measures of data spread and variability hypothesis testingquestion 1 a pharmacy practice resident is...
TRANSCRIPT
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Biostatistics
Kevin M. Sowinski, Pharm.D., FCCP
Pharmacotherapy Webinar Review Course
Tuesday, September 3, 2014
I have no conflict of interest to disclose
Conflicts of Interest
Objectives
By the end of this presentation, participants
should be able to:
Describe the appropriate application and
interpretation of statistical tests commonly
encountered in the pharmacotherapy literature.
Differentiate observational and controlled trial
designs
Detect common errors in the presentation and
interpretation the of clinical study designs.
Descriptive statistics: Numerical methods
Measures of Central Tendency
Mean
Used only for continuous and normally distributed data
Median (a.k.a 50th percentile)
Midpoint of the values when placed in order from highest to lowest. Half above and below.
Used for ordinal or continuous data (especially for skewed populations)
Mode
Most common value in a distribution
Used for nominal, ordinal, or continuous data
Data may have > one mode (bimodal, trimodal)
SD: measure of the variability about the mean,
applied to normally distributed, continuous data
Empirical rule: 68% within ±1 SD, 95% within
±2 SD, and 99% within ±3 SD
CV relates the mean to the SD
(SD/mean×100%)
Variance = SD2
Others: Range and Percentiles (IQR)
Measures of Data Spread and Variability
Null hypothesis (H0): No difference between comparator groups (Tx A = Tx B)
Alternative hypothesis (Ha):
States that there is a difference (Tx A Tx B)
Results of “hypothesis testing” will indicate
whether there is enough “evidence” to reject H0
H0 is “rejected”= statistically significant (SS) difference
H0 is “not rejected” = no SS difference
We are not concluding that the treatments are equal.
Hypothesis Testing
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Decision Errors
Probability of making type I error = significance level (α)
Usually α=0.05, 5.0% of the time, we will conclude there is a
SS difference when actually one does not exist.
Calculated chance that a type I error has occurred is called
the “p-value.”
Lower p-value does not suggest more importance, only SS
and less likely attributable to chance
Type II error (b)
Usually b=0.10-0.20
Concluding that no difference exists when one truly
does (not rejecting H0 when it should be rejected)
Statistical Significance Interpreting p-values
Size of p-value is not related to the importance of the result
Statistically significant does not necessarily mean clinically significant
Lack of statistical significance does not mean results are unimportant
Post hoc power calculations
For negative results…
For positive results (reject Ho)….
Confidence Intervals
Can be reported for many different types of analysis
A CI is a range of values that are likely to cover the
true population parameter Difference between two means:
“range” of values along with a point estimate of the difference between the two groups.
A 95 % CI that includes a value consistent with no difference (i.e. 0) can be interpreted as a p 0.05
OR, RR, Hazard Ratio
Statistical significance assessed based on whether bounds of CI include 1
Choosing A Test
Type of
Variable
2 Samples
(independent)
2 Samples
(related)
> 2 Samples
(independent)
> 2 Samples
(related)
Nominal χ2 or Fisher exact test McNemar test χ2 Cochran Q
Ordinal Wilcoxon rank sum
Mann-Whitney U-test
a.k.a Mann-Whitney-
Wilcoxon test
Wilcoxon signed rank
Sign test
Kruskal-Wallis
(MCP)
Friedman ANOVA
Continuous
No factors
Equal variance t-test
Unequal variance t-test
Paired t-test
1-way ANOVA
(MCP)
Repeated-measures
ANOVA
1 factor ANCOVA
2-way repeated-
measures ANOVA
2-way ANOVA
(MCP)
2-way repeated-
measures ANOVA
Vignette 1 (Choosing Appropriate Measures of Central Tendency)
A pharmacy practice resident is planning a project that compares patient satisfaction with the services of a recently established medication therapy management program. She plans to evaluate several outcomes of the program’s impact (e.g., adherence, goal attainment) including patients’ satisfaction with the services provided. Satisfaction will be assessed using a Likert scale-based instrument. The potential responses to the question, are you satisfied with the services provided?
