Statistical methodology: IV. Analysis of variance, analysis of covariance, and multivariate analysis of variance.

Medical research frequently involves the statistical comparison of >2 groups, often using data obtained through the application of complex experimental designs. Fortunately, inferential statistical methodologies exist to address these situations. Analysis of variance (ANOVA) in its many forms is used to simultaneously test the equality of all groups in a study. One-way (with 1 independent variable), 2-way (with 2 independent variables), and repeated-measures (patients serve as their own controls) ANOVAs are forms of this technique. Each form has been developed to analyze data from a specific experimental design. Analysis of covariance (ANCOVA) allows the researcher to control for confounding variables that may influence the response of the dependent variable. Finally, multivariate analysis of variance (MANOVA) evaluates the simultaneous responses of multiple dependent variables to > or = 1 independent variable. Whereas ANOVA is the correct alternative to statistically inappropriate multiple t-tests, MANOVA is the correct alternative to statistically inappropriate multiple univariate ANOVA calculations. Use of each of these statistical methods requires an appropriate experimental design and data meeting a number of assumptions. When used properly, each of these methods provides a powerful statistical analysis technique.

Mock drug delivery to the proximal aorta during cardiopulmonary resuscitation: central vs peripheral intravenous infusion with varying flush volumes.

OBJECTIVE: To compare mock drug deliveries to the proximal aorta during CPR after peripheral vs central i.v. administration when the mock drug is followed by different postinfusion flush volumes. METHODS: Delivery of indocyanine green (ICG) dye to the proximal aorta of an instrumented 20-kg canine cardiac arrest model was examined. The ICG administration (2.5 mg) preceded either a 2-mL or a 10-mL saline flush, for either a central or a peripheral i.v. route of dye administration. Five dogs each underwent three sets of the four possible route/flush-volume combinations in a stratified randomized order. Real-time dye-absorbance-vs-time curves, as sampled from the proximal aorta, modeled central-circulation drug delivery. Systolic and diastolic blood pressures (BPs) were monitored, and the absorbance-vs-time curve upstroke phases were used to estimate cardiac output during arrest. RESULTS: Times (mean +/- SD) to onset of dye appearance did not differ significantly between peripheral/10 mL (126 +/- 35 sec) and central/10 mL (108 +/- 35 sec), or between central/2 mL (123 +/- 31 sec) and central/10 mL. Times to onset of dye appearance did differ between peripheral/2 mL (161 +/- 70 sec) and central/10 mL [analysis of variance (ANOVA) p = 0.032]. Times to peak dye concentration did not differ significantly between peripheral/10 mL (230 +/- 88 sec) and either central/10 mL (202 +/- 88 sec) or central/2 mL (215 +/- 83 sec), but differed between peripheral/2 mL (326 +/- 134 sec) and every other route/flush-volume combination (ANOVA p = 0.009). Peak dye concentrations and systolic/diastolic BPs (averaging 23/10 for all route/flush-volume combinations) did not differ significantly between any route/flush-volume combinations. CONCLUSION: An adequately sized postinfusion crystalloid flush (0.5 mL/kg) permits peripherally administered model drug to reach the central circulation as quickly and in equivalent concentration as centrally administered drug during CPR in a canine cardiac arrest model.

Seasonal respiratory viral infections. Impact on infants with chronic lung disease following discharge from the neonatal intensive care unit.

OBJECTIVE: To determine the frequency and severity of acute respiratory infections in infants with bronchopulmonary dysplasia following discharge from the neonatal intensive care unit. DESIGN: A prospective cohort study of 30 oxygen-dependent children who were younger than 2 years (mean age, 9.8 months; range, 3 to 24 months) were studied from September 1990 through April 1991. MEASUREMENTS/RESULTS: During the study, 101 (90.2%) of 112 visits for illness were prompted by new or worsening respiratory symptoms. Diagnoses included upper respiratory tract infection (30.4%), otitis media (26.0%), pneumonia (11.1%), acute exacerbation of bronchopulmonary dysplasia (10.4%), reactive airway disease (9.6%), and bronchiolitis (5.9%). Among these children, an increase in the fraction of inspired oxygen was necessary during 43% of visits. Ten children were hospitalized on 25 occasions for a mean of 37.6 hospital days per child (range, 1 to 107 days), and mean length of stay for each hospitalization was 15 days (median, 6 days). Five children were admitted to the pediatric intensive care unit. Respiratory viruses isolated included respiratory syncytial virus (n = 7), parainfluenza 3 virus (n = 3), and adenovirus (n = 2). No isolates of influenza A or B were detected. Anthropometrics at study entry and study end were converted to z scores as descriptors of weight for age, height for age, and weight for height. Growth improved during the 8 months of the study; however, overall, the children were leaner at study end than at study entry. CONCLUSIONS: In children with bronchopulmonary dysplasia, respiratory viral infections led to significant morbidity, which included long and frequent hospitalizations during the peak of the respiratory viral season. Although weight and linear growth increased throughout the study, patients were leaner at study conclusion than at study entry.

