Statistics, Evidence-Based Medicine, and Clinical Trial Design
Purpose statements of RCTs
"PICO" P = population I = intervention C = comparator or strategy of comparison O = outcome or measure of success
Relative Risk Reduction
% of baseline risk removed by the intervention *RRR = 1-RR* Example RRR = 0.15 (15%) Ivabradine removes 15% of the baseline risk of the composite endpoint Patients treated with ivabradine were 15% less likely to experience a composite endpoint
Types of Clinical Studies
*Descriptive* -document and communicate experience -begin to search for explanations -*Examples: case reports, case series, population studies* *Observational* -generates hypotheses about causes, etiologies, predictors -the investigator observes nature -*Examples: case control, cohort (follow-up), cross sectional* *Experimental* -evaluate efficacy of interventions -investigator controls allocation -*Examples: clinical trial*
Overview of Study Designs
*Descriptive: document and communicate experience* -no comparator group -Examples: *case reports, case series, population studies* *Explanatory: examine etiology, efficacy, cause using a comparison strategy* -*Experimental* -evaluate efficacy of interventions -investigator controls allocation -examples: *randomized controlled trial, noninferiority trial, educational intervention* -*Observational* -generates hypotheses about causes, etiologies, predictors -the investigator observes nature -examples: *case-control, cohort (follow up), cross-sectional (prevalence)* Pharmacoeconomic Studies -cost minimization -cost benefit -cost effectiveness -cost utility "Newer Designs" -adaptive trials -comparative effectiveness trials -pragmatic trials
Number needed to treat
*Inverse of ARR (convert % to decimals)* Number needed to harm (NNH) for adverse events *NNT = 1/ARR* ALWAYS ROUND UP ARR and NNT based on absolute rate of events Interpretation NNT = 23.6 = 24 -in order to prevent 1 composite endpoint, 24 patients would need to be treated with ivabradine for a median duration of 22.9 months Applied to clinical outcomes with dichotomous data (e.g. yes/no, alive/dead, MI/no MI) Should only be used for statistically significant effects
Assessing power in RCTs
*Power = 1 - beta* *The ability to detect a difference if a difference exists* Determined by alpha and beta, estimated effect size, variability in data
Types of Resources
*Primary: original data* -provides new info or enhances existing knowledge of a subject Examples: clinical trials, case reports, case series *Secondary: indexing or abstracting services* -allow for efficient access to primary literature -secondary references do not interpret primary literature Examples: PubMed, PsycINFO, International Pharmaceutical Abstracts, Cumulative Index to nursing and allied health literature, Cochrane Library *Tertiary: provide info collected and evaluated from multiple references, organized in a useful way* Examples: textbooks, full-text computer databases (MICROMEDEX), review articles
Types of Bias
*Selection* (how were patients selected? Is the study population adequately defined? We're inclusion and exclusion criteria reasonable? Are groups similar? *Misclassification* -refers to how classifications were made (inclusion/exclusion, outcomes assessment) -to avoid: use structured definitions, describe the criteria for each endpoint, use reliable sources for info to measure outcomes, use adjudication committee) *Confounding* -attributing an outcome to the wrong factor -confounding variable: a characteristic that is associated with the outcome of interest and the actual cause of the outcome and is distributed unequally between groups *Allocation* (was bias introduced when patients assigned to their groups? Was it truly random? Was randomization sequence easy to guess?) *Attrition* (are all patients in the study accounted for? What were the reasons for dropping out?) *Compliance* (was compliance assessed? Are results presented? Can results be explained by differences in compliance?) *Observer, measurement* (were measurements standardized? We're all measurements done by the same lab/person? We're measurements performed at appropriate intervals? We're measurements appropriate to show the effect of the drug? We're measurements sensitive enough to show changes caused by the drugs? We're there enough measurements? We're the measurements objective?) Recall
Sensitivity/specificity/predictive values
*Sensitivity:* Proportion of true positives that are correctly identified by a test A test with high sensitivity means that a negative test can rule OUT that disorder *= TP/ (TP + FN)* *Specificity:* Proportion of true negatives that are correctly identified by a test A test with high specificity means that a positive test can rule IN that disorder *= TN/ (TN + FP)* *Positive Predictive Value:* Proportion of patients with a positive test result who actually HAVE the disease =* TP/ (TP + FP)* *Negative Predictive Value:* Proportion of patients with a negative test result who actually DO NOT HAVE the disease *= TN/ (TN + FN)* Positive likelihood ratio = sensitivity/ (1-specificity) Negative likelihood ratio = (1-sensitivity)/ specificity
