biostatistical considerations
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Biostatistical Considerations. Nae-Yuh Wang, PhD ICTR Clinical Registries Workshop November 3, 2010. OVERVIEW. Descriptive vs Analytic Goals Selection of Controls Confounding Measurement errors Missing data. Purposes of Patient Registry. Document natural history of disease - PowerPoint PPT PresentationTRANSCRIPT
Biostatistical Considerations
Nae-Yuh Wang, PhD
ICTR Clinical Registries Workshop
November 3, 2010
OVERVIEW
Descriptive vs Analytic Goals
Selection of Controls
Confounding
Measurement errors
Missing data
Purposes of Patient Registry
Document natural history of disease
Evaluate effectiveness of treatment
Monitoring safety
Measuring quality
Frequently multi purposes, addressing scientific, clinical, and policy questions
Natural History of Disease
Document characteristics, management, and outcomes
May be variable across subgroups
May be variable over time
Change after new guidelines or treatments
SMOKING PREVALENCE, %, AMONG U.S. MALE ADULTS*AND 1,213 WHITE MALE PHYSICIANS:THE PRECURSORS STUDY
0%
10%
20%
30%
40%
50%
60%
70%
1955 1965 1970 1975 1980 1985 1990 1994
YEAR
PR
EV
AL
EN
CE
,%
US MALE POPULATION
MALE PHYSICIANS,THE PRECURSORS STUDY
*CDC, National Health Interview Surveys, 18 years and older,1965-1994
Effectiveness of Treatment
RCTs usually have well defined populations
RCTs usually are short term
Clinical effectiveness, cost effectiveness
Comparative effectiveness --- indirect comparisons on differences between treatments
Safety Monitoring
Adverse event reporting relies on recognition of AE by clinician, and clinician’s effort in reporting --- frequently nonsystematic
Serves as active surveillance
Provides denominator to estimate incidence
Enables comparison to a reference rate
Health Care Quality
Compare performance measures (treatments provided or outcomes achieved) against evidence based guidelines or benchmarks (adjusted survival, infection rates) between provider or patient subgroups
Identify disparity in access to care
Demonstrate opportunities for improvement
Establish payment differentials
Types of Registry
Product registries (drug, device)
Health services registries (procedure)
Disease or condition registries
Patients defined by exposure to a product, procedure, or disease/condition
Frequently combination of types
Design of Registry
Research questions, stakeholders, and practical factors (regulatory, political, funding) define purpose and type of registry, and other design considerations such as sampling plan, data collection, validity, sample size, and analytic approaches
Types define the patient population
Purposes define the outcomes
Outcomes define the duration
Design of Clinical Research
Research questions (descriptive vs. hypothesis based --- analytic)
Population; outcome and exposure
Sampling (recruitment); measurements, duration and frequency of data collection
Internal / external validity (bias / generalizability)
Sample size (precision of estimates/degree of association, feasibility, resources)
Analytic plan
Sampling Design
External validity (generalizability): all patients, patients from tertiary medical center only? Single center, multiple center? Which way is more representative of the target population under study?
Do I need controls? (CI in children, language outcomes vs. meningitis)
Selection of controls
Match or not to match?
Cohort Design
Sampling based on predictor (exposure variables) of interest (collect as many exposure variables as possible). Good for rare exposure.
Follow up patients for outcomes, could study multiple outcomes (long time for outcomes to develop?)
Census (not feasible when population and per capita cost are large)
SRS, stratified RS (oversampling subgroup), Cluster RS (cluster characteristics as the aim), multistage RS
Nonrandom: case series / consecutive sampling
Case-Control Design
Stratified RS based on case status
Oversampling cases, good for rare diseases
No long follow up for disease development
Study multiple exposure variables
Exposure ascertainment is key
Nested case-control study using existing registry
Selection of controls, match or not to match
Measurement & Data Collection
Data from clinically based electronic sources only?
Linking from different sources (e.g., NDI searches)
Measurement (different labs) and coding consistency
Additional data collections --- potential confounders, nonclinical outcomes (e.g., QoL, QALY), medications
Measurement & Data Collection
Research versus clinical protocol (BP, busy schedule)
New / changes in treatments and guidelines over time
Changes / improvement in measurement precision and generation of technology over time
Change of outcome definition over time (clinical designation or collect and record raw measures)
Analytic corrections could only be done if needed data / information are available
Internal Validity --- Sources of Bias
Information bias: AE under reported if reporter (provider) will be viewed negatively on care quality. Self reported weight
Selection bias: patients included not representative (unintentional incentives for provider / patient), loss to follow-up, common exposure to unaccounted confound
Confounding by indication: newest drug to patients with worse prognosis
Survival bias: live long enough with exposure to be selected
Internal Validity --- Sources of Bias
Confounding:
CVD risk, age, gray hair
Controlled by matching through study design
Accounted for through stratification, covariate adjustment, or propensity score adjustment during analyses
Only work if data on confounders were collected, need to consider at design stage
Internal Validity --- Sources of Bias
Measurement errors: Mean of 3 repeatedly measured BP readings
used in RCT versus single BP used in clinic
Measured versus self reported body weight
Fruit / vegetable availability in an area used as proxy measure of fruit / vegetable consumption value
Areas measured by 2nd vs. 1st generation CT
Measurement Errors
Nondifferentiable ME in outcome causes no bias. Greater variability in outcomes due to ME reduces statistical power
Differentiable ME in outcome causes violation of constant variance assumption in regression.
