David Yens, Ph.D. NYCOM PASW-SPSS STATISTICS David P. Yens, Ph.D. New York College of Osteopathic Medicine, NYIT l PRESENTATION 3 l Descriptive Statistics l Chi-Squared l Risk/Odds Ratio 2010

DESCRIPTIVE STATISTICS When doing data analyses, you usually want to see the nature of the data before you start. You get this from ◦ FREQUENCIES for nonparametric data and ◦ DESCRIPTIVES for parametric data

FREQUENCIES ANALYZE DESCRIPTIVE STATISTICS DESCRIPTIVES You have data on length of stay for a large sample of patients and want to examine the parameters for age and length of stay.

FREQUENCIES ANALYZE DESCRIPTIVE STATISTICS FREQUENCIES In your length of stay data you have included information about gender. How many males and females are in the data?

JOINT FREQUENCIES The next question might be whether there is a difference in the number of admissions by gender.

David Yens, Ph.D. NYCOM CATEGORICAL FREQUENCY DATA: TESTS OF SIGNIFICANCE CHI-SQUARED (χ 2 ) ◦ Contingency table ◦ Test of association; compares proportions ◦ Assesses signal-to-noise ratio ◦ Based on the differences between observed and values and expected values ◦ Most often used with 2 x 2 tables ◦ Yates’ correction ◦ Fisher’s exact test

David Yens, Ph.D. NYCOM THE RELATION BETWEEN OBSERVED AND EXPECTED FREQUENCIES if the null hypothesis is true, the absolute value of the differences between the observed and expected cell frequencies will, on balance, be small; if the null hypothesis is false and the alternate hypothesis is true, the absolute value of the differences between the observed and expected cell frequencies will, on balance, be large.

David Yens, Ph.D. NYCOM CHI SQUARED The test statistic is given by χ 2 = ∑ ( O – e) 2 / e

David Yens, Ph.D. NYCOM CATEGORICAL FREQUENCY DATA: TESTS OF SIGNIFICANCE CHI-SQUARED 2x2 A table in which frequencies correspond to two variables. (One variable is used to categorize rows, and a second variable is used to categorize columns.) Contingency tables have at least two rows and at least two columns. Test of association; compares frequencies ◦ Based on the differences between observed and values and expected values ◦ Most often used with 2 x 2 tables TreatmentControl Positive15520 Negative

David Yens, Ph.D. NYCOM 2x2 CHI-SQUARED First, we create a 2x2 contingency table, as shown below. Assume that in the treatment group 15 subjects had a positive response and 10 and a negative response, and for the control group 5 subjects had a positive response and 20 had a negative response. The letters on the table at the left identify the letters used in the formula below; the sample data table is on the right. For a 2x2 table, the critical value is If the Chi-Squared you calculate is > 3.84, the result is significant at p<.05. TreatmentControl ABA+B Positive Outcome15520 CDC+D Negative Outcome A+CB+DN 25 50

SPSS CROSSTABULATION ANALYZE DESCRIPTIVE STATISTICS CROSSTABS Note that for a Chi-Squared analysis an expected cell frequency of 5 or more is preferred. If less than 5, use Fisher’s Exact Test or Yates’ correction

David Yens, Ph.D. NYCOM Yates’ Correction for Small Numbers Yates’ Correction for Small Numbers Used if expected frequency for a cell is <5 χ 2 = Σ [|O i – E i |-.5] 2 /E i

David Yens, Ph.D. NYCOM Fisher’s Exact Test  For full computation for values as extreme or more extreme than the one observed, must compute the probability for each extreme case and sum the probabilities  Fisher’s Exact Test – for a 2x2 analysis with small numbers in each cell:

PROBLEM Using a database of toothbrushing activity by children, we would like to know whether there is a difference between brushing activity by boys and girls. The data contain gender and whether or not they brush daily. These are frequency data and appropriate for crosstabs with a Chi-Squared statistic. (See Chapt. 7 of IBM SPSS)