Measures of central tendency
*used for continuous data that is normally distributed* Mean -average (sum of all values divided by the total number of values) -should generally be used for continuous and normally distributed data -very sensitive to outliers and tend toward the tail, which has the outliers Median -midpoint of the values when placed in an order from highest to lowest. Half of the observations are above and half are below. When there is an even number of observations, it is the mean of the 2 middle values -also called 50th percentile -can be used for ordinal or continuous data (especially good for skewed populations) -insensitive to outliers Mode -most common value in a distribution -can be used for nominal, ordinal, or continuous data -sometimes, there may be more than one mode (e.g., bimodal, trimodal) -does not help describe meaningful distributions with a large range of values, each of which occurs frequently
Power
1-beta The probability of making a correct decision when the null hypothesis is false; the ability to detect differences between groups if one actually exists Dependent on the following factors -predetermined alpha -sample size -the size of the difference between outcomes you want to detect. Often not known before conducting the experiment, so to estimate the power of your test, you will have to specify how large a change is worth detecting -the variability of the outcomes that are being measured -items above are generally determined from previous data or the literature Power is decreased by the following (in addition to the earlier criteria): -poor study design -incorrect statistical tests (use of nonparametric test when parametric tests are appropriate) Statistical power analysis and sample size collection -sample size estimates should be performed in all studies a priori -necessary components for estimating appropriate sample size: -acceptable type 2 error rate (usually 0.1-0.2) -observed difference in predicted study outcomes that is clinically significant -the expected variability in item above -acceptable type 1 error rate (usually 0.05) -statistical test that will be used for primary end point
Strengths of study design
1. Meta analysis and systematic reviews 2. Randomized controlled trial 3. Case control 4. cross-sectional study 5. Case report or case series; studies with historical controls 6. Opinion, ideas, reviews
Statistical tests used for nominal data
2 groups with different people: Chi square 3 or more groups with different people: Chi square Before and after in same Paterson: McNemar's
Statistical tests used for ordinal data
2 groups with different people: Mann-Whitney rank sum 3 or more groups with different people: Kruskal-Wallis Before and after in same person: Wilcoxon signed rank
Statistical tests used for continuous data
2 groups with different people: unpaired t-test 3 or more groups with different people: ANOVA Before and after in same person: paired t-test
Regression
A statistical technique related to correlation Many different types of regression analysis: Multiple linear regression: one continuous independent variable and 2 or more continuous dependent variables Simple logistic regression: one categorical response (dependent) variable and 2 or more continuous or categorical explanatory (independent) variables Nonlinear regression: variables are not linearly related (or cannot be transformed into a linear relationship). This is where pharmacokinetic equations come from Polynomial regression: any number of response and continuous variables with a curvilinear relationship
Delta in noninferiority trial
Aka "noninferiority margin" Largest clinically acceptable difference Threshold value Amount of efficacy between active control and placebo
Measurement bias
Aka observer - occurs in outcome assessment We're the measurements standardized? We're all measurements done by the same lab person? We're measurements performed at appropriate intervals? We're measurements appropriate to show the effect of the drug? We're measurements sensitive enough to show changes caused by the drugs? We're there enough measurements? We're the measurements objective?
Cross sectional study
Aka prevalence study Identify the prevalence or characteristics of a condition in a group of individuals Advantages -easy design, "snapshot" in time, all data collected at one time, studies are accomplished by questionnaire, interview, or other available biomedical info (e.g. lab values) Disadvantages -does not allow the study of a factor (or factors) in individual subjects over time, just at the time of assessment; difficult-to-study, rare conditions
Type of error in RCTs
Alpha = type 1 error -occurs when we conclude there is a difference, that the observed difference is due to chance Beta = type 2 error -occurs when we conclude that there is no difference, but there is, in fact, a difference Type 1 or Alpha error -conclude a difference exists, but truth is there is no difference Type 2 or Beta error -conclude there is no difference, but truth is there is a difference
Attrition bias
Are all patients in the study accounted for? What were the reasons for dropping out? At end, did both groups still look the same?
