Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 10 - Treating Depression Lab Part 4 (discussion 2)

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2026-01-17T21:14:46-08:00

1. Here are the descriptive statistics and side-by-side boxplots. (Placebo: Treat = 0; Imipramine: Treat = 1; Lithium: Treat = 2). Numbers represent weeks to relapse into depression.

Summary statistics for Time:
Group by: Treat

Treat | n | Mean | Variance | Std. dev. | Std. err. | Median | Range | Min | Max | Q1 | Q3
0 | 37 | 37.725919 | 1666.5156 | 40.822979 | 6.7112564 | 22 | 164.714 | 0.28600001 | 165 | 5.2859998 | 67
1 | 38 | 63.063868 | 2448.794 | 49.485291 | 8.0275742 | 70.714001 | 205.429 | 0.57099998 | 206 | 22 | 102
2 | 34 | 37.584059 | 1621.2744 | 40.265052 | 6.9053995 | 17.785999 | 131 | 0 | 131 | 5 | 63.714001

2. Shape: All three distributions are skewed right (or in this case upwards), which means that the upper half of each distribution has more variability than the lower half. The Placebo and Lithium groups have a stronger right skew, which tells us that the half of the patients below the median tend to relapse into depression relatively quickly.

Center: The distribution of Time in the Imipramine group (coded as 1) has a substantially larger median (70.71 weeks) compared to the other two groups, whose medians are not very different (Placebo: 22 weeks vs. Lithium: 17.79 weeks).

Spread: When we take the variability about the medians into account, we can see that typical relapse times, as measured by the intervals Q1 to Q3, overlap. (Placebo: about 5 to 67 weeks; Imipramine: 22 to 102 weeks; Lithium: about 5 to 64 weeks.) This suggests that the differences we see among the medians is not substantial when viewed in light of the variability about the medians. Particularly noteworthy is the large IQR (roughly 80 weeks) for the Imipramine group. This tells us that Imipramine did not produce consistent results.

3. The results from this study suggest Lithium performs like a placebo, with similar median time to relapse and similar intervals of typical times relapse as represented by Q1 to Q3. The results also suggest that on average Imipramine (median = 71 weeks) is more effective in delaying the recurrence of depression compared to Lithium (median = 18 weeks) or a placebo (median = 22 weeks). However, Imipramine did not produce consistent results; there was a lot of variability overall (range ~ 205 weeks) and also in the middle half of the distribution (IQR ~ 80 weeks.) Because of this variability, the interval of typical relapse times for Imipramine overlapped with the intervals of typical relapse times for Lithium and the placebo. Therefore, when we take variability into account, this data does not suggest that Imipramine is substantially better than the two other treatments.

4. In this exercise we assessed the effectiveness of Lithium and Imipramine as treatments for depression. The two measures of effectiveness were whether or not recurrence of depression occurred, and the time until the recurrence. We found that patients who were treated with Imipramine were less likely to have a recurrence of depression, and if they did, it took longer on average for the recurrence to occur compared to patients who were treated with Lithium or a placebo. But we also found that Imipramine did not produce consistent results and the variability dwarfed any differences we observed in average time to relapse.

Perhaps the most definitive finding is that Lithium does not appear to be an effective treatment for depression. Patients treated with Lithium did not display any substantial differences compared to patients who did not receive any treatment, both in terms of an occurrence of depression, and in terms of the time until a recurrence.