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Medical Stats

TermDefinition
Clinical Trial Planned experiment on human beings which is designed to evaluate the effectiveness of 1 or more forms of treatment
Experiment Series of observations made under conditions controlled or arranged by the investigator
Treatment A pharmaceutical drug or medical treatment (surgery, diet, counselling), or method of organising/delivering health care (education leaflet, phone app)
Classification Systematic arrangement by purpose or phase in drug development
Phase I trial Looks into pharmakinetics of a drug (absorption, metabolism) and toxicity (drug safety). finding maximum tolerated dose.
Phase II trial Initial clinical investigation. Dose finding study. Work out dose and dose schedules and early indication of efficacy
Phase III trial Aim of full scale evaluation, efficacy of a new experimental treatment compared to a standard therapy or placebo, acting as a control
Phase IV trial Effectiveness. Post marketing surveillance for info on long term effects and uncommon side effects.
Effect Difference between what happened to a patient as a result of the treatment vs what would have happened without the treatment
Efficacy The true biological effect of a treatment
Effectiveness Effect of a treatment when widely used in general practice.
Efficiency The time and cost related economics of a treatment.
Research Protocol Formal written document outlining the research plan for a clinical trial
Control group's Purpose Give a yard stick as to what may have happened in absence of experimental treatment. Needed in phase III trials
Use of control group in Phase III trials As investigator/patients expectations and enthusiasm of trial inclusion may affect judgement and outcomes. Some open & uncontrolled trials yeilded spurious results.
Gold standard of trial design Randomised, controlled and double-blinded trial.
Randomisation Treatments assigned according to chance (often equal).
Aim of Randomisation To yield treatment groups that are comparable in terms of extreneous factors.
Purpose of Randomisation Avoid bias due to differences in clinical & demographic characteristics. To support the independence assumption underlying many statistical procedures
Simple Randomisation independent random treatment allocation with fixed probability
Pros of simple randomisation easy to implement can do analysis via standard statistical methods
Cons of simple randomisation likely to get uneven treatment group numbers esp in small samples doesnt ensure balance over confounders (e.g. age and disease severity)
Block randomisation Restricted randomisation that works by balancing participant numbers in each group.
Block randomisation method Choose a block at random and assign patients accordingly. Want to keep block sizes short to prevent incomplete blocks (as may be fixed/randomly varying)
Block size A multiple of the number of treatments
Cons of block randomisation Assignment may become known if blocking factor revealed statistical methods often presume simple randomisation
Pros of block randomisation Has balance. max difference is b/2 for blocks of size b
Stratified randomisation Uses block randomisation in each stratum to aid between group comparability (balance) over important characteristics.
Pros of stratified randomisation Overcomes imbalance with regards to important factors in small samples Increases efficacy and reduces potential bias
Cons of stratified randomisation no. of strata may limit usefulness Complicates proceedings
Adaptive randomisation - Minimisation A non random treatment allocation where allocation probabilities adjusted according to patient imbalance
Minimisation Purpose Balance between treatment groups with regard to important prognastic factors.
Minimisation Method Use simple randomisation when groups are balanced. When imbalanced, allocates next patient to treatment so imbalanced minimised via minimisation score.
Weighted minimisation Weighting in favour of treatment which would minimise imbalance
Purpose of Blinding/Masking Avoid bias due to differences in treatment outcome (conscious or unconscious)
Single-blind trial Patient not know which treatment is being received
Double-blind trial Neither patient nor physician knows treatment allocation. GOLD standard.
Triple-blind trial double-blind plus monitoring group & data analyst don't know which group receives experiences & which control.
Open trial All are knowledgable about treatment allocation.
Double-dummy Compares 2 active treatments with different appearances
Blind alternative Incorporate blind assessment or conceal treatment allocation until patient entered into trial
Cons of blind trial More complex as need independent monitoring committee to deal with ethical aspects & trial termination
Ethical Issues in clinical trials can you obtain informed consent? Should you try to continue until investigators convinced 1 better or until entire medical community convinced?