Confounding bias
Attributing an outcome to the wrong factor Confounding variable: a characteristic that is associated with the outcome of interest and the actual cause of the outcome is distributed unequally between groups
Relative Risk
Based on incidence (denominator known) Type of study -experimental -follow up (A/a+b)/(c/c+d) Example: RR = 0.85 Patients treated with ivabradine 2.5 to 10 mg BID were 0.85 times as likely as placebo-treated patients to experience the composite endpoint
Odds Ratio
Based on prevalence (denominator unknown) Type of study -case control -cross sectional Formula -ad/bc
Intention-to-treat analysis
Compares outcomes on the basis of initial group assignment or "as randomized" The allocation to groups was how they were "intended to be treated" even though they may not have taken the medication for the duration of the study, dropped out, and did not comply with the protocol Determines the effect of treatment under usual conditions of use This is the preferred type of analysis in a superiority trial
What statistical value provides the most clinically relevant information
Confidence interval
Correlation vs regression
Correlation: examines the strength of the association between 2 variables. It does not necessarily assume that one variable is useful in predicting the other Regression: examines the ability of 1 or more variables to predict another variable
Types of pharmacoeconomic studies
Cost of illness evaluation (COI) Cost minimization analysis (CMA) Cost benefit analysis (CBA) Cost effectiveness analysis (CEA) Cost utility analysis (CUA)
Cost effectiveness analysis
Description: compares costs of 2 or more alternatives vs outcomes measured in physical units Application: compare treatment alternatives for a given condition that differ in outcomes and use the same unit of benefit Useful to measure the cost impact when health outcomes are improved Cost unit: money Outcome unit: natural (clinical units or cost per unit health outcome - outcome examples: years of life saved, number of symptom free days, blood glucose, blood pressure, etc) Incremental cost to achieve a one unit increase in outcome (ICER) = change of cost/change of effect = (cost of treatment 1 - cost of treatment 2) / (effect of treatment 1 - effect of treatment 2) Cost effectiveness plane
Cost minimization analysis
Description: identifies intervention cost differences between similar alternatives Differences in cost among comparable therapies are evaluated Only useful to compare therapies that have similar outcomes Application: identify least costly alternative when consequences are identical Cost unit: money Outcome unit: assume equivalent
Cost benefit analysis
Description: identifies net cost impact of an intervention Allows the analysis of both the cost of treatment and the costs saved with beneficial outcomes Application: compare programs or agents with different objectives Cost unit: money Outcome unit: monetary Monetary value is placed on both therapy costs and beneficial health outcomes
Cost utility analysis
Description: subset of cost effectiveness analysis - outcomes are measured in utility units -utilities represent patient preferences and quality of life/functional status associated with disease and/or treatment Assigns utility weights to outcomes so the impact can be measured in relation to cost Compares outcomes related to mortality when mortality may not be the most important outcome Application: useful when treatment extends life and/or effects quality of life Cost unit: money Outcome unit: QALY: quality adjusted life year - factor of life expectancy and utility ICER = (cost of treatment 1 - cost of treatment 2) / (QALY of treatment 1 - QALY of treatment 2)
2 types of statistical analyses
Descriptive -measure of central tendency -measure of variability Inferential -confidence intervals
Costs used in pharmacoeconomic studies
Direct costs (medical/non medical) -medications, lab test, transportation, childcare Indirect costs -lost wages Intangible -pain/suffering
Interpretation of RR and OR
Direction of Risk: *RR < 1, OR < 1* -negative association -RR: risk of disease is lower in the exposed group -OR: odds of exposure is lower in the diseased group *RR = 1, OR = 1* -no association -RR: risk of disease in the 2 groups is the same -OR: odds of exposure in the 2 groups is the same *RR >1 , OR > 1* -positive association -RR: risk of disease is greater in the exposed group -OR: odds of exposure is greater in the diseased group Magnitude of Risk: RR 0.75, OR 0.75 -25% reduction in the risk/odds RR 1, OR 1 -no difference in risk/odds RR 1.5, OR 1.5 -50% increase in the risk/odds RR 3, OR 3 -3-fold (or 200%) increase in the risk/odds
Case Reports/Case Series
Document and describe experiences, novel treatments, and unusual events Allows hypothesis generation that can be tested with other study designs Case report: 1 patient Case series: more than 1 patient with a similar experience or many case reports combined into a descriptive review Advantages: hypotheses are formed, which may be the first step in describing an important clinical problem. Easy to perform and inexpensive Disadvantages: does not provide explanation other than conjecture and does not establish causality or association
How to help control for confounding variables
During the design of the study -randomization -restriction -matching Analysis -stratification -multivariate analysis
Randomized controlled trial description
Each subject has an equal and independent chance of being in any of the treatment arms Types -simple randomization (aka like a coin toss) -block randomization (patients are not randomized 1 by 1, randomized by block) Stratification -occurs prior to randomization
Consequences (outcomes) in pharmacoeconomic studies
Economic - associated with various medical alternatives Clinical - medical events (safety/efficacy endpoints) Humanistic - consequences of disease or treatment on patient function Outcome measure determines type of pharmacoeconomic design that is chosen