Strongly agree (1), Agree (2), No opinion (3), Disagree (4), Strongly disagree (5)
A pharmacy practice resident is planning a project that compares patient satisfaction with the services of a recently established medication therapy management program. She plans to evaluate several outcomes of the program’s impact (e.g., adherence, goal attainment) including patients’ satisfaction with the services provided. Satisfaction will be assessed using a Likert scale-based instrument. The potential responses to the question, are you satisfied with the services provided?
Strongly agree (1), Agree (2), No opinion (3), Disagree (4), Strongly disagree (5)
Question 1 Which measures of central tendency and data dispersion should be used to compare patient satisfaction between the intervention group and a control group?
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Question 1 (Choosing Appropriate Measures of Central Tendency)
Which measures of central tendency and
data dispersion should be used to
compare patient satisfaction between the
intervention group and a control group?
A. Mean and SD
B. Median and SD
C. Median and IQR
D. Mode and SEM
A pharmacy practice resident is planning a project that compares patient satisfaction with the services of a recently established medication therapy management program. She plans to evaluate several outcomes of the program’s impact (e.g., adherence, goal attainment) including patients’ satisfaction with the services provided. Satisfaction will be assessed using a Likert scale-based instrument. The potential responses to the question, are you satisfied with the services provided?
Strongly agree (1), Agree (2), No opinion (3), Disagree (4), Strongly disagree (5)
Question 1a Which statistical test should be used to compare patient satisfaction between the intervention group and a control group?
Question 1a (Choosing Appropriate Statistical Tests)
Which statistical test should be used to
compare patient satisfaction between the
intervention group and a control of group?
A. Fisher’s Exact Test
B. Mann-Whitney U
C. ANOVA
D. Wilcoxon signed-rank
Question 1a-Follow-Up (Choosing Appropriate Statistical Tests)
If the results were presented and analyzed
in the following way, is there an alternative
analysis that could be used?
SA A NO D SD
Control 40% 24% 25% 6% 5%
Intervention 60% 15% 13% 7% 5%
Vignette 2 (Decision Errors)
A recent study comparing two medications on their ability to lower blood pressure concludes no difference between them (p > 0.05). In reviewing the methods section you read that the investigators calculated their sample size by setting alpha at 0.05 and beta at 0.40.
A recent study comparing two medications on their ability to lower blood pressure concludes no difference between them (p < 0.05). In reviewing the methods section you read that the investigators calculated their sample size by setting alpha at 0.05 and beta at 0.40.
Question 2 Which of the following is the best interpretation of the results of this study?
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Question 2 (Decision Errors)
Which of the following is the best interpretation
of the results of this study?
A. Type I error may have occurred, alpha should
be set at < 0.10
B. Type II error may have occurred, beta
should be set at < 0.20
C. Type I error may have occurred, alpha should
be set at < 0.01
D. Type II error may have occurred, beta should
be set at > 0.40
Vignette 3 (Confidence Intervals)
A randomized controlled trial reports that the difference in LDL-concentrations between a new HMG CoA reductase inhibitor and an existing one is 0.65%. The 95% confidence interval for this difference is (0.15% to 1.1%).
A randomized controlled trial reports that the difference in LDL-concentrations between a new HMG CoA reductase inhibitor and an existing one is 0.65%. The 95% confidence interval for this difference is (0.15% to 1.1%).
Question 3 Which of the following would be an appropriate interpretation of these results?
Question 3 (Confidence Intervals)
Which of the following would be an appropriate
interpretation of these results?
A. There is no statistically significant difference
between this drug and placebo (p > 0.05)
B. There is a statistically significant difference
between this drug and placebo (p < 0.05)
C. There is statistically significant difference between
this drug and placebo (p < 0.01)
D. The authors need to report a p-value to indicate if
the observed difference is statistically significant
Correlation and regression
Correlation examines the strength/degree of association between 2 variables
Correlation coefficient (r) ranges from -1 to +1
Regression analysis examines the ability of one or more variables to predict another variable
e.g., Simple/multiple linear regression, simple/multiple logistic regression, non-linear, polynomial,etc……
Y = mx+ b, CrCl from SeCr, etc….
Coefficient of determination (r2) can range 0 to 1.
