Data and Statistical Considerations in Research Study Design ...

Data and Statistical Considerations in Research Study Design and Analysis

Nathan D. Wong, PhD, FACCAssociate Professor and Director

Heart Disease Prevention ProgramUniversity of California, Irvine

Questions to Ask Regarding Study Design and Performance

• Was assignment of patients to treatments randomized?• Were all patients who entered the trial accounted for?• Was follow-up sufficiently long and complete?• Were patients analyzed in the groups to which they were

randomized (intent to treat)?• Were patients, health workers, and study personnel

“blind” to treatment?• Were groups similar (or study sample representative of

population) at start of the trial? (selection bias)• Aside from experimental intervention, were the groups

treated equally? (performance bias)• Were objective and unbiased outcome criteria used?

(detection bias)

Questions to Ask Regarding Statistical Analysis

• Was there sufficient power/sample size?• Was the choice of statistical analysis

appropriate?• Was the choice (and coding/classification) of

outcome and treatment variables appropriate?• Is there an adequate description of magnitude

and precision of effect?• Was there adjustment for potential confounders?

Outline

• Database set-up and structure

• Classification of study variables

• Sample size considerations

• Choice of statistical procedures for different study designs

Data Collection / Management • Always have a clear plan on how to collect data-- design

and pilot questionnaires, case report forms.• The medical record should only serve as source

documentation to back up what you have coded on your forms

• Use acceptable error checking data entry screens or spreadsheet software (e.g., EXCEL) that is convertible into a statistical package (SAS highly recommended and avail via UCI site license)

• Carefully design the structure of your database (e.g, one subject/ record, study variables in columns) so convertible into an analyzable format

Variable Classification• What is your outcome (Y) (dependent variable) of interest?

– Categorical (binary, 3 or more categories) examples: survival, CHD incidence, achievement of BP control (yes vs. no)

– Continuous: change in blood pressure

• What is the main explanatory or independent variable (X) of interest?– Categorical (binary, 3 or more categories) examples:

treatment status (active vs. placebo), JNC-VI blood pressure category (optimal, normal, high normal, stage I, II, or III)

– Continuous: baseline blood pressure

Covariates / Confounders• The relationship between X and Y may be

partially or completely due to one or more covariates (C1, C2, C3, etc.) if these covariates are related to both X and Y

• A comparison of baseline treatment group differences in all possible known covariates is often done and presented

• The effect of confounders can be assessed by:– Stratifying your analysis by levels of these variables

(e.g., examine relationship of X and Y separately among levels of covariates C)

– Adjusting for covariates in a multivariable analysis– Considering interaction terms to test whether effect

of one factor (e.g., treatment) on outcome varies by level of another factor (e.g., gender)

Fallacies in Presenting Results: Statistically vs. Clinically Significant?

• Having a large sample size can virtually assure statistically significant results, but even with a very low correlation or relative risk

• Conversely, an insufficient sample size can hide (not significant) clinically important differences

• Statistical significance directly related to sample size and magnitude of effect or difference, and indirectly related to variance in measure

Sample Size Considerations

• What level of difference between the two groups constitutes a clinically significant effect? (e.g., difference in mean SBP response or difference in treatment vs. control incidence rates of CHD)

• If continuous outcome, know mean and SD.• Find out how large of a sample needed to detect

a true difference between the groups with 80-90% probability (power of study, or 1-beta or Type II error)

• Use a reasonable alpha (or Type I) error of .01 or .05, the likelihood that a difference found to be significant is due to sampling error.

Power of a Test

• Power of a test is the probability of rejecting the null hypothesis when it is false, also 1-beta, where beta error is the probability of accepting a false null hypothesis.

• For instance if the null hypothesis is Mean group A = Mean group B. If this is not true, beta error is likelihood of concluding it is true. Ideally this should be <0.20, so power is 1-beta, or at least 0.80.

Assessing Accuracy of a Test

DISEASED / YES

NONDISEASED / NO

TOTAL

POSITIVE / reject null

a b a+b

NEGATIVE / accept null

c d c+d

TOTAL a+c b+d a+b+c+d

TRUE DISEASE STATUS / TREATMENT DIFFERENCE

TEST RESULT

SENSITIVITY = a / (a+c) SPECIFICITY = d / (b+d)

Pos. Pred. Value = a / (a+b) Neg. Pred. Value = d/(c+d)

False positive error (alpha, Type I) = b / (b+d)

False negative error (beta, Type II) = c/ (a+c)

Questions to ask regarding study results

• How large is the treatment effect (or likelihood of outcome)?– Relative risk reduction (may obscure comparative

absolute risks)– Absolute risk reduction

• How precise is the treatment effect (or likelihood of outcome)?– What are the confidence intervals?– Do they exclude the null value? (e.g., is the result statistically significant– magnitude

of Chi-square or F-value)