Sensitivity analysis of meta analyses
Evaluate the impact of different decisions made in the conduct of study Examples -different study designs -quality of studies
2 models used in analyzing meta analyses
Fixed -assumes 1 true value -considers sample variation with studies -appropriate if the effect sizes are the same Random -assumes a range of effects -considers variation within study and between studies -usually the most appropriate approach
Features of meta-analysis
Focused clinical question -specifies: population, intervention or exposure, outcomes, methodology Comprehensive search for primary literature -must look in all reasonable databases and resources -must have detailed description of search strategies in manuscript Clear inclusion/exclusion criteria for articles -determined before the search begins, multiple reviewers Quality assessment for articles -looking for bias in individual studies Quantitative synthesis of results -hallmark of meta-analysis -study results in pooled into new data set -testing for heterogeneity -performing regression analyses or subgroup analyses
Normal distribution
Gaussian Distribution Symmetric or bell-shaped frequency distributions Landmarks for continuous, normally distributed data -u: population mean is equal to 0 -alpha: population SD is equal to 1 -x and s: these represent the sample mean and SD Median and mean will be about equal for normally distributed data
Multiple comparison procedures
Increase rate of type 1 error Preserve overall significance level Can correct in several ways -Bonferroni - very strict -Tukey's -Scheffe method -Dunnett's test -Hochberg
Analysis of RCTs
Intention-to-Treat -all pts randomized analyzed according to intended therapy Modified Intention to Treat Per Protocol -only those patients who followed protocol As-Treated -all patients randomized according to therapy they actually received
Validity in study design
Internal validity -validity within the confines of the study methods External validity -validity related to generalizing the study results outside the study setting
Bias in meta analyses
Language: studies that are positive are more likely to be published in English Publication: studies that are positive (found differences) are more likely to be published than negative studies Selective Reporting: are all outcomes reported? Sometimes only outcomes that have a difference are reported Others discussed previously
Examples of ordinal data
Likely scales Hierarchy - NYHA functional class Examples from other studies -years of hormone replacement therapy (none, 0-5 years, 5-10 years, greater than 10 years) -age of diagnosis (less than 50, 50-55, 56-65, older than 65)
Prevalence
Measure of the number of individuals who have a condition/disease at any given time Point prevalence: prevalence on a given date Period prevalence: prevalence in a period
Incidence
Measure of the probability of developing the disease Incidence rate: # of new case of disease per population in a specified time Calculated by dividing the number of individuals who develop disease during a given period by the number of individuals who were at risk of developing a disease during the same period
Heterogeneity of meta-analyses
Methodological -patients, interventions, outcomes, study design -are the studies similar in the 1st place Statistical -measures variability in the actual results -does not indicate source of heterogeneity -only look to see if the results between the studies are similar
Examples of continuous data
Most laboratory values Age Weight Time to event Degrees kelvin, heart rate, BP, time, distance
Types of data
Nominal -named categories that have no implied rank or order -there is no arithmetic relationship between classifications -classified into groups in an unordered manner and with no indication of relative severity Ordinal -limited number of categories with implied rank or order -the order is understood, but the distance or interval between the categories is not equal -ranked in a specific order but with no consistent level of magnitude of difference between ranks Continuous -constant and defined units of measure -there is an equal distance between values -can take on any value within a given range -interval: data are ranked in a specific order with a consistent change in magnitude between units; the 0 point is arbitrary -ratio: like "interval" but with an absolute 0
Spearman Rank Correlation
Nonparametric test that quantifies the strength of an association between 2 variables but does not assume a normal distribution of continuous data. Can be used for ordinal data or non normally distributed continuous data
Noninferiority trial vs superiority trial
Null Hypothesis -S: no difference between treatments -N: new treatment is NOT non-inferior to active control by specified margin delta Alternative Hypothesis -S: there is a difference -N: new treatment is non inferior to active control Power: -S: probability of finding a difference if there is a difference -N: probability of concluding that new treatment is non-inferior to the active control if it truly is non-inferior Type 1 error (alpha error) -S: conclude there is a difference when there is no difference -N: conclude noninferioroty when the new treatment is not non-inferior to active control Type II error (beta error) -S: conclude there is no difference when there is a difference -N: conclude the new treatment is not noninferior, when in fact it is noninferior A superiority trial = designed to detect a difference between experiemental treatments Noninferiority = designed to investigate whether a treatment is not clinically worse (not less effective than stated margin, than an existing treatment
Selection bias
Occurs during recruitment How were patients selected? Is the study population adequately defined? We're inclusion and exclusion criteria reasonable? Are groups similar?