Ethical issues regarding placebos Is it ethical if an effective existing treatment is known to exist
Declaration of Helsinki Set of ethical principles regarding human experimentation. For medical community. By WMA. Is a cornerstone document on human research ethics. Not legally binding.
Governance arrangement for NHS research ethics committees Describes what REC's should be like and when their review is needed
Example of a complication of clinical trials Non adherence to protocol - missing follow up visits, not completed full course of treatment
Intention to treat set Analyse as randomised, regardless of adherence. To look at effectiveness.
Per Protocol set Analysis based upon adherers only. To look at efficacy.
Cons of per protocol set Can introduce bias when groups of patients no longer have similar characteristics.
When to use intention to treat set In superiority trials where want to avoid over optimistic estimates
Endpoint Quantative measurement implied or required by the trial objectives. Is determined in each study subject.
Hard endpoint Preferred. Well defined and reliable. No subjectivity. Objectively measured.
Soft endpoint Difficult to define and subjective measures.
Student's T-test Comparison of 2 independent group means. Parametric method.
Assumptions of student's T-test Normality of data and equality of variances across comparison groups.
Order of methodology for student's t-test state research hypothesis (no diff and diff in difference in group means) estimate D = mean(T) - mean(C) Compute test statistic under H0. T = (mean(T)-mean(C)-0)/SE(estimate D) SE(estimate D) = S*sqrt(1/N(T) + 1/N(C)) S depend on underlying variance.
S^2 (pooled variance estimate) in student's T-test if common underlying variance 1/(n-2) * (sum from 1 to N(T) of (each value in T - mean(T))^2 + sum from 1 to N(C) of(each value in C - mean(C))^2
S^2 (pooled variance estimate) in student's T-test if S(T) and S(C) are sample standard deviations ((N(T) -1)*S(T)^2 + (N(C) - 1)*S(C)^2/(N - 2)
Confidence interval for student's T-test T is compared to t-distribution with N-2 degrees of freedom & inference based on if |T| >= t dist (N-2,1 - alpha/2) D +- t dist (N-2, 1 - alpha/2)
Point Estimate Observed difference in group means D = mean(T) - mean(C)
Interpretation if confidence interval for true difference spans zero there is no statistically significant difference between groups so cannot reject null hypothesis
Inference for p value Calculate alpha for T value. if p < alpha = 0.05. Then is statistically significant
Pro of confidence intervals More informative as can assess plausible range of effect size
Welch's test An approximate test if assume non-constant variance
Mann-whitney test Non parametric alternative to student's T-test
1-sample Paired t-test Test based on within-pair differences
Paired t-test method Compute mean of within-pair diffs standard deviation of diffs Sd = sum of squares of differences between diffs and mean diff standard error of mean of diffs SE(D) = Sd/sqrt(n) Compute T under H0. T = D/SE(D)
Paired t-test confidence interval Compare T to t-distribution under n-1 degrees of freedom D +- t(n-1,1-alpha/2)*SE(D)
p_1 and p_2 in binary response data success probabilities for treatment and control groups in binary response data
Risk Difference Difference between risk of an outcome between group 1 and 2. p1 - p2. a/(a+c) - b/(b+d)
Relative Risk Compare risks for 2 groups. p1/p2. (a/(a+ c))/(b/(b+d)). treatment 1 RRx risk of outcome being observed than treatment 2.
Disease odds ratio of success to failure. p_i/(1-p_i)
Odds ratio Measure of association between outcome and exposure. p1/(1-p1) / p2/(1-p2) = ad/bc. treatment 1 ORx more likely to be exposed to outcome than treatment 2.
When does odds ratio equal relative risk? When the occurrence of outcome is less than 10%.
Binary data confidence intervals theta +- z(1-alpha/2)*SE(theta) where theta is risk difference, log of relative risk or log of odds ratio.
Standard error for Risk difference BINARY sqrt(p1(1-p1)/n1 + p2(1-p2)/n2). p1 = a/(a+c) and p2 = b(b+d). n1 = a+c. n2 = b + d
Standard error for log of Relative Risk BINARY sqrt(1/a - 1/(a+c) + 1/b - 1/(b+d)) DONT FORGET TO ANTILOG THE INTERVAL
Standard error for log of Odds Ratio BINARY sqrt(1/a + 1/b + 1/c + 1/d) DONT FORGET TO ANTILOG THE INTERVAL
Parallel group design Different groups of patients are studied in parallel. Estimate of treatment effects is based upon between subject comparisons.