Nondifferentable ME in covariate causes underestimation of association (bias towards the null)
ME in Covariate
β* = λβ, where
λ =
€
σ x2
σ x2 +σε
2
4
ME in Covariate Models
E ( Y | X ) = μ ( Xβ )
Classical error model:W = X + ε , X || ε (Note: non-differential)
i. X the measured weight, W the self reported weight
ii. X the measured BMI, W the self reported BMI
Berkson error model:X = W + ε , W || ε (Note: non-differential)
i. X the “true” F/V consumption, W the proxy value
ME in Covariate Models
Goal: E ( Y | X ) = μ ( Xβ )
Actual: E ( Y | W ) = μ ( Wβ* )
Need to correct the estimate of β* to get proper estimate of β
Need to quantify ME so proper correction of β* is possible:Validation: a subsample with both X and W
Replications: repeated measures of W (e.g., BP)
Transportability: information from another study if valid
ME in Covariate
Non-differential ME key assumption, not testable without validation data
When covariate with ME in the model, covariates w/o ME may also be biased. Directions of such biases depend on directions of association among Y and covariates in the model
ME model could be complicated: combined classical & Berkson’s error model, additive versus multiplicative ME
Differential ME: bias direction depends on how ME relates to Y
Design Considerations for ME
Conduct periodic validation study on small random sample of participants (e.g. self report vs. measured weight, outcomes coded by billing vs. coded under research protocol)
If not available from external sources, repeat assessments using old and new instruments in random sample of participants during transition to collect calibration data.
Sources of external validation/calibration data
Missing Data
Inevitable in population research
Prevention is better than statistical treatments
Too much missing information invalidates a study
Validity of methods accommodating missing data depends on the missing data mechanism and the analytic approach
Missing Data Mechanism
Missing completely at random (MCAR):
Pr (missing) is unrelated to process under study
Missing at random (MAR):
Pr (missing) depends only on observed data potential “ignorability”
Not missing at random (NMAR):
Pr (missing) depends on both observed and unobserved data non-ignorable
Simulations
N = 100, repeated outcome: y0, y1
Group = 0, 1 (n = 50 / 50)
FV = 0:
y0 ~ N(0,1) if Group = 0
y0 ~ N(1,1) if Group = 1
FV = 1:
y1 ~ N(0,1) if Group = 0
y1 ~ N(1,1) if Group = 1
E( y0) = E( y1) = 0.5, SD( y0) = SD( y1) = 1.12
Corr( y0, y1 | Group) = 0.6, Corr( y0, y1 ) = 0.68
Analytic Approach
Likelihood approach
Mixed effects models
Mean model = Intercept + FV versus Intercept + FV + Group
Correlation model: Working independent (WI) versus Unstructured (UN)
Model-based versus robust SE
Simulations
Full Sample:
MCAR: 25% random missing at FV1
N Sample mean Sample SD
y0 (FV=0) 100 0.47 1.04
y1 (FV=1) 100 0.54 1.09
y1 – y0 100 0.069 0.79
N Sample mean Sample SD
y0 (FV=0) 100 0.47 1.04
y1 (FV=1) 75 0.56 1.13
y1 – y0 75 0.088 0.83
Simulations
No Missing MCAR
(y1 – y0) .069 (.079) .088(.096)
Mean Model [ Corr ]
Model-Based
RobustModel-Based
Robust
Int. + FV [ WI ] .069 (.150) .069 (.079) .090 (.166) .090 (.100)
Int. + FV / [ UN ] .069 (.079) .069 (.079) .089 (.094) .089 (.094)
Int. + FV (+ GP) / [ WI ] .069 (.134) .069 (.079) .084 (.149) .084 (.095)
Int. + FV (+ GP) / [ UN ] .069 (.079) .069 (.079) .087 (.093) .087 (.093)
Simulations
Full Sample:
MAR1: 25% missing in Group 0 at FV1
N Sample mean Sample SD
y0 (FV=0) 100 0.47 1.04
y1 (FV=1) 100 0.54 1.09
y1 – y0 100 0.069 0.79
N Sample mean Sample SD
y0 (FV=0) 100 0.47 1.04
