Clinical Trials

❘❙❚■ Chapter 20 | Comparison of ProportionsTable 4. Selected critical values of the chi-squared distribution.Degrees of freedomSignificance level0.05 0.01 0.0011 3.84 6.63 10.832 5.99 9.21 13.823 7.81 11.34 16.274 9.49 13.28 18.475 11.07 15.09 20.516 12.59 16.81 22.467 14.07 18.48 24.328 15.51 20.09 26.129 16.92 21.67 27.8810 18.31 23.21 29.5911 19.68 24.73 31.2612 21.03 26.22 32.9113 22.36 27.69 34.5314 23.68 29.14 36.1215 25.00 30.58 37.7016 26.30 32.00 39.2517 27.59 33.41 40.7918 28.87 34.81 42.3119 30.14 36.19 43.8220 31.41 37.57 45.31AssumptionsThere are two important assumptions when using the chi-squared test. The firstassumption is that the two treatment groups are homogeneous in terms of thepatients’ characteristics (eg, demographic information, disease-related riskfactors, medical histories, concurrent medical treatments). We can check whetherthe two groups are comparable by looking at observed baseline summary statistics.If the two treatment groups are not balanced with regard to some predictor(s) ofoutcome, logistic regression modeling can be used to adjust for these potentialconfounding factors [1–3].The second assumption is that the sample sizes in the two treatment arms arelarge, say >50 [2,3]. If the sample size is small, we need to use the Fisher’s exacttest, which follows [2,3].224