An r2 of 0.80: 80% of the variability in Y is “explained”
by the variability in X
Survival Analysis
Studies the time between entry in a study
and some event (e.g., death, MI)
Kaplan-Meier method: Uses survival times to estimate
the proportion of people who would survive a length of
time
Log-Rank Test: Compare the survival distributions > 2
groups
Cox proportional hazards model
Impact of covariates on survival in > 2 groups
Allows calculation of a hazard ratio (and CI)
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Observational Study Design
Summary of Characteristics Study Design Measure of
Association
Major Advantages Major Disadvantages
Case Report/
Case Series
Generate new information about
natural history of Dz
ID new disease/condition
Usually can’t measure rates
of association
Case-control Odds Ratio Study relatively rare outcomes
Low cost and short duration
Not practical for studying rare
exposures
Inability to study multiple
outcomes in one study
Cohort Relative Risk;
Risk Ratio
Study relatively rare outcomes
Study temporal associations
Estimate direct risk estimates
Not practical for studying rare
exposures
Increased cost and longer
duration (prospective)
Cross-sectional Prevalence Low cost and short duration
Temporal associations can’t
be established
Adapted from Pharmacotherapy 2010;30:973-984
Relative vs. Absolute Differences
and NNT
NNT: The reciprocal of the ARR
NNT = 1/(ARR)…Rounded to the next highest
whole number
Medication Placebo Absolute
Difference
Relative
Difference
40% (4/10) 20% (2/10) 20% 50%
4% (4/100) 2% (2/100) 2% 50%
0.4% (4/1000) 0.2% (2/1000) 0.2% 50%
Relative vs. Absolute Differences
and NNT: Calculations
Medication Placebo Absolute Diff Relative Diff ARR NNT
40% (4/10) 20% (2/10) 20% 50% 0.2 5
4% (4/100) 2% (2/100) 2% 50% 0.02 50
0.4%
(4/1000)
0.2%
(2/1000) 0.2% 50% 0.002 500
Superiority: Detect a difference between Txs
Typical design in a clinical trial.
Equivalence: Confirm the absence of
meaningful difference(s) between Txs
What difference is important?
Non-inferiority: Investigate whether a Tx is
not clinically worse (no less effective)
May be the most effective, or have a similar effect.
If placebo is not possible due to ethical reasons
Superiority vs. Equivalence
vs. Non-inferiority
Vignette 4 (Correlation/Regression/Survival Analysis)
In working with some data concerning the occurrence of adverse effects when taking a new drug, you are deciding whether to carry out a correlation analysis or a regression analysis.
In working with some data concerning the occurrence of adverse effects when taking a new drug, you are deciding whether to carry out a correlation analysis or a regression analysis.
Question 4
Which of the following would be an appropriate consideration in making this decision?
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Question 4 (Correlation/Regression/Survival Analysis)
Which of the following would be an appropriate
consideration in making this decision?
A. Correlation analyses require more data than
regression analysis
B. Regression analyses are useful for detecting
only linear relationships between variables
C. Correlation analyses work best for data that
has been collected in retrospective trials
D. Regression analyses are useful in
predicting the value of one variable based
upon the value of another variable
Vignette 5 (Relative Risk/Odds Ratios)
A case-control trial (n = 102 cases, n = 650 controls) reports that the odds ratio (OR) for myocardial infarction (MI) is 0.7 (95% CI: 0.5, 0.9) in persons who have a history of receiving a certain vaccine in childhood.
A case-control trial (n = 102 cases, n = 650 controls) reports that the odds ratio (OR) for myocardial infarction (MI) is 0.7 (95% CI: 0.5, 0.9) in persons who have a history of receiving a certain vaccine in childhood.
Question 5
Which of the following represents the best interpretation of this result?
Question 5 (Relative Risk/Odds Ratios)
Which of the following represents the best
interpretation of this result?
A. This is a statistically significant difference; the vaccine is associated with a lower risk of MI
B. This is not a statistically significant difference; the vaccine is not associated with a lower risk of MI
C. This is a statistically significant difference; the vaccine decreases the risk of MI
D. This is not a statistically significant difference; the vaccine does not increase the risk of MI
Vignette 6 (Clinical Trials: Randomization Issues)
A randomized, double blind trial is conducted to determine if a new anti-ischemic drug improves symptoms in patients with stable angina and coronary artery disease. Patients are randomized to either the new drug or placebo, in additional to continuing existing standard medications. The intention-to-treat analysis shows no statistical difference in treatments. An actual treatment analysis showed that the new drug was more effective than placebo. Patients who did not take at least 70% of the study drug were reclassified as placebo for the actual treatment analysis.