Compliance bias
Occurs during treatment Was compliance assessed? Are results presented? Can resulted by explained by differences in compliance? Very difficult to assess
Allocation bias
Occurs in inequal distribution of patient characteristics between groups Was bias introduced when patients assigned to their groups? Was it truly random? Was randomization sequence easy to guess?
Blinding of RCTs
Open label (no blinding) Single blind (usually a subject who is blinded) Double blind (usually subject and investigator blinded) Double blind, double dummy -double dummy: used when treatments compared come in different dosage forms (get an active of 1 and sham of other - patient gets both)
Parametric Tests
Parametric tests assume the following: -data being investigated have an underlying distribution that is normal or close to normal or, more correctly, randomly drawn from a parent population with a normal distribution -data measured are continuous data, measured on either an interval or a ratio scale -parametric tests assume that the data being investigated have variances that are homogenous between the groups investigated. This is often called homoscedasticity Student T-test: several different types -one-sample test: compares the mean of the study sample with the population mean -two-sample, independent samples, or unpaired test: compares the mean of two independent smapeles -paired test: compares the mean difference of paired or matched samples. -common error: use of multiple t-test with more than 2 groups Analysis of variance (ANOVA): a more generalized version of the t-test that can apply to more than two groups Analysis of covariance (ANCOVA)
Cost of illness evaluation
Pharmacoeconomic study Description: estimates the cost of disease for a defined population Use: provides baseline to evaluate impact of treatment/prevention alternatives Cost unit = money Outcome unit: Na
P-value
Probability of detecting a difference at least as large as that in the study due to chance alone Compare with level of significant (alpha value) Interpretation -a small p-value does not tell use the size of the difference between treatments -a p-value of >0.05 means that there is lack of evidence to reject the null hypothesis -the size of the p-value has nothing to do with clinical significance -statistics do not determine what is important, statistics determine how certain we are
Calculation of RR and OR
RR = a/(a+b)/ c/(c+d) OR = (a/c) / (b/d) = (Ax D)/(Bx C)
Relative risk vs hazard ratio
RR can easily be calculated from numbers presented in the study Hazard ratio is the same concept but is the weighted relative risk over time -adjusts for change over time -adjusted for "repeated measures" -adjusts for different "slopes" of the line
Measures of variability
Range - difference between the largest and smallest variable -size of range is very sensitive to outliers Interquartile range = difference between the 75th and 25th percentile -generally for ordinal or continuous data that is not normally distributed Standard deviation -measure of variability about the mean; most common measure used to describe the spread of data -square root of the variance (average squared difference of each observation from the mean); returns variance back to original units (non-squared) -appropriately applied only to continuous data that are normally or near normally distributed or that can be transformed to be normally distributed -appropriately applied only to continuous data that are normally or near normally distributed or that can be transformed to be normally distributed -by the empirical rule for normal distributions, 68% of the sample values are found within +/-1 SD, 95% are found within +/-2 SD, and 99% are found within +/-3 SD -the coefficient of variation relates the mean and the SD (SD/mean x 100%)
Confidence Interval
Range of values for the true treatment difference that are statistically significant likely, given the results of a specific trial Calculation based on Standard Error of Mean (SEM) Interpretation *Ratios (RR, HR, OR)* -*if the CI does not include 1, the results are statistically significant* -if the CI includes 1, the results are not statistically significant *Everything else (continuous value)* -*if the CI does not include 0 treatment difference, the results are statistically significant* -if the CI includes a 0 treatment difference, the results are not statistically significant -if the study was repeated 100 times, and a CI is calculated each time, then 95 of the intervals will contain a true value for the larger population of interest, and 5 will not
Misclassification bias
Refers to how classifications were made -inclusion/exclusion -outcomes assessment Example: a blinded endpoint validation committee adjudicated all events Avoiding misclassification -use structured definitions -describe the criteria for each endpoint -use reliable sources for information to measure outcomes -use adjudication committee
Examples of nominal types of data
