Continuous and Binary Endpoints

Outcomes are either continuous or dichotomous. Primary and secondary outcomes must be defined a priori in the protocol. The sample size for the study is based on the primary outcome.

When determining  if a clinical trial is effective we test a hypothesis of a primary outcome, and we may have several secondary outcomes which are more exploratory. We can't define many outcomes and pick the most successful, it would be like rolling dice many times; It increases the chance of type 1 error (rejecting the null hypothesis when it is true). One could also adjust the p-value/type one error rate to account for multiple testing, but more on this later.

When relevant to the study continuous variable can be coded as a binary one, but leads to a loss of information.

Statistical Analysis of Real Clinical Trials

1. Define outcome                                                           <- Statistical Analysis plan/protocol
   • Binary, continuous, etc.
2. State the null hypothesis
   • One or two sided; alpha level
3. Descriptive statistics                                                    <-  Data Analysis
4. Determine appropriate statistical test
5. Parameter estimates, confidence interval, p-value
6. Write conclusions

Superiority Trial - We expect that the new treatment is better than the control
H₀: μ_A = μ_B
H_A: μ_A != μ_B

Note that we test the hypothesis two sided even though we think the effect will be one-directional. This is an FDA recommendation, one sided tests are allowed but use .025 level of significance. Two sided tests require larger samples size than one sided at alpha level .05.

Writing Conclusions

Statistical Methodology Section

• The primary outcome being tested
• Describe tests used, assumptions, and groups tested

Reporting of Results

• Mean and confidence intervals
• Test statistic values
• Reject or accept the null hypothesis

SAS

Generally we only need to specify a single test, but each test has its own assumptions

Parametric Tests

-

We can get the same information from all the following procedures, but there are different options and defaults for each method
        PROC TTEST, PROC GLM, PROC REG, PROC ANOVA

Non-paramteric Tests
        PROC NPAR1WAY, PROC SURVEYSELECT

Generally we only need to specify a single test, but each test has its own assumptions

PROC TTEST

Test difference between means, and differences in variances via an F-Test

proc ttest data=dbp;
    class trt;
    var diff;
run;

Welch's T-Test can be used if treatment groups have different variance

Non-Parametric Tests for Two Groups

Non-parametric groups only pay a very small penalty, if the data is normally distributed the test is ~95% as powerful as a ttest

Non-parametric Tests
        PROC NPAR1WAY, PROC SURVEYSELECT

Wilcoxon Rank-Sum Test

Works very well on skewed data

proc npar1way data=dbp wilcoxon;
	class TRT;
	var diff;
	*exact wilcoxon; /* request for exact p-value - may take a while */
run;