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Be prepared for a variety of questions as the statistician seeks to understand your research and statistical needs.

Although you might think some of these questions are not directly relevant to the statistician’s role on the project, they often uncover issues with statistical implications.

I want to compare weight loss under 3 diets

Are intravenous drug abusers likely to spread the AIDS epidemic to the general population?

Is serum cholesterol level associated with stroke?

Design

Observational study

Experimental study

Subjects

Overweight individuals in the OKC metro plex

New cases of HIV in community health clinics

Patients in

Response Variables

Weight before and after one month on diet

Fasting serum cholesterol

Score on Beck Depression Index

Sample size/Power

What difference interested in detecting

Precision of estimate interested in-how precise are you interested in estimating the mean/proportion

How many subjects can get (recruit) or handle

These items may already be in essentially finished form or still just in the ‘idea/development stage’.

However, before we can assist with the statistical analysis or power/sample size section these rather general concepts must be distilled to explicit concepts or statements that allow quantitative evaluation of information as it relates to the research questions

This requires some self-discipline, but it forces the investigator to clarify his/her own ideas about the plan and to discover specific problems that need attention.

The outline provides a basis for colleagues to react to with specific suggestions.

Most studies have more than one question, but it is useful to focus on a single primary question in designing and implementing the study. This makes our job easier

Quant

Which diet has the greatest weight loss?

Which diet has the better compliance?

Such as: What is the prevalence of antibodies to AIDS virus in i.v. drug abusers?

Descriptive studies estimate-proportions (rates), means (std. dev.)

Analytic Studies-

Usually follow or accompany descriptive studies

Analytic studies analyze associations in order to discover cause-and-effect relationships (what risk factors increase the likelihood of AIDS virus infection in the i.v. drug abuse population?)

Experimental

Final step is often an experiment to establish the effects of an intervention (Does a health education program alter the incidence of HIV infection in the i.v. drug abuse population?)

Experiments usually occur later in the sequence of research studies because they tend to be more difficult and expensive, and tend to attempt to answer more narrowly focused questions.

We can assist in the generation of randomization procedures for studies

Two tables are available on the GCRC web page to assist in organizing the information on data in a form that is most convenient for preparation of statistical methods of protocol.

Estimates of proportions (or percents are often the objectives of studies (descriptive studies). Studies seeking survival rates, prevalence rates, and incidence rates are common in the medical/health are.

Precision

Precision is usually measured as the expected value of the length of a confidence interval and a confidence level of 95% is commonly chosen.

Unfortunately the length of the confidence interval is not only dependent on sample size, but also upon the location of the proportion.

Interval

For a fixed length of confidence interval, largest sample size is required for an estimate of 0.5

This table relates sample size and precision for selected values.

Note that these are exact confidences and are not symmetric about the estimate except at the 0.5.

Examples:

Sample size 100 and observed death rate is 0 then 95% confident that true value is between 0 and 0.036 (3.6%)

Sample size of 100 if observed death rate is 0.5 then 95% confident that true value is between 0.4 and 0.6 (+-10%)

Again, a confidence level of 95% is commonly chosen.

To obtain precision in units for your mean, multiply precision number by your standard deviation.

The term ‘standardized units’ means the differences among the means are expressed as “how many within group standard deviations the means are apart”.

To convert these differences to the units of your study we need estimates of these standard deviations.

Ideally these would come from preliminary or pilot studies you have conducted, but if these are not available, then from the literature.

Next, we need to know what size differences you want to detect. If you say “Any difference.” then the answer is you need an infinite number.

This table is for two independent means – Independent t-test

Once the statistical test is specified, we can formulate in terms of standardized units the ‘generic’ power/sample size considerations for a test involving means derived from independent observations.

The ‘standardized units’ for expressing differences refers in this case to the standard deviation of the “error term” for the test.

For the simplest example, a paired t-test, this is the standard deviation of the differences.

If you have pilot data from your own study, these estimates may be obtained, but it is difficult to find the appropriate numbers reported in the literature.

Even in simple “before and after” studies it seems usual practice to report only the means and standard deviation of the before and the after, but not standard deviation of differences.

This table is for a paired t-test.