A randomized, double blind trial is conducted to determine if a new anti-ischemic drug improves symptoms in patients with stable angina and coronary artery disease. Patients are randomized to either the new drug or placebo, in additional to continuing existing standard medications. The intention-to-treat analysis shows no statistical difference in treatments. An actual treatment analysis showed that the new drug was more effective than placebo. Patients who did not take at least 70% of the study drug were reclassified as placebo for the actual treatment analysis.
Question 6 Which one of the following is the best course of action based on these results?
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Question 6 (Clinical Trials: Analysis Issues)
Which one of the following is the best course of
action based on these results?
A. Recommend the new drug for all patients with HF
B. Recommend the new drug for patients who adhere
to their current therapies
C. Recommend the new drug only for early-stage HF
D. Do not recommend the new drug, wait for
further studies
Vignette 7 (Meta-analysis)
A meta-analysis of 6 randomized, placebo-controlled trials investigating the association between influenza vaccine and cardiovascular outcomes was performed, the results are shown in the figure below.
10 1 0.1
RR
A meta-analysis of 6 randomized, placebo-controlled trials investigating the association between influenza vaccine and cardiovascular outcomes was performed, the results are shown in the figure below.
Question 7 Which one of the following is the following is the best interpretation of these results, as shown in the figure?
10 1 0.1
RR
Question 7
(Meta-analysis)
Which one of the following is the following is the
best interpretation of these results, as shown in the
figure?
A. Influenza vaccine is not associated with a change in
the risk of major adverse CV events
B. Influenza vaccine is associated with a significantly
lower risk of major adverse CV events
C. Influenza vaccine is associated with a significantly
higher risk of major adverse CV events
D. Influenza vaccine’s effect on major adverse CV events
cannot be determined from the figure
Vignette 8 (Relative and Absolute Differences, NNT)
A trial comparing a new antibiotic to ciprofloxacin in the treatment of uncomplicated urinary tract infections shows that 88% of patients receiving the new drug were symptom-free at 3 days, while 82% of the ciprofloxacin patients were symptom-free at 3 days (p < 0.05).
A recent trial comparing a new antibiotic to ciprofloxacin in the treatment of uncomplicated urinary tract infections shows that 88% of patients receiving the new drug were symptom-free at 3 days, while 82% of the ciprofloxacin patients were symptom-free at 3 days (p < 0.05).
Question 8 How many patients would need to be treated with the new drug to have one additional patient symptom-free at 3 days?
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Question 8 (Relative and Absolute Differences, NNT)
How many patients would need to be treated with
the new drug to have one additional patient
symptom-free at 3 days?
A. 2
B. 6
C. 17
D. 167
Vignette R1 (Choosing Appropriate Statistical Tests)
A study compares the plasma concentrations of a new antiretroviral medication both with and without the concomitant administration of ganciclovir. Patients will take a fixed-dose of the new medication and have steady-state plasma concentrations evaluated before receiving ganciclovir and again 2 weeks later after having received ganciclovir for 48 hours.
A study compares the plasma concentrations of a new antiretroviral medication both with and without the concomitant administration of ganciclovir. Patients will take a fixed-dose of the new medication and have steady-state plasma concentrations evaluated before receiving ganciclovir and again 2 weeks later after having received ganciclovir for 48 hours.
Question R1 To determine whether there are differences in steady-state plasma concentrations, which test should be used to compare the results of this investigation?
Question R1 (Choosing Appropriate Statistical Tests)
To determine whether there are differences
in steady-state plasma concentrations,
which test should be used to compare the
results of this investigation?
A. Independent samples t-test
B. Chi-squared with Bonferroni correction
C. Paired t-test
D. Kruskal-Wallis ANOVA
Vignette R2 (Decision Errors)
You are planning a trial to compare the incidence of major depression recurrence with 12 months of antidepressant treatment compared with 24 months of treatment.
You are planning a trial to compare the incidence of major depression recurrence with 12 months of antidepressant treatment compared with 24 months of treatment.
Question R2 Which of the following strategies could be used to increase the power to detect any differences?
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Question R2 (Decision Errors)
Which of the following strategies could be used to increase the power to detect any differences?