SIMVASTATIN: VASCULAR EVENT by LDL

Risk ratio and 95% CISTATIN PLACEBOBaselinefeature (10269) (10267) STATIN better STATIN worse

LDL (mg/dl)

Hetc2

2 = 0.8

< 100 285 360³ 100 < 130 670 881³ 130 1087 1365

ALL PATIENTS 2042 2606(19.9%) (25.4%)

24%SE 2.6reduction(2P<0.00001)

0.4 0.6 0.8 1.0 1.2 1.4

(2.6 mmol/l)

(3.4 mmol/l)

Examining Magnitude of Effect: HPS Study Example of Vascular Event Reduction

Event Yes Event No

Simvastatin/ Treatment

a

2042

b

8227

Placebo / Control

c

2606

d

7661

Control event rate (CER) = c/c+d = 2606/10267=0.254

Experimental event rate (EER) = a/a+b = 2042/10269 = 0.199

Relative Risk (RR) = EER/CER = (.199)/(.254) = 0.78

Relative Risk Reduction (RRR) = CER-EER/CER=(0.254-0.199)/.254=0.22

Absolute Risk Reduction (ARR) = CER-EER = 0.01 – 0.008 = 0.055, or 5.5%

Number Needed to Treat = 1/ARR = 1/0.055 = 18.2 (or 56 events prevented per 1000 treated)

Measures of Precision of Effect

• The p-value, or alpha error, is most commonly an estimate of the precision of the result

• A t-statistic, Chi-square, or r-square value gives the relative magnitude of a relation between two variables.

• An F-statistic (or multiple r-square) identifies the magnitude of the variance in the dependent variable explained by the treatment or explanatory variable(s)

• A Wald or Likelihood Ratio Chi-square statistic is frequently used in logistic or Cox regression survival analysis.

Precision of Effect: The Confidence Interval

• The estimate of where the true value of a result lies is expressed within 95% confidence intervals, which will contain the true relative risk or odds ratio 95% of the time

• 95% Confidence intervals are the RR + 1.96 X SE (since SE is SD/ sqrt(N), confidence intervals are smallest (precision greatest) with larger studies.

• 95% CI of the ARR is + 1.96 X square root of

([CER X (1-CER)/# control patients + EER X (1-EER)/# of exp’l patients]

• 95% CI for NNT = 1 / [95% CI for ARR]

Statistics and Statistical Procedures for Cross-Sectional

and Case-Control Designs– When both independent and

dependent variables are continuous: Pearson correlation or linear/polynomial regression (Cross-sectional only)

– When dependent variable is continuous and independent variables are categorical and continuous: Linear or polynomial regression

Analysis for Cross-Sectional and Case Control Designs (cont.)

– When both independent and dependent variables are categorical: Chi-square test of proportions- prevalence odds ratio for likelihood of factor Y in those with vs. w/o factor X.

– When outcome is binary (e.g., survival) and explanatory variables are categorical and/or continuous:

• Student-test or Chi-square for initial analysis• Logistic regression (multiple logistic regression for

covariate adjustment)

Statistical Procedures for Prospective Cohort Studies

• When outcome is continuous: Linear and/or polynomial regression

• When outcome is binary: Relative risk (RR) for incidence of disease in those with vs. without risk factor of interest, adjusted for covariates and considering follow-up time to event--Cox PH regression: HR (t,zi) = HR0 (t) exp (α’zi)

• If follow-up time is not known, use logistic regression: p (Y=1 | r1,r2,…) = 1/(1+ exp[-a-b1r1-… bnrn)

Statistics and Statistical Procedures for Randomized Clinical Trials

Relative risk (RR) of binary event occurring in intervention vs. control group:

- when follow-up time is known and varies, use Cox PH regression, where RR= ebeta for the trt var.

-- when follow-up time is uniform or unknown, use logistic regression

For continuously measured outcomes, (e.g., changes in blood pressure):

• Pre-post differences in a single group examined by paired t-test

• Treatment vs. control differences examined by Student’s T-test (ANCOVA used when adjusting for covariates)

• repeated measures ANOVA / ANCOVA used for multiple measures across a treatment period and covariates

Will the results help me in caring for my patients?

For a study evaluating therapy:– Can the results be applied to my patient care?

(was the study or meta-analysis large enough with adequate precision?)

– Were all clinically important treatment outcomes considered? (were secondary outcomes and adverse events assessed?)

– Are the likely treatment benefits worth the potential harms and costs? (does the absolute benefit outweight the risk of adverse events and cost of therapy?)

Will the results help me in caring for my patients (cont.)?

For a study evaluating prognosis:– Were the study patients similar to my own?

(demographically representative, stage of disease)

– Will the results lead directly to selecting or avoiding therapy? (useful to know clinical course of pts.)

– Are the results useful for reassuring or counseling patients? (a valid, precise result of a good prognosis is useful in this case)