Statistics for Health Care

Biostatistics

Phases of a Full Clinical Trial

• Phase I – the trial takes place after the development of a therapy and is designed to determine doses, strengths and safety – it is pre-experimental – there is no control group

• Phase II – the trial is looking for evidence of effectiveness – it is pre-experimental or quasi-experimental and similar to a pilot test – it seeks to determine feasibility of further testing and signs of potential side effects

Phases of a Full Clinical Trial

• Phase III – it is a full experimental test of the therapy with randomly assigned treatment and control groups. It is designed to determine whether the intervention is more effective than a standard treatment. It may be referred to as and RCT or randomized clinical trial and often studies large groups from multiple sites.

Phases of a Full Clinical Trial

• Phase IV – it occurs after the decision to adopt an innovative therapy and involves study of its long-term consequences –both side effects and benefits. It rarely requires true experimental design.

Prevalence Studies

• Prevalence studies are a type of descriptive study that come from the field of epidemiology. They are conducted to determine the prevalence rate of some condition. They are cross-sectional designs that obtain data from one population at risk for the condition

Prevalence Studies

• The formula for a prevalence rate (PR) is:

# of cases with the condition at a given point in time

_____________________________________ x K

# in the population at risk for being a case

Example:

80 cases

____________ x 100 (# we want the PR established for) = 16 per 100

500 at risk

Incidence Studies

• Incidence studies measure the frequency of developing new cases. This requires a longitudinal design, because we need to determine who is at risk for becoming a new case.

Incidence Studies

• The formula for an incidence rate (IR) is:

# of new cases with the condition over a given period of time

_____________________________________ x K

# in the population at risk for being a new case

Example:

21 new cases (in one year since original count)

____________ x 100 = 5 per 100

420 at risk (from previous example: 500-80 =420 now at risk

Relative Risk

• Relative risk (RR is the risk of becoming a case in one group compared to another.

• Example: If the risk of becoming a new case was 7 per

hundred in men and 14 per hundred in women, we would divide the rate of women by the rate of men, and find that women were twice as likely to become a new case over a year’s time.

Relative Risk

• Relative Risk can also be used in examining new therapies.

• Relative Risk is the ratio of an outcome (such as PONV) in the treatment group (those receiving a bolus of fluid before induction) to the rate of the outcome (PONV) in the controls. An RR of < 1.0 means the experimental group had

less (PONV) than the control group. An RR of > 1.0 would mean that the experimental group had more (PONV) than did the controls.

Relative Risk

• Relative Risk can also be used in examining other differences in groups.

• Example:

• The risk of LBW with and without smoking• Without smoking: 144/2309 = .06 had LBW• With smoking: 76/746 = .10 had LBW• RR is: .10/.06 = 1.67

Describing Risk

– Absolute risk is the proportion of people who experienced an undesirable outcome in each group

– Absolute risk reduction (ARR) is the number used to describe the estimated proportion of people who would be spared from an adverse outcome through exposure to an intervention

– Relative risk reduction (RRR) is the estimated proportion of untreated risk that is reduced through exposure to the intervention

Odds Ratio

• Ratio of the odds for the treated versus the untreated group, with the odds reflecting the proportion of people with the adverse outcome relative to those without it.

• The OR is at least equal to the RR, but often overestimates it.

Odds Ratio

• When OR = 1.00, it means the odds that something will happen to one group are equal to the odds that it will happen to another group.– If one group smoked and the other did not, we

might obtain an OR of 3.00, meaning that the odds of those who smoked would be 3 x higher than those who did not.

Number Needed to Treat (NNT)

• Estimate of how many people would need to receive the intervention to prevent one adverse outcome

Developing Screening/Diagnostic

Instruments

• Goal is to establish a cutoff point that balances sensitivity and specificity

Positive Predictive Value

• The Positive Predictive Value (PPV) - the precision rate, or the post-test probability of disease - is the proportion of patients with positive test results who are correctly diagnosed. It indicates the probability with which a positive test might show the disease or condition being tested for. It is a measure of the diagnostic test. A low number means a high “false positive” rate.

•  • PPV = No. of true positives

• No. of true positives + No. of false positives

• (total who test positive)

Negative Predictive Value

• The Negative Predictive Value (NPV) is the proportion of patients with negative test results who are correctly diagnosed.

•  • NPV = No. of true negatives• No. of true negatives + No. of false negatives• (total who test negative)•  

Criteria for Assessing Screening/Diagnostic Instruments

• Sensitivity: the instrument’s ability to correctly identify a “case”—i.e., to diagnose a condition

• Specificity: the instrument’s ability to correctly identify noncases, that is, to screen out those without the condition

EMPIRICAL EVIDENCE of

CONDITION 

 

    True False 

 

TestOutcome

Positive True positive False Positive(Type I error)

Positive Predictive Value

  Negative False negative(Type II error)

True negative Negative Predictive Value

    Sensitivity Specificity  

BOWEL CA POSITIVE ON COLONOSCOPY and BIOPSY

  

    True False  

 

FecalOccult Blood Test

Positive True positive = 2

False Positive = 18

PPV2/20 = 10%

  Negative False negative = 1 (Type II error)

True negative = 182

NPV182/183 = 99.5%

    Sensitivity2/ (2+1) = 66.7%

Specificity182/ (18 +182) = 91%

 

Information from Slide 19

• Looking at the slides you can see that the large number of false positives and the low number of false negatives indicate that the occult blood test is poor at confirming colon cancer. However, it is good as a screening test since 99.5 % of the negative tests will be correct and the sensitivity indicates that further testing needs to be done on at least 66.7% of those testing positive.

Confidence Interval

• The Confidence Interval (CI) is the range of values around a sample mean that are calculated to contain the population mean with a 95% (or 99%) degree of certainty. Many researchers believe that these values give more clinical data than do p values.

Confidence Interval

• The POINT ESTIMATE is a single point estimated to be the mean for the population, based on a sample. When a confidence interval (CI) is reported, it is an INTERVAL ESTIMATE, a range of values that estimate the mean for a population. If a math test was given to a sample of nursing students and there was a mean of 55, then 55 would be the point estimate. If the 95% CI was reported as 52-57, there would be a 95% chance that the true mean of all nursing students would be between 52-57.

•  

Confidence Interval

• The STANDARD ERROR OF THE MEAN is used to calculate the CI. The standard error of the mean is the error that is due to sampling. Each sample mean is likely to deviate somewhat from the true population mean. The SEM is the difference between the sample mean and the unknown population mean. It is the margin of error to allow for when estimating the population mean from a random sample. It allows for chance errors. It is calculated as

follows:  • SD (of the sample)

• Square root of the No. of people in the sample

Confidence Interval

• If the SEM is 3 and the mean is 100 and you want a confidence interval of 95% - that is between -1.96 and +1.96 SD from the mean, you would use the following formula: X + (1.96 x SEM) = CI

•  • 100 + (1.96 x 3) = 100 + 5.88 • We can say, with 95% confidence, that the

population mean would fall between 94.12 and 105.88

•  

Confidence Interval

• For a 68% CI, add the standard error of the mean (SEM) to the mean, then subtract it from the mean. For a 95% CI , multiply the SEM by 1.96, then add and subtract. For a 99% CI, multiply by 2.58, then add and subtract. Note: The intervals obtained by using these multipliers are only precise with large numbers (60 or more cases).