Presentation on theme: "KUMC Departments of Biostatistics & Internal Medicine"— Presentation transcript:
1Introduction to Biostatistics for Clinical and Translational Researchers KUMC Departments of Biostatistics & Internal MedicineUniversity of Kansas Cancer CenterFRONTIERS: The Heartland Institute of Clinical and Translational Research
2Course Information Jo A. Wick, PhD Office Location: RobinsonLectures are recorded and posted at under ‘Events & Lectures’
3ObjectivesUnderstand the role of statistics in the scientific process and how it is a core component of evidence-based medicineUnderstand features, strengths and limitations of descriptive, observational and experimental studiesDistinguish between association and causationUnderstand roles of chance, bias and confounding in the evaluation of research
4Course Calendar July 5: Introduction to Statistics: Core Concepts July 12: Quality of Evidence: Considerations for Design of Experiments and Evaluation of LiteratureJuly 19: Hypothesis Testing & Application of Concepts to Common Clinical Research QuestionsJuly 26: (Cont.) Hypothesis Testing & Application of Concepts to Common Clinical Research Questions
6Why is there conflicting evidence? Answer: There is no perfect research study.Every study has limitations.Every study has context.Medicine (and research!) is an art as well as a science.Unfortunately, the literature is full of poorly designed, poorly executed and improperly interpreted studies—it is up to you, the consumer, to critically evaluate its merit.
7Critical Evaluation Validity and Relevance Is the article from a peer-reviewed journal?How does the location of the study reflect the larger context of the population?Does the sample reflect the targeted population?Is the study sponsored by an organization that may influence the study design or results?Is the intervention feasible? available?
8Critical Evaluation Intent Therapy: testing the efficacy of drug treatments, surgical procedures, alternative methods of delivery, etc. (RCT)Diagnosis: demonstrating whether a new diagnostic test is valid (Cross-sectional survey)Screening: demonstrating the value of tests which can be applied to large populations and which pick up disease at a presymptomatic stage (Cross-sectional survey)Prognosis: determining what is likely to happen to someone whose disease is picked up at an early stage (Longitudinal cohort)Therapy--
9Critical EvaluationCausation: determining whether a harmful agent is related to development of illness (Cohort or case-control)
10Critical Evaluation Validity based on intent What is the study design? Is it appropriate and optimal for the intent?Are all participants who entered the trial accounted for in the conclusion?What protections against bias were put into place? Blinding? Controls? Randomization?If there were treatment groups, were the groups similar at the start of the trial?Were the groups treated equally (aside from the actual intervention)?
11Critical EvaluationIf statistically significant, are the results clinically meaningful?If negative, was the study powered prior to execution?Were there other factors not accounted for that could have affected the outcome?Miser, WF Primary Care 2006.
12Experimental DesignStatistical analysis, no matter how intricate, cannot rescue a poorly designed study.No matter how efficient, statistical analysis cannot be done overnight.A researcher should plan and state what they are going to do, do it, and then report those results.Be transparent!
13Types of SamplesRandom sample: each person has equal chance of being selected.Convenience sample: persons are selectedbecause they are convenient or readily available.Systematic sample: persons selected based on a pattern.Stratified sample: persons selected from within subgroup.
14Random SamplingFor studies, it is optimal (but not always possible) for the sample providing the data to be representative of the population under study.Simple random sampling provides a representative sample (theoretically) and protections against selection bias.A sampling scheme in which every possible sub-sample of size n from a population is equally likely to be selectedAssuming the sample is representative, the summary statistics (e.g., mean) should be ‘good’ estimates of the true quantities in the population.The larger n is, the better estimates will be.
15Random SamplesThe Fundamental Rule of Using Data for Inference requires the use of random sampling or random assignment.Random sampling or random assignment ensures control over “nuisance” variables.We can randomly select individuals to ensure that the population is well-represented.Equal sampling of males and femalesEqual sampling from a range of agesEqual sampling from a range of BMI, weight, etc.
