Fill the blanks in the following table:
| Term | Description |
|---|---|
| Descriptional study | |
| Analytical study | |
| Observational study | |
| Interventional study | |
| Retrospective study | |
| Prospective study | |
| Ecological study | |
| Ecological fallacy | |
| Prevalence | |
| Incidence | |
| Cumulative incidence rate | |
| Incidence rate | |
| Case report | |
| Case series | |
| Cross-sectional study | |
| Ecological study | |
| Case-control study | |
| Cohort study | |
| Bias | |
| Selection bias | |
| Recall bias | |
| Randomized controlled trial | |
| Randomized clinical trial | A study where participants receive or or more treatments to answer questions about the safety and/or efficacy of the treatments |
| Parallel design | A trial design where each subject is assigned to either experimental treatment or control group. |
| Cossover design | A trial design where every subject serves as his/her own control |
| Factorial design | |
| Randomization | |
| Simple randomization | |
| Complete randomization | |
| Efron's biased coin randomization | |
| Wei's urn randomization | |
| Cluster randomization | |
| Stratified randomization | |
| Minimization randomization | A dynamic randomization strategy in a clinical trial to balance the assignment in the groups. |
| Superiority design | A trial design whose aim is to show that the efficacy of the experimental treatment is better than that of control. |
| Equivalence design | A trial design whose aim is to show that the results of experimental and control treatment differ by an clinically non-significant amount |
| Non-inferiority design | A trial whose objective is to validate that the results of a treatment are not much worse from the control treatment |
| Blinding | A strategy in a clinical trial where one or more parties involved (e.g., participants, clinicians, statisticians) do not know the treatment assignment for randomized groups. |
| Open-label | A strategy in a clinical trial where all parties know the treatment assignment. |
| Single-blinded | A blinding strategy in a clinical trial where only the participants have no idea of the treatment assignment. |
| Double blinded | A blinding strategy in a clinical trial where neither participants nor clinicians know the treatment assignment. |
| Triple blinded | A blinding strategy in a clinical trial where participants, clinicians and statisticians do not know the treatment assignment. |
| PROBE | Prospective, randomized, open-label |
| Protocol | A document describing the objectives, design, statistical consideration etc. of a certain clinical trial. |
| Intention-to-treat analysis | An analysis that is analyzing every randomized subject as assigned to their randomized treatment group (including violators) |
| Per-protocol analysis | Choose only the participants who perfectly follow the protocol (excluding the protocol violators). |
| As-treatment analysis | Analyzing the results based on the participants real treatment. |
| t-test | A statistical testing method to compare the means for two groups with normal distributions. |
| Paired t-test | A statistical testing method for comparing the means of two matched paired groups. |
| Wilcoxon rank-sum test | A nonparametric testing method for comparing two medians of two independent groups. |
| Wilcoxon signed rank test | A nonparametric testing method for comparing two medians of two correated groups. |
| Chi-squared test | |
| Fisher's exact test | |
| McNemar's test | |
| Analysis of variance (ANOVA) | |
| Analysis of covariance (ANCOVA) | |
| Repeated measures ANOVA | |
| Friedman's test | |
| Cochrane's Q test | |
| Missing data imputation | |
| Dropouts | |
| Fixed-value imputation | An imputation strategy that substitutes each missing or dropout value with a fixed value generated by ad-hoc aprpoach. |
| Multiple imputation | |
| Last observation carried forward (LOCF) | One fixed-value imputation strategy by filling the missing data with the last non-missing value of the same subject. |
- Use R to draw the density curve of
$X \sim N(0, 5)$ and$Y \sim N(2, 5)$ , and mark the type I error$\alpha=0.05$ and the corresponding Type II error$\beta$ . - A randomized clinical trial is designed to evaluate the efficacy of a newly developed drug to reduce pain in patients after joint replacement surgery by comparing with the standard care. 100 patients were assigned to receive either the new drug or the standard care. The primary outcome was a reduction of 3 or 3+ scale points (clinically meaningful reduction). The data are summarized in the following table:
| Treatment | #patients with 3+ reduction | proportion | |
|---|---|---|---|
| New drug | 50 | 23 | 0.46 |
| Stanard care | 50 | 11 | 0.22 |
- How would you analyze the data for this superiority design? Write down the R code.
- A small randomized clinical trial was conducted to test whether treatment
$A$ (new drug) was effective in lowering DBP as compared to$B$ (standard) and to describe changes in DBP across times at which it was measured (DBP.dat).
- Are the baseline (DBP1) and the potential confounding factors balanced in these two groups? How to analyze? Write down the R code and also the results and conclusion.
- Is the treatment
$A$ more effective in lowering the DBP than$B$ ? Use the parametric methods, adjusted by the confounders. - Can you analyze the data using the nonparametric methods?
- Or permutation-based method? Or even bootstrap-based methods?