Response rate Adverse event (yes/no) Percentage Groups or categories -gender, race, presence or absence of disease, death, marital status
Types of bias in experimental trials
Selection Misclassification Confounding Allocation Attrition Compliance Observer, measurement Recall
Hypothesis testing for RCTs
Start with null hypothesis Superiority trial: there is no difference Equivalence: the groups are not equivalent (not very common) Non-inferiority: the therapy is not non-inferior to the standard therapy
Checking for heterogeneity in meta-analyses
Statistical tests -Cochran q test -inconsistency index (I2) Eyeball test -uses a graph (see PowerPoint for example)
As-treated analysis
Subjects are analyzed by the actual intervention received. If subjects were in the active treatment group but did not take active treatment, the data would be analyzed as if they were in the placebo group This analysis essentially ignores/destroys the randomization process for those who did not adhere to study design. Results should be interpreted with caution
Per-protocol analysis
Subjects who do not adhere to allocated treatment are not included in the final analysis; only those who completed the trial and adhered to the protocol (based on some predetermined definition, e.g. 80% adherence) Subject to several issues because of factors such as lower sample size and definitions of adherence Preferred type of analysis in noninferiority trials, although intention-to-treat analysis is often used also
Systematic review vs meta-analysis
Systematic Review -summary that uses explicit methods to perform a comprehensive literature search, critically appraise it, and synthesize the world literature on a specific topic Meta-Analysis -systematic review that utilizes mathematic/statistical techniques to summarize the results of the evaluated studies -elements: research question, identification of available studies, criterial for inclusion/exclusion, data collection and presentation of findings, calculation of summary estimate: ideally with a forest plot, assessment of heterogeneity, assessment of publication bias (funnel plot), sensitivity analysis
Survival analysis
Takes into account the timing of events Results is Hazard Ratio (HR) -weighted relative risk over the entire study Data presented in Kaplan-Meier curves Cox proportional hazards regression the most common statistical analysis
Cochran Q
Testing for heterogeneity in meta-analyses Based on Chi square statistic Null hypothesis: all variability between studies is due to chance Look at p-value -p-value < 0.05: significant heterogeneity (results may still be useful) -p-value < 0.01: results are very unlikely to be useful *ideally want a p-value > 0.05* Limitations -underpowered for studies with few patients -overpowered for large sample sizes
I2 statistics
Testing for heterogeneity in meta-analyses Based on the Cochran Q, but adjusted for power Gives estimate of the % of heterogeneity due to factors other than chance < 25%: heterogeneity low 25-50%: heterogeneity medium >50%: high heterogeneity - unlikely to be useful 0%: no likelihood results are due to something other than chance *want low heterogeneity*
Absolute Risk Reduction
The difference in the risk of an event in intervention group vs control group *ARR = (c/c+d) - (a/a+b)*
Confounders in observational studies
The outcome is attributed to the exposure of interest, but is distorted by another factor Prognostically (though not necessarily causally) linked to the outcome of interest Must be unequally distributed between groups Must be a risk factor for the disease or a surrogate marker for the actual cause Must be associated with the exposure in the source population Must not be affected by the exposure of the disease Must not be on the causal pathway -smoking —> elevated BP —> heart disease
Type 2 error
The probability of making this error is called beta Concluding that no difference exists when one truly does (not rejecting null hypothesis when it should be rejected) It has become convention to set beta at 0.2-0.1
Type 1 error
The probability of making this error is defined as the significance level alpha Convention is to set the alpha to 0.05, effectively meaning that, 1 in 20 times, a type 1 error will occur when the null hypothesis is rejected -thus, 5% of the time, a researcher will conclude that there is a statistically significant difference when one dose not actually exist The calculated chance that a type 1 error has occurred is called the p-value The p-value tells us the likelihood of obtaining a given (or a more extreme) test result if the null hypothesis is true -when the alpha level is set a priori, the null hypothesis is rejected when p is less than alpha. In other words, the p-value tells us the probability of being wrong when we conclude that a true difference exists (false positive) A lower p-value does not mean the result is more important or more meaningful but only that it is statistically significant and not likely to be attributable to chance
