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Chapter-8(A) Confirmatory Trials-Safety Data I
Introduction to Statistics in Pharmaceutical Clinical Trials

  • Benefits associated with new treatment outweigh the risks. All drugs carry side-effects, some of which are more serious than others. Therefore, a drug to be approved, the regulatory agency needs to be presented with evidence of likely benefits to target population that outweigh the likely risks

Rationale for Safety
Assessments

  • How likely is it that my patient will experience an adverse drug reaction?
  • How likely is it that my patient will experience an adverse drug reaction that is so serious that it may be life threatening?
  • How will the risk of an adverse drug reaction vary with different doses of the drug?
  • Are there specific parameters that should be monitored more closely in my patient?

Best information available upon which clinician can form an answer to these questions is the information gathered during pre-approval clinical trials

Regulatory view on
safety assessment

In usual case, any apparent finding emerges from assessment of dozens of adverse events, making description of statistical uncertainty very difficult. Approach taken is best described as one of exploration & estimation of event rates. It should be appreciated that exploratory analyses are a critical & essential part of a safety evaluation.

Safety evaluations focus primarily on estimating the risk of unwanted events associated and on risk of those events relative to what would be expected in the patient population as a whole if the drug were to be approved.

Adverse
Events

  • Any untoward medical occurrence which does not have a causal relationship with the treatment
  • Any unfavorable & unintended sign, symptom, or disease temporally associated with the use of a medicinal (investigational) product

Reporting AEs

  • By study investigators on the basis of their own observations
  • By the study participant as a self-reported event

Using reported AEs
for all participants

Calculating the proportion of individuals reporting any AE for all treatment groups in a study enables us to see whether AEs are more or less likely in the test treatment group than in other groups

Absolute &
Relative Risks

  • To do this in a standardized manner it is necessary to “code” the AE descriptions
    • e.g., 25 participants received treatment A & 5 reported a headache, the proportion is 5/25 = 0.20, which can also be expressed as 20%

1

  • Only 1% of participants in placebo group reported dizziness compared with 3–4% of participants treated with the active drug.
  • How might a regulatory reviewer interpret these data?
  • The first conclusion is, dizziness was not reported very often, so, if drug is approved, most patients treated would probably not have a problem. However, the difference might generate some concern.
  • Initially, absolute difference may not seem extreme. However, in relative terms, those treated with the investigational drug are 3 to 4 times as likely to experience dizziness. This measure of risk is called a relative risk

Accounting for
Sampling Variation

Interval estimation is the standard error of estimator, which quantifies how much sample estimate would vary from sample to sample if we were to conduct same clinical study over & over again. Larger the sample size, smaller the standard error.

Reliability factor is determined by shape of the sampling distribution of interest & is the value that defines an area under the curve of (1-α). In case of a two-sided interval, reliability factor defines lower & upper tail areas of size α/2

Confidence Interval for
a Sample Proportion

Research
Ques.

image

Standard Error
image image

  • Is probability of experiencing a headache after treatment with active drug, higher than risk after treatment with placebo?

Study
Design

  • An antihypertensive drug was evaluated doses in a parallel-group, placebo-controlled study. An important feature of design was randomization to treatment, which provides unbiased estimates of treatment differences
  • Another feature, as we have seen, any difference between treatments that we may find may be a type I error resulting from large number of AEs that could have been selected for this particular analysis

Data

  • The data are participants treated in each group & participants within each group who reported a headache during study. As research question involved all active dose groups combined, it is necessary to pool data across active dose groups to calculate confidence interval of interest. 6 out of 98 participants in placebo group reported a headache, & 25 out of 302 participants in combined active groups

Analysis - Placebo

  • Step 1: Point estimate = 0.06
  • Step 2: Standard error image
  • Step 3: Reliability factor - For two sided 95% confidence interval, we select value of Z from table corresponding to α of 0.05, that is, 1.96
  • Step 4: Confidence interval - Lower limit is 0.06–1.96(0.02)=0.02.
    Upper limit is 0.06+1.96(0.02)=0.10.
    We write 95% confidence interval as (0.02, 0.10)

Analysis - Active

  • Step 1: Point estimate = 0.08
  • Step 2: Standard error =0.016
  • Step 3: Reliability factor - 1.96
  • Step 4: Confidence interval - Lower limit is 0.08–1.96(0.016)=0.05.
    Upper limit is 0.08+1.96(0.016)=0.11

Interpretation &
Decision-Making

  • In the case of placebo group, we are 95% confident that population proportion of participants experiencing a headache is enclosed in interval (0.02, 0.10). For active dose group, we are 95% confident interval is (0.02, 0.10)
  • The overlapping within-group confidence intervals suggest that there is insufficient evidence to conclude that observed difference is real

Confidence intervals for
difference between 2 proportions

In this approach, we calculate a confidence interval about difference in proportions for two independent groups

Data

image

Standard Error
image

Confidence interval for difference with Correctional Factor
image

  • 6 out of 98 participants in placebo group reported a headache & 25 out of 302 participants in combined active groups reported a headache

Analysis

  • Step 1: Point estimate = 0.06-0.08=-0.02
  • Step 2: Standard error = image
  • Step 3: Reliability factor - 1.96 and for this interval, we use continuity factor 0.5(1/98 + 1/302) = 0.007
  • Step 4: Confidence interval -
    Lower limit is -0.02-1.96(0.03)-0.007 = -0.09
    Upper limit is -0.02+1.96(0.03)-0.007 = 0.04

Interpretation &
Decision-Making

  • We are 95% confident that true difference in proportions of individuals reporting headache as an AE is within interval (-0.09, 0.04). As interval includes 0, there is not enough evidence to suggest that two groups are statistically significantly different with respect to risk of headache as an AE