Suppose that the screening test is based on analysis of a blood sample taken from women early in pregnancy. For example, suppose a study is proposed to evaluate a new screening test for Down Syndrome. ![]() However, in many studies, the sample size is determined by financial or logistical constraints. The formulas presented here generate estimates of the necessary sample size(s) required based on statistical criteria. Studies that are much larger than they need to be to answer the research questions are also wasteful. These situations can also be viewed as unethical as participants may have been put at risk as part of a study that was unable to answer an important question. ![]() Studies that have either an inadequate number of participants or an excessively large number of participants are both wasteful in terms of participant and investigator time, resources to conduct the assessments, analytic efforts and so on. Studies should be designed to include a sufficient number of participants to adequately address the research question. This module will focus on formulas that can be used to estimate the sample size needed to produce a confidence interval estimate with a specified margin of error (precision) or to ensure that a test of hypothesis has a high probability of detecting a meaningful difference in the parameter. The partial correlation quantifies that adjusted association just as a standard simple correlation does with the unadjusted linear association between two variables.Boston Univeristy School of Public HealthĪ critically important aspect of any study is determining the appropriate sample size to answer the research question. The cardiologists believe that subjects whose tHcy is relatively higher than expected will also have a PBI that is relatively higher than expected. Thus each subject has "expected" tHcy and PBI values based on the six covariates. You use partial regression plots like that shown in Figure 67.9 to teach the team that the partial correlation between PBI and tHcy is the correlation of two sets of residuals obtained from ordinary regression models, one from regressing PBI on the six covariates and the other from regressing tHcy on the same covariates. This greatly simplifies matters, especially the elicitation of the conjectured effect. Most clinicians are familiar with simple correlations between two variables, so you decide to pose the statistical problem in terms of estimating and testing the partial correlation between = tHcy and = PBI, controlling for the six other predictor variables ( ). ![]() All eight variables will be measured during one visit. Subjects will be screened so that about half will have had a heart problem. This is a correlational study at a single time. You wonder whether 100 subjects will provide adequate statistical power. You will regress PBI on tHcy and the six other predictors (plus the intercept) and use a Type III test to assess whether tHcy is a significant predictor after adjusting for the others. The planned analysis is an ordinary least squares regression to assess the relationship between total homocysteine level (tHcy) and a plaque burden index (PBI), adjusting for six other variables: age, gender, plasma levels of folate, vitamin, vitamin, and a serum cholesterol index. You are working with a team of preventive cardiologists investigating whether elevated serum homocysteine levels are linked to atherosclerosis (plaque buildup) in coronary arteries. Example 67.5 Multiple Regression and Correlation
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