Selective intrapartum prophylaxis for group B streptococcus colonization: management and outcome of newborns.

OBJECTIVE: Intrapartum antibiotic prophylaxis (IAP) in mothers with group B streptococcus (GBS) colonization presents difficult neonatal management decisions. IAP was instituted in response to an increased incidence of early-onset GBS sepsis (EOGBSS), and a study was conducted to evaluate the outcome of these newborns. METHODS: A study was undertaken at Truman Medical Center-East, a county hospital with a level 1 nursery. During the 20-month study period, prenatal GBS cultures were obtained on all mothers in their third trimester of pregnancy. At time of delivery, GBS-positive women who had at least one risk factor were to receive IAP. Risk factors included fever and/or amnionitis, premature labor, and prolonged rupture of membranes defined as > 6 hours. Screening laboratory tests were performed on all newborns whose mothers received IAP. Only the newborns with positive screening laboratory tests or symptoms of sepsis received further laboratory evaluation and antibiotic treatment. RESULTS: During the study, 2040 mothers gave birth to 2054 newborns. Three hundred thirty-two mothers (16.3%) were colonized with GBS and 122 (37.0%) had at least one risk factor. IAP was given to 70 GBS-positive mothers. Thirty-three (27%) GBS-positive mothers with risk factors did not receive IAP for logistical reasons. Eleven full-term newborns had EOGBSS: For case newborns, the mean duration of ruptured membranes was 13.7 hours (range 2.5 to 28 hours). Vertical transmission occurred as follows: Cutaneous colonization was found in 33 (12.5%) newborns born to 261 mothers who received no IAP, and symptomatic EOGBSS was diagnosed in 9 (3.4%). Mothers who received one dose (n = 43) had three (6.9%) newborns with GBS colonization and two (4.7%) asymptomatic newborns with EOGBSS: No newborns born to 28 mothers who received two doses IAP had GBS colonization or were ill. Cutaneous vertical transmission was reduced (P = .03). Newborns born to GBS-positive mothers with one or more risk factors who received IAP had significantly less EOGBSS (P < .05) than those who did not receive IAP. CONCLUSIONS: Selective IAP was administered safely to 21% of GBS-positive women, or 3.5% of all deliveries. IAP prevented EOGBSS when it could be given to GBS-positive mothers with a risk factor. Accurate identification of mothers with GBS colonization and their risk factors is essential for effective use of IAP. Earlier institution of IAP after rupture of membranes may reduce the risk of EOGBSS and the need for extensive infant evaluation.

Non-normality of distribution of Glasgow Coma Scores and Revised Trauma Scores.

STUDY OBJECTIVE: Inferential and descriptive statistics continue to be used incorrectly when analyzing biomedical data. Glasgow Coma Score (GCS) and Revised Trauma Score (RTS) data have recently been described and analyzed using parametric statistical methods in several studies despite the ordinal nature of these data scales. The objective of this study was to determine whether GCS and RTS data are normally distributed, despite their ordinal nature. HYPOTHESIS: Neither GCS nor RTS data are normally distributed. DESIGN: A retrospective review of GCS and RTS data obtained at a medical school teaching and county hospital that is a Level I trauma center. PARTICIPANTS: Patients who met criteria for trauma team activation at the hospital. METHODS: GCS and RTS data distributions were compared to a standard normal distribution using the chi 2 goodness of fit test. RESULTS: GCS and RTS data distributions differed significantly from the normal distribution for all data sets examined. CONCLUSION: Parametric statistical descriptors and inferential methods are inappropriate for use with GCS and RTS data. Ordinal data should be tested for normality before statistical analysis with parametric statistical methods.

Oral ranitidine as prophylaxis for gastric stress ulcers in intensive care unit patients: serum concentrations and cost comparisons.

OBJECTIVES: a) To determine whether enteral ranitidine in intensive care unit (ICU) patients would produce serum levels that would reduce stimulated gastric acid by > or = 50%, and b) to evaluate the differences in cost between enteral and parenteral administration of ranitidine. DESIGN: Prospective, nonrandomized clinical trial. SETTING: A surgical ICU in a public primary teaching hospital for a medical school. PATIENTS: Postoperative or posttraumatic surgical patients who met one or more main criteria for stress. INTERVENTIONS: Two groups of patients were given ranitidine through a nasogastric tube. Group 1 (n = 10) received 150 mg every 12 hrs, and group 2 (n = 8) received 300 mg every 12 hrs. MEASUREMENTS AND MAIN RESULTS: Serum samples for measurement of ranitidine concentrations were collected at 2, 6, and 12 hrs after the fifth dose of oral ranitidine. Patients were monitored for upper gastrointestinal bleeding. All patients had therapeutic serum ranitidine concentrations at 2 and 6 hrs, while 88% of patients had therapeutic levels at 12 hrs. CONCLUSIONS: a) Enteral administration of ranitidine every 12 hrs leads to effective absorption of the drug from the upper gastrointestinal tract of ICU patients. b) Serum concentrations of ranitidine for both 150-mg and 300-mg enteral doses remained within, or exceeded, the therapeutic range in > 90% of ICU patients with clinically important criteria of stress.

