• Emphasize confidence limits, which can be computed from adjusted or unadjusted analyses, with or without taking into account multiple comparisons
• $$P$$-values can accompany CLs if formal hypothesis testing needed
• When possible construct $$P$$-values to be consistent with how CLs are computed

## 12.1 Types of Analyses

• Except for one-sample tests, all tests can be thought of as testing for an association between at least one variable with at least one other variable
• Testing for group differences is the same as testing for association between group and response
• Testing for association between two continuous variables can be done using correlation (especially for unadjusted analysis) or regression methods; in simple cases the two are equivalent
• Testing for association between group and outcome, when there are more than 2 groups which are not in some solid order1 means comparing a summary of the response between $$k$$ groups, sometimes in a pairwise fashion
• 1 The dose of a drug or the severity of pain are examples of ordered variables.

Appropriate when

• Only interested in assessing the relationship between a single $$X$$ and the response, or
• Treatments are randomized and there are no strong prognostic factors that are measureable
• Study is observational and variables capturing confounding are unavailable (place strong caveats in the paper)

See Chapter 13

### 12.2.1 Analyzing Paired Responses

Type of Response Recommended Test Most Frequent Test
binary McNemar McNemar
continuous Wilcoxon signed-rank paired $$t$$-test

### 12.2.2 Comparing Two Groups

Type of Response Recommended Test Most Frequent Test
binary $$2\times 2~\chi^{2}$$ $$\chi^{2}$$, Fisher’s exact test
ordinal Wilcoxon 2-sample Wilcoxon 2-sample
continuous Wilcoxon 2-sample 2-sample $$t$$-test
time to event2 Cox model3 log-rank4
• 2 The response variable may be right-censored, which happens if the subject ceased being followed before having the event. The value of the response variable, for example, for a subject followed 2 years without having the event is 2+.

• 3 If the treatment is expected to have more early effect with the effect lessening over time, an accelerated failure time model such as the lognormal model is recommended.

• 4 The log-rank is a special case of the Cox model. The Cox model provides slightly more accurate $$P$$-values than the $$\chi^2$$ statistic from the log-rank test.

• ### 12.2.3 Comparing $$>2$$ Groups

Type of Response Recommended Test Most Frequent Test
binary $$r\times 2~\chi^{2}$$ $$\chi^{2}$$, Fisher’s exact test
ordinal Kruskal-Wallis Kruskal-Wallis
continuous Kruskal-Wallis ANOVA
time to event Cox model log-rank

### 12.2.4 Correlating Two Continuous Variables

Recommended: Spearman $$\rho$$
Most frequently seen: Pearson $$r$$

• Continuous response: multiple linear regression with appropriate transformation of $$Y$$