16Random SamplesRandomly assigning subjects to treatment levels to ensure that the levels differ only by the treatment administered.weightsagesrisk factors
17Nuisance VariationNuisance variation is any undesired sources of variation that affect the outcome.Can systematically distort results in a particular direction—referred to as bias.Can increase the variability of the outcome being measured—results in a less powerful test because of too much ‘noise’ in the data.
18Example: Albino RatsIt is hypothesized that exposing albino rats to microwave radiation will decrease their food consumption.Intervention: exposure to radiationLevels exposure or non-exposureLevels 0, 20000, 40000, uWMeasurable outcome: amount of food consumedPossible nuisance variables: sex, weight, temperature, previous feeding experiencesWeight is positively correlated with food consumption, so it could systematically distort the results.uW = microwatts
19Experimental Design Types of data collected in a clinical trial: Treatment – the patient’s assigned treatment and actual treatment receivedResponse – measures of the patient’s response to treatment including side-effectsPrognostic factors (covariates) – details of the patient’s initial condition and previous history upon entry into the trial
20Experimental Design Three basic types of outcome data: Qualitative – nominal or ordinal, success/failure, CR, PR, Stable disease, Progression of diseaseQuantitative – interval or ratio, raw score, difference, ratio, %Time to event – survival or disease-free time, etc.
21Experimental DesignFormulate statistical hypotheses that are germane to the scientific hypothesis.Determine:experimental conditions to be used (independent variable(s))measurements to be recordedextraneous conditions to be controlled (nuisance variables)
22Experimental DesignSpecify the number of subjects required and the population from which they will be sampled.Power, Type I & II errorsSpecify the procedure for assigning subjects to the experimental conditions.Determine the statistical analysis that will be performed.
23Experimental Design Considerations: Does the design permit the calculation of a valid estimate of treatment effect?Does the data-collection procedure produce reliable results?Does the design possess sufficient power to permit and adequate test of the hypotheses?
24Experimental Design Considerations: Does the design provide maximum efficiency within the constraints imposed by the experimental situation?Does the experimental procedure conform to accepted practices and procedures used in the research area?Facilitates comparison of findings with the results of other investigationsEfficiency: When comparing competing designs, the design that can achieve the same precision with fewer resources is more efficient. This comes into play when we are powering the study—for a given precision, the more efficient design will require fewer subjects to be enrolled to achieve minimally acceptable power.
25Types of Studies Purpose of research To exploreTo describe or classifyTo establish relationshipsTo establish causalityStrategies for accomplishing these purposes:Naturalistic observationCase studySurveyQuasi-experimentExperimentAmbiguityControl
26Complexity and Confidence 1/9/2013Generating EvidenceStudiesDescriptive StudiesPopulationsIndividualsCase ReportsCase SeriesCross SectionalAnalytic StudiesObservationalCase ControlCohortExperimentalRCTIn fact, the quality of your evidence is not only dependent upon the size of your study but also on the study design you choose and implement. For instance, the literature may consist only of a few case reports and case series. These are very simple, observational, descriptive studies on individual patients and provided very little more than anecdotal data. They were, in essence, step 0. Any of the study designs to the right of these would provide stronger evidence, with the randomized controlled trial providing the strongest scientific evidence from the design perspective.Why do they increase in confidence? One reason is the size—case reports and case series are small, and in general RCTs are larger. Another reason is directly listed—they are more complex. And the reason they are more complex is because we are being deliberate about eliminating sources of bias and noise in order to get the most reliable estimates possible. In the next several slides we will discuss a few of the more common types of study designs.Complexity and Confidence
27Observation versus Experiment A designed experiment involves the investigator assigning (preferably randomly) some or all conditions to subjects.An observational study includes conditions that are observed, not assigned.
28Example: Heart StudyQuestion: How does serum total cholesterol vary by age, gender, education, and use of blood pressure medication? Does smoking affect any of the associations?Recruit n = 3000 subjects over two yearsTake blood samples and have subjects answer a CVD risk factor surveyOutcome: Serum total cholesterolFactors: BP meds (observed, not assigned)Confounders?