What inference test to use for parallel group design? 2 independent samples t-test
Paired design Patient recieves both treatments. Then estimate of treatment effect based on within subject comparison
What inference test to use to paired design 1-sample t-test on within subject differences
Crossover Design Patient recieves sequence of treatments. Order determined by randomisation. Treatment effect based on within-subject comparisons
Treatment Periods times treatments are administered
Pros of cross-over design Patients act as own control as uses within-subject comparisons - eliminates between patient variation. Smaller sample size required for same no of observations Same degree of precision in estimation with fewer observations
Cons of cross-over design Inconvinience to patients as multiple treatments mean longer time under observation Patients may withdraw Treatment effect not constant over time (p-by-t interaction) Carry over effect Analysis more complex - may be systematic diffs between periods
Carry over effect Persistence of treatment applied in one period in a subsequence period of treatment
How to deal with carry over effect Wash out period
Wash out Period Period in trial during which effect of treatment given previously believed to disappear.
When are cross-over trials useful? Chronic diseases that are relatively stable Single dose trials of biological equivalence rather than long term trials Drugs with rapid and reversible effects
AB/BA design A 2 treatment x 2 period cross over trial.
Simple analysis for a cross over design with no period effect Use paired t-test
Assumptions underlying use of paired t-test Normally distributed differences Unbiased - that E(d) is the true treatment effect
Factors that may cause differences to not be distributed at random about true treatment effect period effect period by treatment interaction carry over effect patient by treatment interaction patient by period interaction
When is a treatment effect estimate unbiased If expectation of estimate is the estimate.
Why do you need adequate sample sizes? ethics budget constraints time constraints trial should be large enough to give reliable answer to research question
P value Probability, p, of obtaining test result at least as extreme as that observed assuming H0 is true
Size of test Given by alpha, usually alpha = 0.05
When p value less than alpha? Reject H0 and conclude data is inconsistent with null.
Type I error rate alpha, probability of rejecting H0 given H0 is true (saying theres a diff when theres not)
Type II error rate beta, probability of failing to reject H0 when H1 true (saying no diff when there is a diff)
Power of test 1 - beta, probability of rejecting H0 when H1 is true (correctly saying is a diff)
What does power of a test depend on? the statistical test being used size of test (alpha) variability of observations (sigma^2) H1 (size of diff 'triangle')
What does symbol triangle* represent? The clinically relevant difference in a gauss test per say
One & two sample one sided gauss test Used to determine sample size
Epidemiology Study of distributions and determinants of disease in human populations
What are descriptive studies used for? Generating research hypotheses and resource allocation Gaining info regarding disease frequency in populations Info on distributions - age, geography, time, etc
Disease Determinants aka risk factors Factors precipitating disease (biological or enviro or social)
Target population Population about which we wish to draw inferences for
Study population Population from which data is collected
Generalisability Whether can use study population results to draw accurate conclusions about target pop
Factors affecting study sample choice generalisability of results trading off with availability and cost opportunistic sample is readily identifiable and likely to be cooperative Preference is a random sample of target population
Routinely collected data A source for data in epidemiological studies. E.g. hospital data bases, birth/death registers, census data)
Sources for data in epidemiological studies routinely collected data data purposely collected by investigators via surveys and follow up
Purpose of routinely collected data vital to monitor public health and health planning can use to investigate possible associations between routinely available attributes and rate of indecence from a particular disease
Con of routinely collected data May be of limited quality - subject to regional variation and often dont contain required individual level info.