- 1. DE-MYSTIFYINGDE-MYSTIFYING BIOSTATISTICSBIOSTATISTICS Minimum Set of Items Needed for Protocol Preparation Meeting with GCRC Biostatisticians Christie E. Burgin, PhD, GCRC Biostatistician Donald E. Parker, PhD, GCRC Biostatistician
- 2. Sequence & Cycle of Research 1. Choosing the research question 2. Developing the protocol 3. Pretesting and revising the protocol 4. Carrying out the study 1. Analyzing the findings 2. Drawing and disseminating the conclusions
- 3. Why Plan a Research Project? To Avoid Unanticipated Problems! Improper assignment of subjects to treatments Unexpected large variability among subjects Unrealistic schedule for study completion Inadequate or no data management
- 4. The Exercise and Value of Mental Planning – with colleagues familiar with the research topic and with related research – with research facilitators – with a statistical consultant – with current/recent literature – with friends – with family members – with self
- 5. Ten Steps for Designing a Study 1. Develop a good idea 2. Decide on objectives and establish priorities 3. Determine the variables required 4. Select and describe the study population 5. Refine objectives into quantitative addressable hypotheses or estimates 6. Anticipate error and bias 7. Develop the study design 8. Estimate the sample size needed 9. Write a research proposal for review 10. Plan the data collection
- 6. Minimum Set of Items to Bring to First Meeting with Statistician • General research question(s) • The design of the study • Who the subjects will be • What information (response variables) you wish to obtain from each subject • Information for sample size/power calculations
- 7. Developing Research Question(s) • State the Aim(s) of the research project • Prioritize (rank) the Aims • Categorize the Aims – Primary Aims – Secondary Aims • Obtain Feedback on Decisions – from colleagues – from self
- 8. Refining the Research Aims into Quantitative Expression Once the research aims have been written they need to be refined so that Aims may be addressed in a quantitative manner.
- 9. Choosing the Study Design • Observational Study (Observing subjects under existing conditions) – Descriptive study – Analytical study • Experimental Study (Random allocation of subjects)
- 10. Choosing the Study Subjects 1. Conceptualize the target population The large group of people with a specified set of characteristics to which the results of the study will be generalized 2. Identify an accessible subset of the population Sample that will represent the target population 3. Design an approach to sampling the population Probability sampling Nonprobability sampling 4. Design approaches to recruiting Design contact mechanisms for acquiring a sample of subjects that is large enough to meet the study needs, and that has acceptable levels of technical error and nonresponse bias
- 11. Defining Response Variables • Categorical Variables – Nominal (gender, ethnicity, blood type) – Ordinal (degree of pain, severity of accident, tumor grade) • Measurement Variables – Discrete ( number of cigarettes smoked/day, number of children in family) – Continuous (weight, blood pressure, cholesterol, fasting blood sugar)
- 12. Variables of Interest Variable Name Variable Type Upper/ Lower Limits Example Notes Gender Categorical LL=0 UL=1 0=Female 1=Male Weight Measure 150 lbs Number Cigarettes Measure 12 per day Tumor Grade Categorical LL=1 UL=4 Level 1
- 13. Variable Time Line Variable Visit #1 Visit #2 Visit #3 Visit #4 Gender X Weight X X X X Number Cigarettes X X X X Tumor Grade X
- 14. Sample Size Techniques for Descriptive Studies Estimates for Proportions The sample size needed depends on two things: – To what precision you wish to estimate the proportion – Where in the interval from zero to one the proportion resides
- 15. Width of Exact 95% Confidence Intervals for Sample Sizes 25-500 and Proportion Values 0.5, 0.75 (0.25), 1.00 (0.0) Sample Size Value of Proportion 1.00 (0.0) 0.75 (0.25) 0.5 500 0.00735 0.07775 0.08943 400 0.00918 0.08714 0.10018 300 0.01222 0.10098 0.11600 200 0.01828 0.12436 0.14268 100 0.03622 0.17777 0.20336 50 0.07112 0.25266 0.28945 25 0.13719 0.36189 0.40926
- 16. Sample Size Techniques for Descriptive Studies Estimates for Means The sample size needed depends on two things: – To what precision you wish to estimate the mean – The standard deviation of the observations from which mean was obtained
- 17. Sample Size & Precision for 95% Confidence Intervals about Mean Sample Precision Size 0.715 10 0.468 20 0.373 30 0.320 40 0.284 50 0.258 60 0.238 70 0.223 80 0.209 90 0.198 100
- 18. Sample Size & Precision for 95% Confidence Intervals about Mean Precision vs N with C.C.=0.95 S=1.000 C.I. Mean Precision N 0.1 0.3 0.5 0.7 0.9 0 20 40 60 80 100
- 19. Power/Sample Size Considerations for Experimental/Analytical Studies Tests of Means • The statistical test must be specified • Researcher must specify the size differences he/she wants to detect
- 20. Sample Size/Power for Independent t-test for Equal Size Groups and Equal Variances Assumed Difference in Means* N for Each Group 90% Power N for Each Group 80% Power Population Between Means 0.25 337 252 10% 0.50 86 64 19% 0.75 39 29 27% 1.00 23 17 34% 1.25 15 12 39% 1.50 11 9 43% 1.75 8 7 46% 2.00 7 6 48% 2.25 6 5 49% *Standard Units-to convert to study units multiply standard units by estimate of within group standard deviation
- 21. Sample Size/Power for Paired (One Sample) t-test Difference in Means* Number Pairs 90% Power Number Pairs 80% Power Population Between Means 0.25 171 128 10% 0.50 44 34 19% 0.75 21 16 27% 1.00 13 10 34% 1.25 9 8 39% 1.50 7 6 43% 1.75 6 5 46% 2.00 5 5 48% 2.25 5 4 49% *Standard Units-to convert to study units multiply standard units by estimate of standard deviation of differences

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