PHEBP: Precision in Estimates of Treatment Effects

Question 1

How to Interpret a confidence interval for a sample estimate

Answer 1

A confidence interval (CI) provides a range of values, derived from a statistical procedure, that is likely to contain the true value of an unknown population parameter

In other words, a confidence interval quantifies the uncertainty in estimation

It’s usually presented with a confidence level that quantifies the level of confidence that the parameter lies within the interval. Commonly used confidence levels include 95% and 99%

Interpretation of a Confidence Interval:

Suppose you have a 95% confidence interval for a sample mean estimate that ranges from 5 to 10

1) Correct Interpretation:

• You can be 95% confident that the true population mean is between 5 and 10
• In other words, if you were to take many samples and build a confidence interval from each sample, you’d expect about 95% of those intervals to contain the true population mean

2) Incorrect Interpretation:

• It does not mean that 95% of the sample data falls between 5 and 10, nor does it mean there’s a 95% probability that the true population mean is between 5 and 10
• The confidence level is about the method used to build the interval, not about specific intervals from specific samples

How it relates to precision:

• A narrower confidence interval indicates greater precision because the estimate is pinned down to a smaller range of values
• A wider interval suggests less precision
• The width of the confidence interval depends on the standard error of the estimate and the sample size
• For example, if you have two confidence intervals for the mean difference in blood pressure after a treatment, one from Study A: 5 to 15 mmHg (a 10 mmHg interval) and another from Study B: 7 to 12 mmHg (a 5 mmHg interval), Study B provides a more precise estimate of the treatment effect than Study A

Purpose:

This precision in the estimate is particularly valuable in biomedical science and health care, where decisions about implementing new treatments need to balance effectiveness (evidenced by point estimates) against uncertainties in their effectiveness (evidenced by confidence intervals)

Question 2

Describe how estimates are based on samples from a population and recall potential biases that can arise

Answer 2

When conducting research, it’s often impossible or impractical to gather data from every individual in a population

As a result, scientists use samples, or subsets of the population, to make inferences about the population as a whole

As a result, scientists use samples, or subsets of the population, to make inferences about the population as a whole

How Estimates are based on samples:

1. Sample Selection: Researchers choose a sample from the population intended to represent that population. The manner in which the sample is selected can significantly impact how representative it is of the population
2. Data Collection: Researchers choose a sample from the population intended to represent that population. The manner in which the sample is selected can significantly impact how representative it is of the population
3. Data Analysis: Researchers analyse the data, often using statistical methods, to make an estimate about a population parameter (such as the mean, proportion, correlation coefficient, etc.)
4. Inference: Researchers infer from the sample data to the population. The sample estimate is used to provide an approximation of the true population parameter

Potential Biases in Sampling and Estimation:

Bias refers to systematic errors that can skew results in one direction. Several types of bias can impact the reliability of estimates:

1. Selection Bias: This occurs when the sample is not representative of the population. It could be due to non-random sampling or non-response bias (where certain kinds of individuals are less likely to respond)
2. Information Bias: This can occur due to inaccuracies in the way data is collected, measured, or interpreted. Examples include recall bias (where participants do not accurately remember past events) and observer bias (where the researchers’ expectations influence the measurement or interpretation of results)
3. Confounding Bias: This occurs when the effect of one factor (a confounding variable) on the outcome of interest is mixed up with the effect of the factors under study

To reduce the effect of these biases, researchers use strategies like random sampling, blinding, ensuring the validity and reliability of data collection tools, and adjusting for confounding variables in the analysis. Despite these measures, it’s important to remember that all estimates have a degree of uncertainty, often quantified through confidence intervals

Question 3

Describe how sample size can influence the confidence interval

Answer 3

Sample size is an essential factor in determining the width of a confidence interval, which is an estimate of the uncertainty around a measured value or statistic

As the sample size increases, the confidence interval around an estimate typically becomes narrower, assuming all other factors are constant

This is because a larger sample size reduces the standard error of the estimate, leading to a tighter confidence interval

This is because:

1) Precision and Accuracy:

• Larger sample sizes tend to provide estimates that are closer to the true population parameter, enhancing precision.
• In statistical terms, larger samples decrease the standard error of the estimate, which directly influences the width of the confidence interval.
• As the standard error decreases, the confidence interval narrows, indicating more precision

2) Reduced Variability:

• Larger samples are also more likely to be representative of the population from which they are drawn, reducing the likelihood of sampling bias and providing a better approximation of the population variance

3) Consistent Results:

• A larger sample size increases the likelihood that the study’s results can be replicated, an important aspect of scientific research

Question 4

Explain how the interpretation for a confidence interval differs between ratio and absolute differences