Limits of routinely collected data Coverage - difficult to define morbidity so incomplete coverage Accuracy - diagnosis of cause of death and illness can be wrong Availability - confidential safe guards may limit data availability
Reasons for incomplete coverage of routinely collected data Inconsistent reporting of infectious diseases by practitioners and cancer registers may miss non hospital cases
Disease Iceberg moving down it, cases increase but severity decreases died, hospital, GP, self report, population screening
Incidence (I) of disease number of new cases of disease within a specified time period
Prevalence (P) of disease number of existing cases of disease at particular point of time. Probabiity of disease prior to seeing test result. (a+c)/N
Calculation for incidence of disease number of develop disease in specified time period / sum of length of time in which each person in population is at risk for
Calculation for prevalence of disease number with disease at time t / number in population at risk at time t
Person-time of observation Total observation time. Often express as person-years. Used for incidence rates.
Purpose of prevalence measures better for descriptive studies than analytical, suggests possible causes
Purpose of incidence measures Better to study as can establish sequence of events. Not susceptible to bias by survival
Cumulative Incidence Risk Alternative measure of disease occurance. Calculate: number of people who get disease in specified period / number of people free of disease at beginning of period. Is the risk of developing a disease.
Crude mortality rate number of deaths in a specified time period divided by average population at risk in period, multiplied by length of study period
How to assess utility of a diagnostic test Apply test to a number of individuals where true disease status known (based on GOLD standard)
Sensitivity Errors in testing. Proportion of truly diseased persons in tested population who are identified as diagnosed by screening test. P(T|D) (prob of pos test given diseased). a/(a+c)
Specificity Proportion of truly non diseased who are identified as so by screening test. P(bar(T)|bar(D)). d/(b+d)
Positive Predictive Value PPV Proportion truly diseased of those testing positive. Probability of diseased after a positive test. P(D|T). a/(a+b)
Negative Predictive Value NPV Proportion not diseased of those testing negative. P(bar(D)|bar(T)). Probability of not diseased after a negative test. c/(c+d)
High cut off value More specific test
Low cut off value More sensitive test
Intermediate cut off value Smaller overall errors. Need to balance high sensitivity and low specificity.
Receiver Operating Characteristic curve Plot of sensitivity against (1-specificity) for various cut off points. Cut off choice is top-left-most plot on curve.
PPV using sensitivity, prevalence and specificity (sens x prev)/((sens x prev) + (1 - spec)(1-prev))
NPV using sensitivity, prevalence, specificity (spec x (1-prev))/((spec x (1- prev))+((1-sens) x prev))
Likelihood Ratio Used to make therapeutic decisions regarding tests. P(T|D)/P(T|bar(D)) = sens/(1-spec). Test informative if value high. Is the ratio of posterior disease odds after pos test to prior disease odds, so tells how much odds of disease increase after pos test.
Weight Relative importance to give to sensitivity
When to give high weight to sensitivity? If disease high threatening and treatment has few side effects. (dont want false negatives).
When to give high weight to specificity? If disease not serious and treatment has many side effects. (dont want false positives)
How to maximise weight with respect to study Choose w = number of positive samples/total number of samples. Want to maximise M = w x sens + (1-w) x spec. 1-w is weight of spec.
How to maximise weight with respect to population criterion w = number with disease in population / total population size. Which is disease prevalence.
Screening test Test for particular disease given to population at risk who are asymptomatic
Criteria for disease screening Natural history of disease should be well understood should be an important health issue test should be acceptable to population there should exist a suitable screening test
Why must be careful in disease screening As truly diseased population likely to be small so many disease free will test positive
Observational studies Investigator role is passive so exposures not manipulated
Intervention studies Investigator role is active. Groups exposed to intervention of interest (eg treatment). Are experimental studies (clinical trials)
Why are intervention studies the gold standard in terms of causality can handle confounding with randomisation and exposure known to preceed disease.
ethical Issue with intervention studies rarely acceptable to force exposures on people
Cross-sectional studies surveys also feature but only to give info for snapshot in time - are less useful. Can only use to measure prevalence.
Most common observational studies cohort and case studies.
