leptokurtic) >3, Flat peak(platykurtic) <3. Higher peak = small # of extreme differences from mean. |

Hypothesis Testing | (Ho) No difference between treatments. (H1) difference between treatments. Ability to reject Ho is dependent on statistical analysis. |

Descriptive/Cross Sectional | Experience or Observation. May be only available e.g. toxicity. looks for relationships between characteristics and outcomes at point in time. case reports, case series, surveys. Insufficient evidence, multiple bias (observer, selection, classification) |

Case Control (observational, comparison groups) | Retrospective, identify outcome, then cases, then controls. Cases,controls may be matched for similarties. Good rare disease, long latency. Examines risk factors. Weaker than cohort or randomized. Selection, informational, recall classification bias. |

Cohort (observational, comparison groups) | Retro or prospective. Excludes cases w/ outcome , classifies based on risk, follows longitudinally, strongest observational for cause & effect, temporality, calc incidence. Neg-$$, long time, loss to f/u, confounding, Select, classify, attrition bias, HE |

(HE) | Hawthorne Effect - cohort - did participants change behavior due to observation. |

Controlled Clinical Trial (experimental, comparison groups) | Gold standard. assignment, intervention, outcome. (X-over, wash out, other tx) cause and effect, stratification, randomization, most difficult & expensive. Not good for rare dx, selection, allocation, observers. Need for identical tx. |

Randomizaton | sample = chance of selection for study, allocation=chance for each group, nonrandom allocation =group assigned preferentially, biases results. removes selection bias, best w/lg group. |

Simple Random Allocation | coin toss, groups may be unequal in size at any point, difficult to detect true difference. |

Blocked Random Allocation | Ensures equal size. multiple possible different arrangements, but equal group size. |

Stratification | Assigns data based on characteristics that affect outcome. Evaluates for confounding factors and pools data accordingly. e.g disease severity, smoking, sex, race. |

Rating scales | Psych = ordinal scales, lack accuracy and precision. |

Inter-rater reilability | Assessed by Kappa statistic if at or above 7, satisfactory. |

Bias | Attrition - high drop out. Channeling - selection based on prognosis. Information - accuracy of info not equal among subject. (mis) classification - elibility, outcome, severity, exposure, interviewer, recall, measurement, publication, referral, |

Confounding Bias | Lack of control for factor that is associated with both exposure and outcome. Restriction -excluding based on characteristic, Matching-selecting based on characteristic, Stratified- analysis conducted separately in subgroups. Regression adjustment. |

Intention to treat | “once randomized, always analyzed” •Inclusion occurs regardless of deviations after randomisation,: •protocol violations •losses to follow up•withdrawals from the study•non-compliance•refusal of the allocated treatment |

Per Protocol | Only data from precisely followed protocol. Problems if adherence related to prognosis. info on late occurring side effects. generous estimate of difference. |

As Treated | Based on intervention actually received. better estimate of effectiveness. better for safety evaluations. |

Last Observation Carried Forward (LCOF) | Last observation carried forward to all time points. May result in loss of power d/t drop outs. May underestimate late SE's |

Incidence | absolute risk of new disease, rate, #of new cases over period of time divided by the total population at risk |

Prevalence | Probability of disease at point in time or over specified point in time. #of cases in point in time divided by total population. |

Table | Outcome Outcome Total Present Not Present Exposure A B A+B No Exposu C D C+D |

Relative Risk | Compares probability of an outcome with characteristic or exposure. RR<1 Therapy decreased risk. RR =1 No difference. RR>1 Treatment increased risk. If RR includes 1 not significant. |

Relative Risk Table | RR = [A/(A+B)] / [C/(C+D)] |

Odds Ratio | Case control Cross Sectional. Control grp represents gen pop for risk factors. 2. A and C are relatively uncommon. OR<1 exposure less common in cases. OR=1 no difference in exposure for case vs. control. OR >1 Exposure more common in cases.. |