Answer 4

A confidence interval (CI) provides a range of values that likely contains the true population value for a parameter, and the way to interpret it depends on the type of measure it’s applied to

Two commonly used measures in biomedical research are ratio measures (like relative risk or odds ratio) and absolute difference measures (like risk difference)

1) Confidence interval for a ratio measure:

When interpreting a confidence interval for a ratio measure (like a relative risk or odds ratio), the key value of interest is typically 1

• If the CI includes 1, then we cannot conclude there is a statistically significant difference between the groups because 1 implies a ratio of event rates or odds that are identical in both groups
• If the entire CI is above 1, the risk or odds of the outcome is significantly higher in the exposed (or treatment) group than in the unexposed (or control) group
• If the entire CI is below 1, the risk or odds of the outcome is significantly lower in the exposed (or treatment) group than in the unexposed (or control) group

**2) Confidence Interval for an Absolute Difference Measure:

When interpreting a confidence interval for an absolute difference measure (like risk difference), the key value of interest is typically 0

• If the CI includes 0, we cannot conclude there’s a statistically significant difference between the groups because 0 implies no difference in rates between the two groups
• If the entire CI is above 0, the rate or mean is significantly higher in the exposed (or treatment) group than in the unexposed (or control) group
• If the entire CI is below 0, the rate or mean is significantly lower in the exposed (or treatment) group than in the unexposed (or control) group

Question 5

What are some key concepts around the study design of clinical trials

Answer 5

1) Randomisation:

• the process of randomly allocating participants into either the treatment group or the control group
• It helps to reduce selection bias and ensures that known and unknown confounding factors are evenly distributed between the groups, making any differences in outcomes more likely to be due to the treatment

2) Control Group:

• A control group is necessary to compare the effect of the treatment
• The control group may receive a placebo (an inactive substance that looks like the treatment), standard treatment, or no treatment, depending on the trial design and ethical considerations

3) Blinding:

• Blinding (or masking) refers to hiding the treatment allocation from the participants, caregivers, or those assessing the outcomes to prevent bias

4) Primary and Secondary Outcomes:

• Before the trial begins, researchers define primary and secondary outcomes
• The primary outcome is the main question that the trial is aiming to answer, while secondary outcomes are other questions of interest
• Defining these outcomes in advance helps to prevent outcome reporting bias or cherry-picking results

5) Sample Size:

• The sample size of the trial needs to be large enough to detect a meaningful difference between the treatment and control groups, if one exists

6) Ethical Approval and Informed Consent:

• All clinical trials must receive ethical approval before they start, to ensure they will be conducted in a way that respects the rights and safety of the participants
• Informed consent must also be obtained from all participants, meaning they have been fully informed about the trial’s purpose, what it will involve, any potential risks and benefits, and their rights to withdraw at any time

7) Data Analysis:

• The statistical analysis plan should be pre-specified before the trial begins to avoid data-driven results or p-hacking
• The plan includes the specific methods that will be used to compare the outcomes in the treatment and control groups, handle missing data, and adjust for any potential confounders

8) Monitoring and Reporting:

• Trial data should be monitored for safety and efficacy, and serious adverse events must be reported promptly
• The results of the trial should be reported in a transparent and complete manner, regardless of the findings

Question 6

How would you interpret results of clinical trials (including point estimates, confidence intervals and probability value

Answer 6

Interpreting results from clinical trials involves analysing key pieces of data: point estimates, confidence intervals (CIs), and p-values

Point Estimates:

• A point estimate is a single value that represents the best guess or most probable value of the unknown population parameter based on the sample data
• E.g. a point estimate might be the mean difference in blood pressure between two treatment groups or the relative risk of disease in a treated group versus a control group
• Interpretation: The point estimate gives the most likely effect of the treatment. However, it’s important to remember that this is just an estimate, and the true population parameter might be different

Confidence Intervals (CIs):

• A confidence interval gives a range of values that likely contains the true population parameter
• The interval is based on the point estimate and takes into account the variability in the data (standard error) and the desired level of confidence (often 95%)
• Interpretation: If a 95% CI for a mean difference or relative risk includes 0 or 1, respectively, the result is not statistically significant at the 0.05 level, meaning the difference or ratio observed could be due to chance. If the CI doesn’t include 0 or 1, the result is statistically significant. The CI also gives a range of plausible values for the true effect size

Probability Values (p-values):

• A p-value is a measure of the probability that the data observed in your sample could have occurred by chance, assuming the null hypothesis is true (Null hypothesis means no effect or difference)
• Interpretation: A small p-value (usually less than 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis and infer that a significant difference or effect exists. A large p-value is not evidence in favour of the null hypothesis