DATA LAYOUT Gender Daily Brushing M Y M N M Y M N F Y F N F Y

OUTPUT

CROSSTABULATION ANALYZE DESCRIPTIVE STATISTICS CROSSTABS Crosstabs provides access to other analyses: ◦ Risk Ratios and Odds Ratios (pp ) ◦ Relative Risk: The ratio of incidence in exposed (or group) of persons to incidence in nonexposed (other group) persons ◦ Odds Ratio – The odds that a case is exposed divided by the odds that a control is exposed

RELATIVE RISK RELATIVE RISK (Cohort studies) Ratio of the risk of disease in exposed individuals to the risk of disease in nonexposed individuals Relative Risk = David P. Yens, Ph.D. NYCOM =

ODDS RATIO ODDS RATIO (Cohort studies) Ratio of the odds of development of disease in exposed individuals to the odds of development of the disease in nonexposed individuals Odds Ratio = David P. Yens, Ph.D. NYCOM

PROBLEM Consider the data taken from a study that attempts to determine whether the use of electronic fetal monitoring (EFM) during labor affects the frequency of cesarean section deliveries. The 5824 infants included in the study, 2850 were electronically monitored and 2974 were not. The outcomes are as follows: Calculate the odds ratio associated with EFM exposure. EFM Exposure Cesarean Delivery YesNoTotal Yes No Total

SOLUTION For this analysis, the raw data are reduced to a 2 by 2 table with Crosstabs and then subsequently analyzed by hand

CROSSTABULATION ANALYZE DESCRIPTIVE STATISTICS CROSSTABS Crosstabs provides access to other analyses: ◦ Kappa – provides measure of agreement between 2 judges: Cohen's kappa measures the agreement between the evaluations of two raters when both are rating the same object. A value of 1 indicates perfect agreement. A value of 0 indicates that agreement is no better than chance. Kappa is available only for tables in which both variables use the same category values and both variables have the same number of categories.

CROSSTABULATION ANALYZE DESCRIPTIVE STATISTICS CROSSTABS Crosstabs provides access to other analyses: ◦ The 2 by 2 tables also provide the basis for several other epidemiological computations

PROPORTIONS/PERCENTAGES PROPORTIONS/PERCENTAGES The relationship between prior condom use and tubal pregnancy was assessed in a population-based case- controlled study at Group Health Cooperative of Puget Sound during The results are: Compute the proportion of subjects in each group who never used condoms. Condom UseCasesControls Never Ever 51186

SENSITIVITY SENSITIVITY -  Accuracy of the test in detecting the condition in patients who actually have it  Sensitivity Se = DISEASE PRESENTABSENT TESTPOSITIVEaba+b NEGATIVEcdc+d a+cb+da+b+c+d David P. Yens, Ph.D. NYCOM

SPECIFICITY SPECIFICITY -  How well the test correctly identifies patients who do not have the condition  Specificity Sp = DISEASE PRESENTABSENT TESTPOSITIVEaba+b NEGATIVEcdc+d a+cb+da+b+c+d David P. Yens, Ph.D. NYCOM

PROBLEM Consider the following data: Calculate the sensitivity and specificity of X-ray as a screening test for tuberculosis. SOLUTION: SENSITIVITY = 22/30 =.73 SPECIFICITY = 1739/1790 =.97 Tuberculosis X-RayNoYesTotal Negative Positive Total

EPIDEMIOLOGY INCIDENCE - EXPOSED  Number of new cases of a disease that occur during a specified period of time in a population at risk for developing the disease Incidence in exposed = David P. Yens, Ph.D. NYCOM

EPIDEMIOLOGY INCIDENCE - NONEXPOSED  Number of new cases of a disease that occur during a specified period of time in a population at risk for developing the disease Incidence in Nonexposed = David P. Yens, Ph.D. NYCOM

EPIDEMIOLOGY PREVALENCE -  Proportion of patients in a given population who have a given disease  Prevalence, P = DISEASE PRESENTABSENT TESTPOSITIVEaba+b NEGATIVEcdc+d a+cb+da+b+c+d David P. Yens, Ph.D. NYCOM

EPIDEMIOLOGY LIKELIHOOD RATIO -  The odds that a test result occurs in patients with the disease versus those without the disease Positive Likelihood Ratio, LR+ = DISEASE PRESENTABSENT TESTPOSITIVEaba+b NEGATIVEcdc+d a+cb+da+b+c+d David P. Yens, Ph.D. NYCOM

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