29Example: DiabetesQuestion: Will a new treatment help overweight people with diabetes lose weight?N = 40 obese adults with Type II (non-insulin dependent) diabetes (20 female/20 male)Randomized, double-blind, placebo-controlled study of treatment versus placeboOutcome: Weight lossFactor: Treatment versus placebo
30Cross-Sectional Studies Designed to assess the association between an independent variable (exposure?) and a dependent variable (disease?)Selection of study subjects is based on both their exposure and outcome status, thus there is no direction of inquiry
31Cross-Sectional Studies Defined PopulationGather data on Exposure & DiseaseExposedDiseasedNo DiseaseNot ExposedIn a design like this, we can answer questions like—is disease independent of exposure, or does exposure increase/decrease the prevalence of disease? Often, a chi-square test or a fisher’s exact test would be used to answer these questions, since what you have is a correlation of two yes/no outcomes.
32Cross-Sectional Studies Cannot determine causal relationships between exposure and outcomeCannot determine temporal relationship between exposure and outcome“Exposure is associated with Disease”Some of the limitations include the inability to conclude causality and the lack of directional relationship.“Exposure causes Disease”“Disease follows Exposure”
33Analysis of Cross-Sectional Data Disease+-ExposureabcdPrevalence of disease compared in exposed versus non-exposed groups:Prevalence of exposure compared in diseased versus non-diseased groups:
34Case-Control StudiesDesigned to assess the association between disease and past exposuresSelection of study subjects is based on their disease statusDirection of inquiry is backward
35Case-Control Studies Exposed Unexposed Diseased Defined Population Gather data on DiseaseDiseasedUnexposedExposedNo DiseaseDirection of InquiryCases and controls need to be from same source populationTime
36Analysis of Case-Control Data Disease+-TotalExposureaba+bcdc+da+cb+dOdds ratio: odds of case exposure .odds of control exposure
37Cohort StudiesDesigned to assess the association between exposures and disease occurrenceSelection of study subjects is based on their exposure statusDirection of inquiry is forward
38Gather data on Exposure Cohort StudiesDefined PopulationGather data on ExposureExposedDiseaseNo DiseaseNot ExposedDirection of InquiryConcurrent or nonconcurrent cohorts; concurrent is referred to as prospective or longitudinal; nonconcurrent is retrospective or historical;Time
39Cohort Studies Attrition or loss to follow-up Time and money! Inefficient for very rare outcomesBiasOutcome ascertainmentInformation biasNon-response bias
40Analysis of Cohort Data Disease+-TotalExposureaba+bcdc+da+cb+dRelative Risk: risk of disease in exposed .risk of disease in unexposed
41Randomized Controlled Trials Designed to test the association between exposures and diseaseSelection of study subjects is based on their assigned exposure statusDirection of inquiry is forward
42Randomized Controlled Trials Defined PopulationRandomize to ExposureExposed (Treated)DiseaseNo DiseaseNot Exposed (Control)Direction of InquiryConcurrent or nonconcurrent cohorts; concurrent is referred to as prospective or longitudinal; nonconcurrent is retrospective or historical;Time
43Why do we randomize?Suppose we wish to compare surgery for CAD to a drug used to treat CAD. We know that such major heart surgery is invasive and complex—some people die during surgery. We may assign the patients with less severe CAD (on purpose or not) to the surgery group.If we see a difference in patient survival, is it due to surgery versus drugs or to less severe disease versus more severe disease?Such a study would be inconclusive and a waste of time, money and patients.
44How could we fix it? Randomize! Randomization is critical because there is no way for a researcher to be aware of all possible confounders.Observational studies have little to no formal control for any confounders—thus we cannot conclude cause and effect based on their results.Randomization forms the basis of inference.
45Other Protections Against Bias BlindingSingle (patient only), double (patient and evaluator), and triple (patient, evaluator, statistician) blinding is possibleEliminates biases that can arise from knowledge of treatmentControlNull (no treatment), placebo (no active treatment), active (current standard of care) controls are usedEliminates biases that can arise from the natural progression of disease (null control) or simply from the act of being treated (placebo)
46Analysis of RCT Data What kind of outcome do you have? Continuous? Categorical?How many samples (groups) do you have?Are they related or independent?