Cohort study Most useful observational study in disease causes. Tracks 2 or more groups forward from exposure to outcome. classify according to exposures. exposure vs non exposure rows and outcome vs non outcome columns
Pros of cohort study Strongest evidence for causal r.ship as exposure known to preceed outcome Can measure risk, incidence rate & survival time can examine many events after 1 exposure maintain temporal sequence best way to ascertain incidence & natural disease history
Rationale of cohort studies Follow cohorts through time - record disease occurrance and compare exposure groups with respect to disease outcome- then interpret
Cons of cohort studies large & costly selection bias loss to follow up confounding variables exposure can change in study period
Case control study Case & control groups defined & selected according to disease status. Look back in time to ascertain each person's exposure status
Pros of case control study efficient in terms of time and money (if exposure frequency not too low) can study rare diseases
Cons of case control study choosing control group can lead to selection bias obtaining exposure history so may have recall bias
Risk difference for cohort studies (binary exposure) p1 - p0. a/(a+b) - c/(c+d)
Relative risk for cohort studies (binary exposure) p1/p0. (a/(a+b)/c/(c+d)).
Disease odds in cohort studies. binary exposure p/1-p. Ratio of success to failure
Odds ratio in cohort studies. binary exposure. Compares exposed and not exposed groups. p1/(1-p1) / p0/(1-p0) = ad/bc
In case control studies - estimate disease odds ratio not disease risk... p1/(1-p1) / p0/(1-p0)
Disease odds ratio similar to odds ratio if disease is rare.
Exposure odds for cases (D) P(E|D)/P(bar(E)|D)
Exposure odds for controls (bar(D)) P(E|bar(D))/P(bar(E)|bar(D))
Exposure odds ratio Ratio of 2 exposure odds. Equal to disease odds ratio. ad/bc
How to increase precision of estimate of disease odds ratio? More controls.
A confounder 3rd variable associated with exposure of interest. Independently associated with risk of disease. partially or fully explains relationship between E and D.
Consequences of confounders Creates a false relationship between E and D Masks true relationship between E and D
Design based approaches to control confounding Randomisation (balance over potential confounders) Restriction (Limit participation to individuals similar in relation to confounders) Matching (select controls to be similar to cases in terms of confounders)
Analysis based approaches to control confounding Stratification Standardisation (control confounding using external pop to adjust for age, gender etc) Multivariate analysis/regression models (include confounding variable in model)
Stratification (in analysis based approach to control confounding) Examine exposure-disease associations within strata of confounding variable. Estimate pooled estimate of association measure, adjusting for confounding effect.
Mantel-haenszel estimate Estimate of association between outcome and exposure after adjusting for confounding. Estimates a common odds ratio so use log in confidence interval
Standard error for mantel-haenszel very long. sum(a+d/n x ad/n)/2xsum(ad/n)^2 + same for bc + sum((a+d/n x ad/n)+(same for bc))/2sum(ad/n)sum(bc/n)
If odds ratio confidence interval spans 1 for mantel-haenzel association between exposure and outcome not significant at 5% level
If reduction in odds ratio from joint odds ratio to individual in mantel-haenzel is small The degree of confounding is small
Unstratified matching in case control studies Choose controls randomly
Stratified matching in case control studies Match controls to cases according to confounding variable. May be group or individual matching.
Rationale of matched case control study Eliminate confounders by design
Pros of matching in case control study control confounders by elimination gain in efficiency minimises selection bias
Cons of matching in case control study More complex study design cant study effect of matching variables on outcome of interest overmatching (matching variable linked to exposure not disease)
Maximum likelihood estimate of exposure odds ratio in matched case-control study b/c. standard error is log of estimate = sqrt(1/b + 1/c)
Standardisation process aimed at removing confounding by choosing a standard population with known distribution of confounders
Direct standardisation disease rates in population of interest are applied to standard population counts
Indirect standardisation disease rates in standard population applies to population of interest
Direct standardised event rate expected event rate in standard population, if age-specific event rates in study population prevailed
How to adjust event rate for age category specific event rates for each population being compared will be applied to a single standard population
Direct age standardised event rate per 1000 1000/total size of standard pop x sum of ((observed number of events in ith age group of study population/size of ith age group of study population)x size of ith age group of standard population)
Person years average population size x study length
When to use indirect standardisation of event rates when age specific rates aren't available for population of interest
Methods of indirect standardisation of event rates Produce standardised event ratio (SER) or standardised mortality rate (SMR)
SMR O/E. where O is total number of observed events in all age groups of study population and E is sum of (observed number of events in ith age gorup of standard population / size of ith age group of standard population) x size of ith age group of study pop
Requirement for direct standardised rates need age specific rates for all population studies
Requirement for indirect standardised rates need total number of cases observed
Standardised incidence / mortality rate ratio of 2 indirectly standardised rates
Pro of indirect standardised rates More stable in case of small numbers of events
Con of indirect standardised rates Need age specific rates for standard population
Survival analysis data analysis in the form of time from some well defined time origin to occurrence of some event or endpoint.