Odds Ratio Table | OR = A X D/B X C derived from (A/B) / (C/D) |

Absolute Risk Reduction (ARR) | Absolute risk of outcome (adverse in clinical trial) between treatment groups. Cohorts and Clinical Trials ARR = 0 no difference between groups. ARR = [C/(C=D)] - [A/(A+B)] |

Relative Risk Reduction | Estimates percentage of baseline risk removed due to tx. compares RRR = 0 no effect. RRR = 1-RR X 100. |

NNT | # who require tx to prevent one event. NNH is inverse. NNH rounded up, "NNH rounded down. Must specify comparator, outcome and duration of tx. NNT = 1/ARR |

Type I Error | Concluding significant difference exists when doesn't. Alpha = probability of making type I, false positive rate tolerated, set before data collected. Lower Alpha decreases likelihood. |

Type II Error | Concluding no significant difference exists when it does. Beta= probability of making TypeII, false negative rate tolerated, increasing sample size reduces likelihood. |

Power | Percentag 0% - 100%. 1-Beta. Studies powered at 80% or 90% have Betas = 0.2 or 0.1 respectively. Type II errors are more probable |

Effect Size | Measures strength or effect of association. Larger effect size more likely statistically significant. 0.2 is small, 0.5 is medium and 0.8 is large. Also reported as Cohen's d = difference in means divided by the pooled SD. |

Sample Size Calculation | Determining required subjects for outcome. Investigators specify Alpha, Beta, effect size, and variability of outcome Depends one sided or two sided test. One sided - non-inferiority trials, more powerful, Two sided difference in pos and neg direction |

Failure to Detect Significant Difference | Low power, small sample size, high false negative, or difference doesn't exist. Given large enough sample size anything can be statistically significant. Does not necessarily correlate with Clinical Significance. |

P-values | Probability of obtaining observed difference when not there. Due to chance. If Alpha is 0.05 P> 0.05 insufficient evidence. <0.05 results statistically significant. Smaller P = stronger evidence some difference, not large difference. |

Confidence Intervals | Precise objective way to specify how good a sample is. Defines boundaries where true population likely . If includes zero statistical significance is not achieved, if not achieved. If Crosses 1 possible no difference exists. No cross 1 stat sig |

Chi Square (Fisher Exact if <5 in any cell or N < 20) | NOMINAL - 2 or 3 treatment groups with different subjects. NOMINAL - Associations between 2 variables. Data are in counts. Useful for rates, proportions, frequencies for independent variables. |

Mann-Whitney U or Wilcoxon rank-SUM test | ORDINAL - 2 groups with different subjects. CONTINUOUS NON NL DIST - 2 tx groups with differenct subjects. Nonparametric equiv. to t-test. |

t-test | CONTINUOUS NL DIST - 2 tx groups different subjects. Compares means from 2 independent samples. Ho means 2 pops equal. |

Kaplan Meier Log rank test, Cox regression | TIME TO EVENT COMPARING (2 survival curves) - 2 tx groups with different subjects. KM - exact survival time maintained and not maintained grps, Log compares relative death rates between survival curves. Cox - RR survival and variables. |

Kruskal - Wallis | ORDINAL - 3 or more tx groups different subjects. CONTINUOUS NON NL DIST. - 3 or more tx groups, different subjects |

Analysis of Variance (ANOVA) | CONTINUOUS NL DIST. - 3 or more tx groups, different subjects. Comparisons of means in 3 or more groups. F test does not reject Ho - test finished. F test does reject Ho post hoc test need to determine difference |

McNemar's Test | NOMINAL - Before and after tx in same subjects. Variant of Chi Square, used when samples are paired |

Wilcoxan rank SIGNED test | ORDINAL - Before and after tx , same subjects. CONTINUOUS NON NL DIST - Before and after tx, same subjects. |

Paired t-test | CONTINUOUS NL DIST - Before and after tx, same subjects. Compares means from 2 matched or paired samples |

Cochrane Q | NOMINAL - Multiple tx., in same subjects |

Friedman Statistic | ORDINAL - Multiple tx, same subjects. CONTINUOUS NON NL DIST - Multiple tx, same subjects. |