47Types of TestsParametric methods: make assumptions about the distribution of the data (e.g., normally distributed) and are suited for sample sizes large enough to assess whether the distributional assumption is metNonparametric methods: make no assumptions about the distribution of the data and are suitable for small sample sizes or large samples where parametric assumptions are violatedUse ranks of the data values rather than actual data values themselvesLoss of power when parametric test is appropriate
48Analysis of RCT DataTwo independent percentages? Fisher’s Exact test, chi-square test, logistic regressionTwo independent means? Mann-Whitney, Two-sample t-test, analysis of variance, linear regressionTwo independent time-to-event outcomes? Log-rank test, Wilcoxon test, Cox regressionAny adjustments for other prognostic factors can be accomplished with the appropriate regression models (e.g., logistic for yes/no outcomes, linear for continuous, Cox for time-to)
49Threats to Valid Inference Statistical Conclusion ValidityLow statistical power - failing to reject a false hypothesis because of inadequate sample size, irrelevant sources of variation that are not controlled, or the use of inefficient test statistics.Violated assumptions - test statistics have been derived conditioned on the truth of certain assumptions. If their tenability is questionable, incorrect inferences may result.Many methods are based on approximations to a normal distribution or another probability distribution that becomes more accurate as sample size increases—using these methods for small sample sizes may produce unreliable results.
50Threats to Valid Inference Statistical Conclusion ValidityReliability of measures and treatment implementation.Random variation in the experimental setting and/or subjects.Inflation of variability may result in not rejecting a false hypothesis (loss of power).
51Threats to Valid Inference Internal ValidityUncontrolled events - events other than the administration of treatment that occur between the time the treatment is assigned and the time the outcome is measured.The passing of time - processes not related to treatment that occur simply as a function of the passage of time that may affect the outcome.
52Threats to Valid Inference Internal ValidityInstrumentation - changes in the calibration of a measuring instrument, the use of more than one instrument, shifts in subjective criteria used by observers, etc.The “John Henry” effect - compensatory rivalry by subjects receiving less desirable treatments.The “placebo” effect - a subject behaves in a manner consistent with his or her expectations.
53Threats to Valid Inference External Validity—GeneralizabilityReactive arrangements - subjects who are aware that they are being observed may behave differently that subjects who are not aware.Interaction of testing and treatment - pretests may sensitize subjects to a topic and enhance the effectiveness of a treatment.
54Threats to Valid Inference External Validity—GeneralizabilitySelf-selection - the results may only generalize to volunteer populations.Interaction of setting and treatment - results obtained in a clinical setting may not generalize to the outside world.
55Clinical Trials—Purpose Prevention trials look for more effective/safer ways to prevent a disease in individuals who have never had it, or to prevent a disease from recurring in individuals who have.Screening trials attempt to identify the best methods for detecting diseases or health conditions.Diagnostic trials are conducted to distinguish better tests or procedures for diagnosing a particular disease or condition.
56Clinical Trials—Purpose Treatment trials assess experimental treatments, new combinations of drugs, or new approaches to surgery or radiation therapy for efficacy and safety.Quality of life (supportive care) trials explore means to improve comfort and quality of life for individuals with chronic illness.Classification according to the U.S. National Institutes of Health
57Clinical Trials—Phases Pre-clinical studies involve in vivo and in vitro testing of promising compounds to obtain preliminary efficacy, toxicity, and pharmacokinetic information to assist in making decisions about future studies in humans.
58Clinical Trials—Phases Phase 0 studies are exploratory, first-in-human trials, that are designed to establish very early on whether the drug behaves in human subjects as was anticipated from preclinical studies.Typically utilizes N = 10 to 15 subjects to assess pharmacokinetics and pharmacodynamics.Allows the go/no-go decision usually made from animal studies to be based on preliminary human data.
59Clinical Trials—Phases Phase I studies assess the safety, tolerability, pharmacokinetics, and pharmacodynamics of a drug in healthy volunteers (industry standard) or patients (academic/research standard).Involves dose-escalation studies which attempt to identify an appropriate therapeutic dose.Utilizes small samples, typically N = 20 to 80 subjects.