Examples of time origins for survival analysis time of trial entry or diagnosis time
Time-to-event data can be time to death or time to failure of prosthetic etc
Positive event example in time-to-event data hospital discharge
Adverse event example in time-to-event data Death
Neutral event example in time-to-event data Cessation of breast feeding
Lifetime random variable time-to-event rate is random variable T
Why can't apply time-to-event data to standard methods of analysis Event times are positive continuous, typically skewed, and subject to censoring
When does censoring occur? if endpoint not observed
Right censoring event time greater than last follow up time
Left censoring Event time before time of last follow up but is unknown
Interval censoring event time falls in a specified interval
Reasons for right censoring period of observation end prior to event occurrence loss to follow up completing event precludes further follow up - eg death event may not be inevitable (eg pregnancy)
Why one treatment may have more censoring at the end than other results in increased survival
Why does period of observation time vary between patients? patients accrued sequentially over time and followed up to fixed date so period of observation varies between patients
Assumption of survival analysis when acru patients over time Prognosis doesn't depend on entry time to study
Aims of survival analysis model survival times for a group & make predictions assess effects of covariates on survival compare survival distribution for 2 or more groups
The functions of interest when summarising survival data Survivor function & hazard function
Survival time of individual i observation of a non negative r.v. T
Distribution function of T F(t)
Probability density function of T f(t)
Link between Distribution and pdf of T F(t) = integral (from 0 to t) of f(s) ds = P(T <= t). f(t) = d/dt F(t)
Survivor function Probability an individual survives to time t. S(t) = P(T>t) = 1 - F(t) = integral (from t to infinity) f(s) ds. Monotone decreasing function S(0) = 1
Link between pdf and survivor function f(t) = -d/dt S(t)
Hazard function specify instantaneous rate of failure at T=t given survival to time t. h(t) = f(s)/S(t). RATE not probability
How to approximate probability an individual who survived to time t will experience event in interval (t,t+delta*t) h(t)*delta*t
Cumulative/integrated hazard function H(t) = integral (from 0 to t) of h(u) du. Probability of failure at time t given survival until time t
Decreasing hazard function Clinically less likely, such as in risk after organ transplantEs
Emperical survivor function estimate of survivor function. hat(S)(t). Step function with steps at observed failure times.
Kaplan-meier estimate Estimates survivor function. first step in presence of censored data. Is the product limit estimator
event times and number in sample at risk at each event time and number who fail at this time notation t_j and n_j and d_j
Estimated probability of survival through interval j in kaplan meier survivor function p_j = (n_j - d_j)/n_j) = 1 - d_j/n_j
Assumptions for kaplan-meier estimate independence of event times
Kaplan meier estimator S(t) = multiplication of all p_j's for k=r+1 subintervals
Kaplan-meier when no censoring emperical survivor estimator
Greenwood's formula for estimated variance. S(t)^2 x sum of (d_j/(n_j(n_j - d_j)))
Make a smoother plot for survivor function estimate More data and more distinct failure times
End point of the kaplan-meier estimator curve the estimated survival % at t years
Why can't use t-test to compare group means in survival distribution? Because of censoring
Log-rank test formal comparison of 2 groups survival distribution. Can compare more than 2 groups.
Informal comparison of 2 groups survival distribution Use Kaplan-meier curve
Cox proportional hazards model commonly used to flexibly model covariate effects on the hazard function.
Created by: Rebeka