A. Decrease the sample size
B. Decrease alpha
C. Decrease beta
D. Decrease the size of the difference you wish to detect
Vignette R3 (Confidence Intervals)
In a large (n=4218) randomized controlled trial a new drug is compared to placebo to assess its effect on raising HDL cholesterol. Compared to placebo the new drug is demonstrated to increase HDL cholesterol by 2 mg/dL, 95% CI (0.6, 3.4).
In a large (n=4218) randomized controlled trial a new drug is compared to placebo to assess its effect on raising HDL cholesterol. Compared to placebo the new drug is demonstrated to increase HDL cholesterol by 2 mg/dL, 95% CI (0.6, 3.4).
Question R3 Which of the following represents the best interpretation of such results?
Question R3 (Confidence Intervals)
Which of the following represents the best
interpretation of such results?
A. The results are neither statistically, nor clinically
significant (i.e., don’t use the drug)
B. The results are not statistically significant, but are
clinically significant (i.e., use the drug)
C. The results are statistically significant, but may not
be clinically significant
D. The results are statistically significant, and clinically
significant
Vignette R4 (Relative Risk/Odds Ratios)
A cohort study reports a relative risk (RR) of breast cancer of 1.4 (1.1,1.7) in women who reported having used an over-the-counter, herbal “antidepressant” in the past 5 years.
A cohort study reports a relative risk (RR) of breast cancer of 1.4 (1.1,1.7) in women who reported having used an over-the-counter, herbal “antidepressant” in the past 5 years.
Question R4 Which of the following is the best way to interpret these results?
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Question R4 (Relative Risk/Odds Ratios)
Which of the following is the best way to interpret these
results?
A. the herbal product should not be used, it increases
the risk of breast cancer substantially
B. the herbal product may be associated with
increased risk of breast cancer
C. the herbal product is not associated with any
increase in breast cancer risk
D. the herbal product appears safe and effective
Vignette R5 (Regression Analysis)
A study was conducted investigating the relationship between a the dose of a beta-agonist and FEV1. The results shown in the figure were: r=-0.46, p<0.05.
A study was conducted investigating the relationship between the dose of a beta-agonist and FEV1. The results shown in the figure were: r=-0.46, p<0.05.
Question R5 Which of the following represents the percent in the variability in FEV1 that is explained by the variability in the dose of the beta-agonist?
Question R5 (Regression Analysis)
Which of the following represents the percent in the
variability in FEV1 that is explained by the variability in
the dose of the beta-agonist?
A. 70 percent
B. 21 percent
C. 46 percent
D. 92 percent
Question R5-Follow-Up (Regression Analysis)
When reporting the results in the table as described,
was the reporting correct?
If not, which statistical parameter is more appropriate
to report in this situation?
Vignette R6 (Meta-analysis)
In reporting the results of a meta-analysis designed to assess the impact of pharmacist interventions to improve medication adherence, the authors report the results of their analyses testing their data for heterogeneity.
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In reporting the results of a met-analysis designed to assess the impact of pharmacist interventions to improve medication adherence, the authors report the results of their analyses testing their data for heterogeneity.
Question R6 Which of the following would be appropriately associated with such an analysis?
Question R6 (Meta-analysis)
Which of the following would be appropriately
associated with such an analysis?
A. The use of ANOVA
B. The reporting of a Χ2 or Cochrane’s Q test
C. A summary odds ratio
D. A regression analysis using multivariate techniques
Vignette R7 (Risk Reduction and NNT)
The results of a prospective, randomized, double-blind, placebo-controlled trial show that over a 6-month period 27/1232 patients receiving a medication required hospitalization for symptoms of asthma, while 42/1230 patients receiving the gold standard therapy required hospitalization for symptoms of asthma (p < 0.05).
The results of a prospective, randomized, double-blind, placebo-controlled trial show that over a 6-month period 27/1232 patients receiving a medication required hospitalization for symptoms of asthma, while 42/1230 patients receiving the gold standard therapy required hospitalization for symptoms of asthma (p < 0.05).
Question R7 Which of the following statements best represents these results?
Question R7 (Risk Reduction and NNT)
Which of the following statements best represents
these results?
