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## Statistical Methods in Clinical Research

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**Statistical Methods in Clinical Research**James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC**Overview**• Data types • Summarizing data using descriptive statistics • Standard error • Confidence Intervals**Overview**• P values • One vs two tailed tests • Alpha and Beta errors • Sample size considerations and power analysis • Statistics for comparing 2 or more groups with continuous data • Non-parametric tests**Overview**• Regression and Correlation • Risk Ratios and Odds Ratios • Survival Analysis • Cox Regression**Further Study**• Medical Statistics Made Easy • M. Harris and G. Taylor • Informa Healthcare UK • Distributed in US by: Taylor and Francis 6000 Broken Sound Parkway, NW Suite 300 Boca Raton, FL 33487 1-800-272-7737**Types of Data**• Discrete Data-limited number of choices • Binary: two choices (yes/no) • Dead or alive • Disease-free or not • Categorical: more than two choices, not ordered • Race • Age group • Ordinal: more than two choices, ordered • Stages of a cancer • Likert scale for response • E.G. strongly agree, agree, neither agree or disagree, etc.**Types of data**• Continuous data • Theoretically infinite possible values (within physiologic limits) , including fractional values • Height, age, weight • Can be interval • Interval between measures has meaning. • Ratio of two interval data points has no meaning • Temperature in celsius, day of the year). • Can be ratio • Ratio of the measures has meaning • Weight, height**Types of Data**• Why important? • The type of data defines: • The summary measures used • Mean, Standard deviation for continuous data • Proportions for discrete data • Statistics used for analysis: • Examples: • T-test for normally distributed continuous • Wilcoxon Rank Sum for non-normally distributed continuous**Descriptive Statistics**• Characterize data set • Graphical presentation • Histograms • Frequency distribution • Box and whiskers plot • Numeric description • Mean, median, SD, interquartile range**HistogramContinuous Data**No segmentation of data into groups**Frequency Distribution**Segmentation of data into groups Discrete or continuous data**Box and Whisker Plots**Popular in Epidemiologic Studies Useful for presenting comparative data graphically**Numeric Descriptive Statistics**• Measures of central tendency of data • Mean • Median • Mode • Measures of variability of data • Standard Deviation • Interquartile range**Sample Mean**• Most commonly used measure of central tendency • Best applied in normally distributed continuous data. • Not applicable in categorical data • Definition: • Sum of all the values in a sample, divided by the number of values.**Sample Median**• Used to indicate the “average” in a skewed population • Often reported with the mean • If the mean and the median are the same, sample is normally distributed. • It is the middle value from an ordered listing of the values • If an odd number of values, it is the middle value • If even number of values, it is the average of the two middle values. • Mid-value in interquartile range**Sample Mode**• Infrequently reported as a value in studies. • Is the most common value • More frequently used to describe the distribution of data • Uni-modal, bi-modal, etc.**Interquartile range**• Is the range of data from the 25th percentile to the 75th percentile • Common component of a box and whiskers plot • It is the box, and the line across the box is the median or middle value • Rarely, mean will also be displayed.**Standard Error**• A fundamental goal of statistical analysis is to estimate a parameter of a population based on a sample • The values of a specific variable from a sample are an estimate of the entire population of individuals who might have been eligible for the study. • A measure of the precision of a sample in estimating the population parameter.**Standard Error**• Standard error of the mean • Standard deviation / square root of (sample size) • (if sample greater than 60) • Standard error of the proportion • Square root of (proportion X 1 - proportion) / n) • Important: dependent on sample size • Larger the sample, the smaller the standard error.**Clarification**• Standard Deviation measures the variability or spread of the data in an individual sample. • Standard error measures the precision of the estimate of a population parameter provided by the sample mean or proportion.**Standard Error**• Significance: • Is the basis of confidence intervals • A 95% confidence interval is defined by • Sample mean (or proportion) ± 1.96 X standard error • Since standard error is inversely related to the sample size: • The larger the study (sample size), the smaller the confidence intervals and the greater the precision of the estimate.**Confidence Intervals**• May be used to assess a single point estimate such as mean or proportion. • Most commonly used in assessing the estimate of the difference between two groups.**Confidence Intervals**Commonly reported in studies to provide an estimate of the precision of the mean.**P Values**• The probability that any observation is due to chance alone assuming that the null hypothesis is true • Typically, an estimate that has a p value of 0.05 or less is considered to be “statistically significant” or unlikely to occur due to chance alone. • The P value used is an arbitrary value • P value of 0.05 equals 1 in 20 chance • P value of 0.01 equals 1 in 100 chance • P value of 0.001 equals 1 in 1000 chance.