Repeated measures - ANOVA | CONTINUOUS NL DIST. - Multiple tx, same subjects |

Spearman rank correlation | ORDINAL - Association between 2 variables. CONTINUOUS NON NL DIST - Association between 2 variables. |

Pearson correlation, linear regression | CONTINUOUS NL DIST. - Assn 2 variables. Quantitates cause / effect. Method least squares find line best fits. r2 0 to 1 1 = all variance explained. Logistic- log odds outcome (case-control, cross section) cohort/clinical trial with same follow up. |

Post hoc tests | Bonferroni and Tukey. Subset of pairwise comparisons Bonferroni, All pairwise comparisons Tukey. |

Mantel-Haenszel Chi Test | Variant of Chi Square. Multivariable analysis. NOMINAL DATA. Independent samples controlling for effect of categorical confounder. |

Correlation Coefficient (r) | Defines strength and direction of relationship between 2 variables. Range -1 to +1. Positive increase in both variables. Negative one increases, other decreases. r=0 not linear relationship. Does not prove cause and effect |

Coefficient of Determination (r2) | Measures the proportion in one variable if can be explained by variation in second variable. Magnitude, not direction. r2 = 0 no variance in Y can be attributed to x. r2 = 1 all of variance in Y is due to relation with x. If r stat sig, r2 stat sig |

Internal Validity | Lack of systemic bias. Review of inclusion/exclusion criteria, medications, doses, administration, endpoints, measurement of outcomes, statistical analyis |

External Validity | Extent to which study can be generalized to other situations and other people. |

Clinical Significance | Intervention has an effect of practical meaning for patients and clinicians. |

Noninferiority and Equivalence | Noninferiority - Product not clinically inferior to comparative agent (active control) Equivalence - two or more treatments differ by an amount that is clinically insignificant. Superiority - response to investigational agent is superior to comparator. |

Study Sensitivity | Distinguish between active an inactive tx. Affected by; adherence, concomitant meds, characteristics, signs/symptoms, exclusion criteria, diagnostic critieria, excessive variability, biased endpoint, reason for drop outs. |

Active Control | Equivalence and non-inferiority trials require accepted standard of care. Efficacy proven in placebo controlled trial. Equivalence trials typically prove pharmacokinetics are not different in generic form of drug |

Noninferiority Trial | Newer drug may have secondary advantages. Assumes active control effect as good/better than earlier studies. Better objective measurements as opposed to pain, psych. Variability due to varying response, waxing and waning. high placebo response. |

Appropriateness of noninferiority trial | Control - effect size large, effect size small but consistent, Ethical considerations. |

Analysis of Noninferiority trial | Intention to treat and per protocol should be performed. CI = equivalence margin ( non-inferiority margin) difference should be specified and justified a priori. If difference of interest in neg delta direction CI should be to right of. |

Noninferiority CI graph | negative delta (control agent better) zero positive delta (test agent better) If line crosses zero but does not exceed CI range then noninferiority shown. Equivalence can cross zero or not, but must not be outside of CI |

Pre-Post or "Mirror" Design | Observational non-randomized outcomes before and after change in same subject. Need to monitor response to treatment, and exclusion criteria. |

Enriched Enrollment Designs | Higher risk sample improves power and efficiency. Maintenance limited to responders, randomizing continue or to placebo answers benefit of continuation. Randomization to another tx does not enrich, favors current med. review abrupt discontinuation SEs |

Goals of Literature Interpretation | Establish significance or importance, relate results to objectives, compare with data from other trials |

Problems in Literature | Flawed design, invalid statistical analysis, fraud, unintentional errors, poor research, poor manuscript, data dredging |

Systematic Approach (1) | Descriptive, accurate, writer qualified, used statistician, funding, journal, peer review, essence in perspective, how done, hypothesis, clear, bias free, rationale, significance, inclusion & exclusion criteria, objectives stated, measured, reasonable. |

Systematic Approach (2) | Subjects - representative, stratified, randomized, dosing, adherence, other tx, diet, lifestyle, measurements, specimen, # of measure, reproduce, AEs, safety, clear, complete, analyzed, illustrated, limitations, other work, conclusions, future direction, |