1.Clinical Trial of Contraception (Source: Machin et al., 1988)

This is another longitudinal clinical trial, where women received an injection of either 100 mg or 150 mg of depot-medroxyprogesterone acetate (DMPA) on the day of randomiza- tion and three additional injections at 90-day intervals. There was a final follow-up visit 90 days after the fourth injection, i.e., one year after the first injection. Throughout the study each woman completed a menstrual diary that recorded any vaginal bleeding pat- tern disturbances. The diary data were used to determine whether a women experienced amenorrhea, the absence of menstrual bleeding for a specified number of days. A total of 1151 women completed the menstrual diaries and the diary data were used to generate a binary sequence for each woman according to whether or not she had experienced amen- orrhea in the four successive three month intervals. In clinical trials of modern hormonal contraceptives, pregnancy is exceedingly rare (and would be regarded as a failure of the contraceptive method), and is not the main outcome of interest in this study. Instead, the outcome of interest is a binary response indicating whether a woman experienced amenor- rhea in the four successive three month intervals. A major problem of this clinical trial is that there was substantial dropout. The dataset, amenorrheaFinal.dat, was uploaded into the Canvas and the variables are defined as follows.

Variable list

ID=Patient ID

Dose=Dose (0=Low (100mg),1=High (150mg)) Month=four successive three month intervals

Status=Amenorrhea Status (1=Amenorrhea,0=No Amenorrhea,.=Missing)

Questions

Based on the description of the study above, the following research questions are of main interest and apply your LDA knowledge to answer them.

(a)Fit a marginal model that describes the eect of month, Dose and interaction between Dose and month on the probability of having Amenorrhea over time.Summarize your results. What conclusions do you draw about the eects of dose on changes in the probability of having Amenorrhea over time? Provide results that support your conclusion.

i.Based on the final results from above, compute the predicted probability that a patient receiving Low Dose will have Amenorrhea over time.

ii.Compute the predicted probability that a patient receiving High Dose will have Amenorrhea over time.

iii.Plot the computed probabilities on the same graph. Interpret the result.