**P Values and Confidence Intervals**• P values provide less information than confidence intervals. • A P value provides only a probability that estimate is due to chance • A P value could be statistically significant but of limited clinical significance. • A very large study might find that a difference of .1 on a VAS Scale of 0 to 10 is statistically significant but it may be of no clinical significance • A large study might find many “significant” findings during multivariable analyses. “a large study dooms you to statistical significance” Anonymous Statistician**P Values and Confidence Intervals**• Confidence intervals provide a range of plausible values of the population mean • For most tests, if the confidence interval includes 0, then it is not significant. • Ratios: if CI includes 1, then is not significant • The interval contains the true population value 95% of the time. • If a confidence interval range is very wide, then plausible value might range from very low to very high. • Example: A relative risk of 4 might have a confidence interval of 1.05 to 9, suggesting that although the estimate is for a 400% increased risk, an increased risk of 5% to 900% is plausible.**Errors**• Type I error • Claiming a difference between two samples when in fact there is none. • Remember there is variability among samples- they might seem to come from different populations but they may not. • Also called the error. • Typically 0.05 is used**Errors**• Type II error • Claiming there is no difference between two samples when in fact there is. • Also called a error. • The probability of not making a Type II error is 1 - , which is called the power of the test. • Hidden error because can’t be detected without a proper power analysis**Errors**Test Result Truth**Sample Size Calculation**• Also called “power analysis”. • When designing a study, one needs to determine how large a study is needed. • Power is the ability of a study to avoid a Type II error. • Sample size calculation yields the number of study subjects needed, given a certain desired power to detect a difference and a certain level of P value that will be considered significant. • Many studies are completed without proper estimate of appropriate study size. • This may lead to a “negative” study outcome in error.**Sample Size Calculation**• Depends on: • Level of Type I error: 0.05 typical • Level of Type II error: 0.20 typical • One sided vs two sided: nearly always two • Inherent variability of population • Usually estimated from preliminary data • The difference that would be meaningful between the two assessment arms.**One-sided vs. Two-sided**• Most tests should be framed as a two-sided test. • When comparing two samples, we usually cannot be sure which is going to be be better. • You never know which directions study results will go. • For routine medical research, use only two-sided tests.**Sample size for proportions**Stata input: Mean 1 = .2, mean 2 = .3, = .05, power (1-) =.8.**Sample Size for Continuous Data**Stata input: Mean 1 = 20, mean 2 = 30, = .05, power (1-) =.8, std. dev. 10.**Statistical Tests**• Parametric tests • Continuous data normally distributed • Non-parametric tests • Continuous data not normally distributed • Categorical or Ordinal data**Comparison of 2 Sample Means**• Student’s T test • Assumes normally distributed continuous data. T value = difference between means standard error of difference • T value then looked up in Table to determine significance**Paired T Tests**• Uses the change before and after intervention in a single individual • Reduces the degree of variability between the groups • Given the same number of patients, has greater power to detect a difference between groups**Analysis of Variance**• Used to determine if two or more samples are from the same population- the null hypothesis. • If two samples, is the same as the T test. • Usually used for 3 or more samples. • If it appears they are not from same population, can’t tell which sample is different. • Would need to do pair-wise tests.**Non-parametric Tests**• Testing proportions • (Pearson’s) Chi-Squared (2) Test • Fisher’s Exact Test • Testing ordinal variables • Mann Whiney “U” Test • Kruskal-Wallis One-way ANOVA • Testing Ordinal Paired Variables • Sign Test • Wilcoxon Rank Sum Test**Use of non-parametric tests**• Use for categorical, ordinal or non-normally distributed continuous data • May check both parametric and non-parametric tests to check for congruity • Most non-parametric tests are based on ranks or other non- value related methods • Interpretation: • Is the P value significant?**(Pearson’s) Chi-Squared (2) Test**• Used to compare observed proportions of an event compared to expected. • Used with nominal data (better/ worse; dead/alive) • If there is a substantial difference between observed and expected, then it is likely that the null hypothesis is rejected. • Often presented graphically as a 2 X 2 Table**Chi-Squared (2) Test**• Chi-Squared (2) Formula • Not applicable in small samples • If fewer than 5 observations per cell, use Fisher’s exact test**Correlation**• Assesses the linear relationship between two variables • Example: height and weight • Strength of the association is described by a correlation coefficient- r • r = 0 - .2 low, probably meaningless • r = .2 - .4 low, possible importance • r = .4 - .6moderate correlation • r = .6 - .8 high correlation • r = .8 - 1 very high correlation • Can be positive or negative • Pearson’s, Spearman correlation coefficient • Tells nothing about causation**Correlation**Source: Harris and Taylor. Medical Statistics Made Easy**Correlation**Perfect Correlation Source: Altman. Practical Statistics for Medical Research**Correlation**Correlation Coefficient .3 Correlation Coefficient 0 Source: Altman. Practical Statistics for Medical Research**Correlation**Correlation Coefficient .7 Correlation Coefficient -.5 Source: Altman. Practical Statistics for Medical Research**Regression**• Based on fitting a line to data • Provides a regression coefficient, which is the slope of the line • Y = ax + b • Use to predict a dependent variable’s value based on the value of an independent variable. • Very helpful- In analysis of height and weight, for a known height, one can predict weight. • Much more useful than correlation • Allows prediction of values of Y rather than just whether there is a relationship between two variable.