60Clinical Trials—Phases Phase II studies assess the efficacy of the drug and continue the safety assessments from phase I.Larger groups are usually used, N = 20 to 300.Their purpose is to confirm efficacy (i.e., estimation of effect), not necessarily to compare experimental drug to placebo or active comparator.
61Clinical Trials—Phases Phase III studies are the definitive assessment of a drug’s effectiveness and safety in comparison with the current gold standard treatment.Much larger sample sizes are utilized, N = 300 to 3,000, and multiple sites can be used to recruit patients.Because they are quite an investment, they are usually randomized, controlled studies.
62Clinical Trials—Phases Phase IV studies are also known as post-marketing surveillance trials and involve the ongoing or long-term assessment of safety in drugs that have been approved for human use.Detect any rare or long-term adverse effects in a much broader patient population
63The Size of a Clinical Trial Lasagna’s LawOnce a clinical trial has started, the number of suitable patients dwindles to a tenth of what was calculated before the trial began.
64The Size of a Clinical Trial “How many patients do we need?”Statistical methods can be used to determine the required number of patients to meet the trial’s principal scientific objectives.Other considerations that must be accounted for include availability of patients and resources and the ethical need to prevent any patient from receiving inferior treatment.We want the minimum number of patients required to achieve our principal scientific objective.
65The Size of a Clinical Trial Estimation trials involve the use of point and interval estimates to describe an outcome of interest.Hypothesis testing is typically used to detect a difference between competing treatments.
66The Size of a Clinical Trial Type I error rate (α): the risk of concluding a significant difference exists between treatments when the treatments are actually equally effective.Type II error rate (β): the risk of concluding no significant difference exists between treatments when the treatments are actually different.
67The Size of a Clinical Trial Power (1 – β): the probability of correctly detecting a difference between treatments—more commonly referred to as the power of the test.TruthConclusionH1H01 – βαβ1 – α
68The Size of a Clinical Trial Setting three determines the fourth:For the chosen level of significance (α), a clinically meaningful difference (δ) can be detected with a minimally acceptable power (1 – β) with n subjects.Depending on the nature of the outcome, the same applies: For the chosen level of significance (α), an outcome can be estimated within a specified margin of error (ME) with n subjects.
69Example: Detecting a Difference The Anturane Reinfarction Trial Research Group (1978) describe the design of a randomized double-blind trial comparing anturan and placebo in patients after a myocardial infarction.What is the main purpose of the trial?What is the principal measure of patient outcome?How will the data be analyzed to detect a treatment difference?What type of results does one anticipate with standard treatment?How small a treatment difference is it important to detect and with what degree of uncertainty?
70Example: Detecting a Difference Primary objective: To see if anturan is of value in preventing mortality after a myocardial infarction.Primary outcome: Treatment failure is indicated by death within one year of first treatment (0/1).Data analysis: Comparison of percentages of patients dying within first year on anturan (π1) versus placebo (π2) using a χ2 test at the α = 0.05 level of significance.
71Example: Detecting a Difference Expected results under placebo: One would expect about 10% of patients to die within a year (i.e., π2 = .1).Difference to detect (δ): It is clinically interesting to be able to determine if anturan can halve the mortality—i.e., 5% of patients die within a year—and we would like to be 90% sure that we detect this difference as statistically significant.
72Example: Detecting a Difference We have:H0: π1 = π2 versus H1: π1 π2 (two-sided test)α = 0.051 – β = 0.90δ = π2 – π1 = 0.05The estimate of power for this test is a function of sample size:n = 583 patients per group is required
73Example: Detecting a Difference 1 - ββα/21 - αα/2-zα/2zα/2Reject H0Conclude differenceFail to reject H0Conclude no differenceReject H0Conclude difference
74Power and Sample Sizen is roughly inversely proportional to δ2; for fixed α and β, halving the difference in rates requiring detection results in a fourfold increase in sample size.n depends on the choice of β such that an increase in power from 0.5 to 0.95 requires around 3 times the number of patients.Reducing α from 0.05 to 0.01 results in an increase in sample size of around 40% when β is around 10%.Using a one-sided test reduces the required sample size.