Definition of pharmacoeconomics
The process of identifying, measuring, and comparing the costs, risks, and benefits of programs, services, or therapies
Pearson correlation
The strength of the relationship between 2 variables that are normally distributed, ratio or interval scaled, and linearly related is measured with a correlation coefficient Often called the degree of association between the 2 variables Does not necessarily imply that 1 variable is dependent on the other (regression analysis will do that) Pearson correlation (r) ranges from -1 to +1 and can take any value in between -1: perfect negative linear relationship 0: no linear relationship +1: perfect positive linear relationship Hypothesis testing is performed to determine whether the correlation coefficient is different from 0. This test is highly influenced by sample size Pearls: -the closer the magnitude of r to 1 (either + or -), the more highly correlated the 2 variables. The weaker the relationship between the 2 variables, the closer r is to 0 -there is no agreed-on or consistent interpretation of the value of the correlation coefficient. It is dependent on the environment of the investigation (laboratory vs clinical experiment)
Case control study
Type of observational study Subjects are identified on the basis of their disease state (outcome) Determine the association between exposures/risk factors and disease/condition Direction of inquiry is backward in time Retrospective studies Useful method to study exposures in rare diseases or diseases that take long periods to develop Approach -identify cases who have the disease of interest (outcome) -identify controls who do not have the disease of interest -look back in time to assess exposures (risk factors) -compare proportions with and without exposures (risk factors) between cases and controls Advantages -inexpensive and can be conducted quickly -allows investigational of several possible exposures or associations Disadvantages -confounding must be controlled for -observational and recall bias: looking back to recall exposures and their possible levels of exposure -selection bias: case selection and control matching are difficult *Measure of association OR*
Cohort study
Type of observational study Subjects are identified on the basis of their exposure status (risk factors) Determines the association between exposures/factors and disease/condition development. Allows an estimation of the risk of outcome (and teh RR between the exposure groups). Study of outcome of interest in those with and without the exposure of interest Describes the incidence or natural history of a disease/condition and measures it in time sequence "Retrospective" (historical): begins and ends in the present but involves a major backward look to collect info about events that occurred in the past Direction of inquiry is forward in time Prospective or longitudinal: being in the present and progress foward, collecting data from subjects whose outcomes lie in the future Approach -identify a study population -exclude individuals with the outcome of interest -classify based on exposure (risk factor) -follow patients forward in time -compare proportions with outcomes between exposed and unexposed (or between different exposures) Advantages -less expensive and time-consuming; no loss to follow-up, ability to investigate issues not amenable to a clinical trial or ethical or safety issues Disadvantages -only as good as the data available, little control of confounding variables through non statistical approaches, recall bias
Reasons to conduct a noninferiority trial
Unethical to conduct a placebo-controlled trial Treatment expected to be similar in efficacy to standard treatment -therapeutic noninferiority to active control Establish similarity with comparator if new treatment has other advantages (safety, cost, convenience)
Estimates of effect
Used for dichotomous data Relative risk (RR), odds ratio (OR), hazard ratio (HR) Relative risk reduction Absolute risk reduction Number needed to treat (NNT0
Nonparametric tests
Used when data are not normally distributed or do not meet other criteria for parametric tests (e.g. discrete data) These tests may also be used for continuous data that do not meet the assumptions of the t-test or ANOVA Tests for independent samples -Wilcoxon rank sum test, Mann-Whitney U test, or Wilcoxon Mann-Whitney test: compare two independent samples (related to a t-test) -Kruskal-Wallis one-way ANOVA by ranks -compares 3 or more independent groups -post hoc testing Tests for related or paired samples -sign test and Wilcoxon signed-rank test: compares 2 matched or paired samples (related to a paired t-test) -Friedman ANOVA by ranks: compares 3 or more matched or paired groups
Hazard ratio
Weighted RR during the entire study period Type of study -survival analysis Calculus based (likely do not have to know how to calculate -very complicated)