- Bioequivalence, crossover clinical trial
In this exercise we will use a dataset from a bioequivalence clinical trial described in Chow and Liu
(2009). The trial utilized a standard two-sequence (i.e., 1=RT and 2=TR), two-period, two-formulation
(T=Test; R=Reference) (i.e.,
$2 \times 2 \times 2$ ) crossover design to compare two oral formulations of a drug, and was conducted with 26 healthy volunteers (subjects). Subjects were randomized to either five 50mg tablets (T) or 5 mL of a suspension (R) at the first period baseline, and then crossed over to the alternative formulation at the second period baseline. And the bioavailability outcome is the area under the concentration-by-time curve (AUC) over the interval from 0 to 48 hours. The data file isChowLiu2009data.csv.
- Write an R code to compute the area under the concentration-by-time curve (AUC):
$$
AUC = \sum_{\tau=1}^k \frac{(c_{\tau}+c_{\tau-1})\times (t_{\tau} - t_{\tau-1})}{2}
$$
where
$t_{\tau}$ is the$\tau$ -th time point of blood sample collection and$c_{\tau}$ is the$\tau$ -th blood or plasma concentration and$\tau=0,1,2,\dots,k$ . - Test for the carryover effect
- Compute the subject totals across two periods:
$$
U_{ik} = Y_{i1k} + Y_{i2k}
$$
where
-
- Calculate the sample mean across all the subjects in each sequence: $$ \overline{U_{*k}} = \frac{1}{n_k} \sum_{i=1}^{n_k} U_{ik}, k=1,2 $$
- Compute the differential carryover effect
$C$ :
$$
\hat{C} = \overline{U_{*2}} - \overline{U_{*1}}
$$
-
$\hat{C}$ is normally distributed with mean$C$ and variance: $$ \widehat{Var}(\hat{C}) = \hat{\sigma_u^2}(\frac{1}{n_1} + \frac{1}{n_2}) $$ and
$$
\hat{\sigma_u^2} = \frac{1}{n_1+n_2-2}\sum_{k=1}^2 \sum_{i=1}^{n_k} (U_{ik} - \overline{U_{*k}})^2 $$
- Compute the statistic: $$ T = \frac{\hat{C}}{\sqrt{\widehat{Var}(\hat{C})}} \sim t(n_1 + n_2 - 2) $$
- Compute the
$p$ -value, and draw the conclusion.
- Test for direct formulation effect:
- Compute the difference in periods for each subject within each sequence: $$ d_{ik} = \frac{1}{2}(Y_{i2k} - Y_{i1k}), i=1,\dots,n_k; k=1,2 $$
- Compute the sample means for the period differences for each sequence: $$ \overline{d_{*k}} = \frac{1}{n_k} \sum_{i=1}^{n_k} d_{ik} $$
- Compute the direct differential formulation effect: $$ \hat{F} = \overline{d_{*1}} - \overline{d_{*2}} $$
- If no carryover effect,
$\hat{F} \sim N(F, \widehat{Var}(\hat{F}))$ , where- (1)
$\widehat{Var}(\hat{F}) = \hat{\sigma}_d^2(\frac{1}{n_1} + \frac{1}{n_2})$ - (2)
$\hat{\sigma}^2_d = \frac{1}{n_1+n_2-2} \sum_{k=1}^2 \sum_{i=1}^{n_k}(d_{ik} - \overline{d}_{*k})^2$
- (1)
- Similarly, compute the
$t$ -statistic: $$ T_F = \frac{\hat{F}}{\sqrt{\widehat{Var}(\hat{F})}} $$ - Compute the
$p$ -value and reach the conclusion.
- Analysis of variance (ANOVA)
Data <- data.frame(subj = as.factor(dat$subj),
formu = as.factor(dat$formulation),
seq = as.factor(dat$seq),
prd = as.factor(dat$prd),
auc = dat$auc)
summary(aov(auc ~ seq*formu + Error(subj), data=Data))
- Two one-sided t-test
FDA has specified a decision criterion for concluding bioequivalence of a test formulation (T) to a reference formulation (R): T is bioequivalent to R if the 90%CI on the ratio of the mean of T to the mean of R is between 80% and 125% for bioequivalent outcome AUC.
- Compute the mean AUC for each formulation
- Determine the decision CI
$(\theta_L, \theta_R)$ for the difference in means calculated using the mean of the reference formulation (R). - Use two one-sided t-test to validate the bioequivalence of the two formulations. $$ \begin{aligned} T_L = \frac{\overline{Y}_T - \overline{Y}_R - \theta_L}{\sqrt{\hat{\sigma}_d^2 (\frac{1}{n_1} + \frac{1}{n_2})}}\\ T_U = \frac{\overline{Y}_T - \overline{Y}_R - \theta_U}{\sqrt{\hat{\sigma}_d^2 (\frac{1}{n_1} + \frac{1}{n_2})}} \end{aligned} $$