Question

Treatment for Cocaine Addiction Cocaine addiction is very hard to break. Even among addicts trying hard to break the addiction, relapse is common. (A relapse is when a person trying to break out of the addiction fails and uses cocaine again.) Data 4.7 on page 323 introduces a study investigating the effectiveness of two drugs, desipramine and lithium, in the treatment of cocaine addiction. The subjects in the six-week study were cocaine addicts seeking treatment. The 72 subjects were randomly assigned to one of three groups (desipramine, lithium, or a placebo, with 24 subjects in each group) and the study was double-blind. In Example 4.34 we test lithium vs placebo, and in Exercise 4.181 we test desipramine vs placebo. Now we are able to consider all three groups together and test whether relapse rate differs by drug. Ten of the subjects taking desipramine relapsed, 18 of those taking lithium relapsed, and 20 of those taking the placebo relapsed. (a) Create a two-way table of the data. (b) Find the expected counts. Is it appropriate to analyze the data with a chi-square test? (c) If it is appropriate to use a chi-square test, complete the test. Include hypotheses, and give the chi-square statistic, the p-value, and an informative conclusion. (d) If the results are significant, which drug is most effective? Can we conclude that the choice of treatment drug causes a change in the likelihood of a relapse?

Short answer

Firstly, a two-way table is constructed, followed by calculating the expected counts. The chi-square test is appropriate if the expected counts in all cells are greater than 5. The chi-square test is performed by forming hypotheses, calculating the chi-square statistic and the p-value and interpreting the result. If significant, you can identify which drug is most effective but can't conclusively establish causation due to potential lurking variables.

Step-by-step solution

Create a two-way table

Based on the information provided, a two-way table can be produced. The rows represent the different groups (Desipramine, Lithium, and Placebo) and the column represents the number of patients who relapsed and didn't relaps.

Find the expected counts

The expected count for each cell in the table can be found using the formula (row total * column total) / grand total. Each value should be calculated for all cells.

Check for chi-square test applicability

A chi-square test can be applied only if the expected counts for all cells in the table are greater than 5.

Perform the chi-square test

To perform the chi-square test, the null and the alternative hypotheses should be defined first. The null hypothesis will state that there is no association between the type of drug used and the relapse occurrence, while the alternative hypothesis will state that there is an association between the two. Once the hypotheses are set, calculate the chi-square statistic using the formula Σ [ (O-E)^2 / E ], where O stands for the observed frequency and E for the expected frequency. The p-value can be obtained from a chi-square distribution table using the calculated chi-square statistic and the degree of freedom (df) which is (number of rows - 1) * (number of columns - 1).

Conclusion and Interpretation of results

Conclude the chi-square test by comparing the p-value with the significance level (usually 0.05). If the p-value is less than the significance level, then reject the null hypothesis, indicating that there is enough evidence to suggest that the type of drug used has an effect on relapse occurrence. If the results are significant, investigate which drug lead to fewer relapses and hence, is more effective. However, we can only suggest a correlation and not causation based on this data as the study might not take into account other influencing variables.