75Example: Detecting a Difference Primary objective: To see if treatment A increases outcome W.Primary outcome: The primary outcome, W, is continuous.Data analysis: Comparison of mean response of patients on treatment A (μ1) versus placebo (μ2) using a two-sided t-test at the α = 0.05 level of significance.
76Example: Detecting a Difference Expected results under placebo: One would expect a mean response of 10 (i.e., μ2 = 10).Difference to detect (δ): It is clinically interesting to be able to determine if treatment A can increase response by 10%—i.e., we would like to see a mean response of 11 (10 + 1) in patients getting treatment A and we would like to be 80% sure that we detect this difference as statistically significant.
77Example: Detecting a Difference We have:H0: μ1 = μ2 versus H1: μ1 μ2 (two-sided test)α = 0.051 – β = 0.80δ = 1For continuous outcomes we need to determine what difference would be clinically meaningful, but specified in the form of an effect size which takes into account the variability of the data.
78Example: Detecting a Difference Effect size is the difference in the means divided by the standard deviation, usually of the control or comparison group, or the pooled standard deviation of the two groupswhere
79Example: Detecting a Difference 1 - ββα/21 - αα/2-zα/2zα/2Reject H0Conclude differenceFail to reject H0Conclude no differenceReject H0Conclude difference
80Example: Detecting a Difference Power Calculations an interesting interactive web-based tool to show the relationship between power and the sample size, variability, and difference to detect.A decrease in the variability of the data results in an increase in power for a given sample size.An increase in the effect size results in a decrease in the required sample size to achieve a given power.Increasing α results in an increase in the required sample size to achieve a given power.
81Prognostic FactorsIt is reasonable and sometimes essential to collect information of personal characteristics and past history at baseline when enrolling patient’s onto a clinical trial.These variables allow us to determine how generalizable the results are.
82Prognostic FactorsPrognostic factors known to be related to the desired outcome of the clinical trial must be collected and in some cases randomization should be stratified upon these variables.Many baseline characteristics may not be known to be related to outcome, but may be associated with outcome for a given trial.
83Comparable Treatment Groups All baseline prognostic and descriptive factors of interest should be summarized between the treatment groups to insure that they are comparable between treatments. It is generally recommended that these be descriptive comparisons only, not inferentialNote: Just because a factor is balanced does not mean it will not affect outcome and vice versa.
84Subgroup AnalysisDoes response differ for differing types of patients? This is a natural question to ask.To answer this question one should test to see if the factor that determines type of patient interacts with treatment.Separate significance tests for different subgroups do not provide direct evidence of whether a prognostic factor affects the treatment difference: a test for interaction is much more valid.Tests for interactions may also be designed a priori.
85Multiplicity of DataMultiple Treatments – the number of possible treatment comparisons increases rapidly with the number of treatments. (Newman-Keuls, Tukey’s HSD or other adjustment should be designed)Multiple end-points – there may be multiple ways to evaluate how a patient responds. (Bonferroni adjustment, Multivariate test, combined score, or reduce number of primary end-points)
86Multiplicity of DataRepeated Measurements – patient’s progress may be recorded at several fixed time points after the start of treatment. One should aim for a single summary measure for each patient outcome so that only one significance test is necessary.Subgroup Analyses – patients may be grouped into subgroups and each subgroup may be analyzed separately.Interim Analyses – repeated interim analyses may be performed after accumulating data while the trial is in progress.
87SummaryStatistics plays a key role in pre-clinical and clinical researchStatistics helps us determine how ‘confident’ we should be in the results of a studyConfidence in a study is based on (1) the size of the study, (2) its safeguards against biases (complexity), (3) how it was actually undertakenStatistical support is available and should be sought out as early as possible in the process of designing a study
88Next Time . . . Basic Descriptive and Inferential Methods Hypothesis TestingP-valuesConfidence IntervalsInterpretationExamples