y1 (FV=1) 75 0.75 1.16
y1 – y0 75 0.094 0.76
Simulations
No Missing MAR1
(y1 – y0) .069 (.079) .094(.088)
Mean Model [ Corr ]
Model-Based
RobustModel-Based
Robust
Int. + FV [ WI ] .069 (.150) .069 (.079) .279 (.159) .279 (.102)
Int. + FV / [ UN ] .069 (.079) .069 (.079) .137 (.086) .137 (.086)
Int. + FV (+ GP) / [ WI ] .069 (.134) .069 (.079) .129 (.147) .129 (.093)
Int. + FV (+ GP) / [ UN ] .069 (.079) .069 (.079) .103 (.085) .103 (.085)
Simulations
Full Sample:
MAR2: 25% missing depends on values of y0
N Sample mean Sample SD
y0 (FV=0) 100 0.47 1.04
y1 (FV=1) 100 0.54 1.09
y1 – y0 100 0.069 0.79
N Sample mean Sample SD
y0 (FV=0) 100 0.47 1.04
y1 (FV=1) 75 0.29 1.04
y1 – y0 75 0.213 0.78
Simulations
No Missing MAR2
(y1 – y0) .069 (.079) .213(.090)
Mean Model [ Corr ]
Model-Based
RobustModel-Based
Robust
Int. + FV [ WI ] .069 (.150) .069 (.079) -.187 (.158) -.187 (.117)
Int. + FV / [ UN ] .069 (.079) .069 (.079) .154 (.090) .154 (.090)
Int. + FV (+ GP) / [ WI ] .069 (.134) .069 (.079) -.194 (.138) -.194 (.115)
Int. + FV (+ GP) / [ UN ] .069 (.079) .069 (.079) .106 (.091) .106 (.091)
Simulations
Full Sample:
NMAR: 25% missing depends on values of y1
N Sample mean Sample SD
y0 (FV=0) 100 0.47 1.04
y1 (FV=1) 100 0.54 1.09
y1 – y0 100 0.069 0.79
N Sample mean Sample SD
y0 (FV=0) 100 0.47 1.04
y1 (FV=1) 75 0.11 0.83
y1 – y0 75 -0.127 0.72
Simulations
No Missing NMAR
(y1 – y0) .069 (.079) -.127(.083)
Mean Model [ Corr ]
Model-Based
RobustModel-Based
Robust
Int. + FV [ WI ] .069 (.150) .069 (.079) -.367 (.141) -.367 (.090)
Int. + FV / [ UN ] .069 (.079) .069 (.079) -.228 (.080) -.228 (.080)
Int. + FV (+ GP) / [ WI ] .069 (.134) .069 (.079) -.360 (.120) -.360 (.090)
Int. + FV (+ GP) / [ UN ] .069 (.079) .069 (.079) -.257 (.081) -.257 (.081)
Simulations
ModelMean / Corr
No Missing
MCAR MAR1 MAR2 NMAR
(y1 – y0) .069 (.079) .088(.096) .094(.088) .213(.090) -.127(.083)
Int. + FV /WI (Model-based) .069 (.150) .090 (.166) .279 (.159) -.187 (.158) -.367 (.141)
Int. + FV /UN (Robust) .069 (.079) .089 (.094) .137 (.086) .154 (.090) -.228 (.080)
Int. + FV (+ GP) /WI (Model based) .069 (.134) .084 (.149) .129 (.147) -.194 (.138) -.360 (.120)
Int. + FV (+ GP) /UN (Robust) .069 (.079) .087 (.093) .103 (.085) .106 (.091) -.257 (.081)
Observations
MCAR:» Requires only correct mean model for valid
inferences» Complete case analysis is valid, but not
efficient for estimating fully observed variables
» Approaches valid for MAR also valid under MCAR
» Unlikely to be true in population based research
Observations
MAR: » Ignorablility of missing is possible but not
given
» Requires correct specification of likelihood (both mean and covariance model) for the observed data to achieve valid inferences
» Empirically cannot be confirmed without auxiliary data
Observations
NMAR: » Empirically cannot be ruled out without
auxiliary data» Likelihood, multiple imputation, propensity
score, inverse weighting approach cannot completely eliminate bias
» Need to conduct sensitivity analyses under various plausible NMAR scenarios to evaluate potential impacts on inferences
Observations
Observational studies face similar issues as RCTs with missing data: » Bias due to missing data selection bias» Proper selection of analytic models may
eliminate bias if the “selection” is based on observed data values, i.e. we have data to adjust for selection
» Bias due to “selection” according to data values not observed will be hard to correct
Sample Size Considerations
Descriptive: estimation precision
Hypothesis based: power to detect association
Design effects
Longitudinal correlations