A. Relative Reduction in events = 35%, NNT = 83
B. Relative reduction in events = 55%, NNT = 8
C. Relative reduction in events = 15%, NNT = 83
D. Relative reduction in events = 83%, NNT = 35
Vignette E1 (Approaches to Analyses)
In deciding an approach to statistical analysis, investigators wish to focus on demonstrating the maximum effectiveness of a new medication when it is used correctly.
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In deciding an approach to statistical analysis, investigators wish to focus on demonstrating the maximum effectiveness of a new medication when it is used correctly.
Question E1 In pursuing such a goal, which of the following types of analysis would be most appropriate?
Question E1 (Approaches to Analyses)
In pursuing such a goal, which of the
following types of analysis would be most
appropriate?
A. Intention-to-treat
B. Intention-to-randomize
C. Per-protocol
D. As-treated
Vignette E2 (Composite End-Points)
During your residency program you are presenting a journal club article regarding a new drug for hypertension. The primary outcome of the study is the occurrence of the combination of stroke, myocardial infarction (MI), and cardiovascular (CV) death.
During your residency program you are presenting a journal club article regarding a new drug for hypertension. The primary outcome of the study is the occurrence of the combination of stroke, myocardial infarction (MI), and cardiovascular (CV) death.
Question E2 In discussing this trial during your departmental journal club, which of the following would be appropriate comments regarding this type of end-point?
Question E2 (Composite End-Points)
In discussing this trial during your departmental journal club, which of the following would be appropriate comments regarding this type of end-point?
A. Composite end-points provide increased power, without any risks to trial validity or interpretability
B. Composite end-points create additional issues around multiple (statistical) testing
C. Composite end-points that combine non-fatal outcomes with death are the most robust
D. Composite end-points that include “soft” (i.e., subjective) end-points can be unduly influenced by one or more component end-points
Vignette E3 (Subgroup Analysis)
In a study of a new drug used to treat heart failure the authors describe several subgroups that were analyzed separately after the trial concluded based upon age, sex, and smoking history, history of stroke, and history of diabetes. They report that while the drug did not show effectiveness in the overall sample, that patients who were greater than 70 years of age did benefit from decreased hospitalizations due to HF (p < 0.05).
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In a study of a new drug used to treat heart failure the authors describe several subgroups that were analyzed separately after the trial concluded based upon age, sex, and smoking history, history of stroke, and history of diabetes. They report that while the drug did not show effectiveness in the overall sample, that patients who were greater than 70 years of age did benefit from decreased hospitalizations due to HF (p < 0.05).
Question E3 Which of the following statements represents the best interpretation of these results?
Question E3 (Subgroup Analysis)
Which of the following statements represents the
best interpretation of these results?
A. Patients over 70 years old with HF should
receive the medication
B. Any patient with HF should receive the
medication
C. Post-hoc subgroup analyses like this one,
should be considered hypothesis
generating
D. Any patient with HF and additional risk factors
should receive the medication
Vignette E4 (Descriptive Statistics)
A drug interaction study is conducted to assess the effects on the time to maximum concentrations (Tmax) of one drug when a p-glycoprotein inhibitor is taken concomitantly.
A drug interaction study is conducted to assess the effects on the time to maximum concentrations (Tmax) of one drug when a p-glycoprotein inhibitor is taken concomitantly.
Question E4 Which of the following would be the best way to report the results of this study?
Question E4 (Descriptive Statistics)
Which of the following would be the best way to
report the Tmax results of this study?
A. Mode and SEM
B. Mean and median
C. Median and range
D. Mean and standard deviation
Vignette E5 (Observational Study Designs)
You wish to investigate whether or not patients being treated pharmacologically for hypertension have an increased occurrence of memory loss. This hypothesis was suggested by a recent first-ever case-series published in the medical/pharmacy literature. You also hope to ascertain if certain medications or medication classes have more or less of this potential effect on memory.
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You wish to investigate whether or not patients being treated pharmacologically for hypertension have an increased occurrence of memory loss. This hypothesis was suggested by a recent first-ever case-series published in the medical/pharmacy literature. You also hope to ascertain if certain medications or medication classes have more or less of this potential effect on memory.
Question E5 Which of the following would be an appropriate strategy for investigating this hypothesis initially?
Question E5 (Observational Designs)
Which of the following would be an appropriate
strategy for investigating this hypothesis initially?
A. cohort trial
B. case-control trial
C. randomized, controlled trial
D. meta-analysis