Effect of intravenous erythromycin on postoperative ileus.

We attempted to determine whether the administration of erythromycin shortens the period of postoperative ileus by a prospective, double-blind, placebo-controlled study. Seventy-seven patients were randomized and included in the statistical calculations. The patients were stratified according to the operation performed (cholecystectomy, celiotomy, or other major abdominal operations). Forty-one patients (group 1) received 250 mg erythromycin intravenously every 8 h for nine doses upon admission to the recovery room. Thirty-six patients (group 2) received placebo. The time (in hours) to first passage of flatus, first liquid meal, first bowel movement, and total length of hospital stay was recorded. There was no significant difference between group 1 and group 2 in time to first flatus (54.9 +/- 29 vs. 53.9 +/- 27 h, respectively), first meal (70.4 +/- 44 vs. 71.7 +/- 65), first bowel movement (81.8 +/- 32 vs. 80.1 +/- 28), or length of hospital stay (185.2 +/- 183 vs. 182.1 +/- 163). Erythromycin, in the dosage tested in this study, does not seem to alter clinical parameters of gastrointestinal motility after an abdominal operation. New prokinetic agents may deserve further studies.

Mean platelet volume during coagulase-negative staphylococcal sepsis in neonates.

Coagulase-negative staphylococci are the most common cause of late-onset septicemia in neonates in intensive care nurseries. Clinical and laboratory diagnosis of infection with coagulase-negative staphylococci can be difficult. The authors reviewed serial mean platelet volumes of 18 infants in whom coagulase-negative staphylococci sepsis developed and found a significant increase in the mean platelet volume at the time of diagnosis and a return to baseline after resolution of the infection. The increase in mean platelet volume occurred although thrombocytopenia developed in only two of the infants and no difference was found in the mean platelet counts before and at the time of diagnosis of the infection. This finding may be a useful adjunct to the current laboratory tests used to diagnose coagulase-negative staphylococci sepsis in neonates.

Objectives to direct the training of emergency medicine residents on off-service rotations: research.

This is the 16th in a series of objectives to direct resident training in Emergency Medicine. Research is recognized as an important component of physician training, yet it is often neglected in medical school and residency curricula. We offer here an objective-based program for resident physicians' exposure to research design and methodology.

Introduction to biostatistics: Part 6, Correlation and regression.

Correlation and regression analysis are applied to data to define and quantify the relationship between two variables. Correlation analysis is used to estimate the strength of a relationship between two variables. The correlation coefficient r is a dimensionless number ranging from -1 to +1. A value of -1 signifies a perfect negative, or indirect (inverse) relationship. A value of +1 signifies a perfect positive, or direct relationship. The r can be calculated as the Pearson-product r, using normally distributed interval or ratio data, or as the Spearman rank r, using non-normally distributed data that are not interval or ratio in nature. Linear regression analysis results in the formation of an equation of a line (Y = mX + b), which mathematically describes the line of best fit for a data relationship between X and Y variables. This equation can then be used to predict additional dependent variable values (Y), based on the value or the independent variable X, the slope m, and the Y-intercept b. Interpretation of the correlation coefficient r involves use of r2, which implies the degree of variability of Y due to X. Tests of significance for linear regression are similar conceptually to significance testing using analysis of variance. Multiple correlation and regression, more complex analytical methods that define relationships between three or more variables, are not covered in this article. Closing comments for this final installment of this introduction to biostatistics series are presented.

Improved survival and reduced myocardial necrosis with cardiopulmonary bypass reperfusion in a canine model of coronary occlusion and cardiac arrest.

STUDY QUESTION: Does cardiopulmonary bypass (CPB) improve resuscitation rates and limit infarct size after cardiac arrest and acute myocardial infarction? DESIGN: Controlled randomized trial with all animals undergoing left anterior descending coronary artery occlusion and subsequent ventricular fibrillation and resuscitation. All animals were supported for four hours after resuscitation in an intensive care setting. INTERVENTION: Group 1 (eight) was resuscitated with standard external CPR and advanced life support. Group 2 (eight) was resuscitated with CPB. MEASUREMENTS AND MAIN RESULTS: Group hemodynamic, resuscitation variables, number resuscitated, and number of four-hour survivors were compared. Ischemic and necrotic myocardial weights were determined with histochemical staining techniques in four-hour survivors. Infarct size was measured as the ratio of necrotic weight to ischemic weight. Significantly fewer dogs were resuscitated in group 1 (four of eight) than in group 2 (eight of eight) (P less than .05). Group 2 survivors required significantly less epinephrine and lidocaine than group 1 survivors (P less than .05) and higher aortic diastolic and coronary perfusion pressures after CPB (P less than .001). The ratio of myocardial necrotic weight to ischemic weight at four hours was 0.82 +/- 0.25 in group 1 and 0.22 +/- 0.25 in group 2 (P less than .05). However, collateral blood flow was not measured in this study. CONCLUSION: This pilot study further substantiates the improvement in resuscitation rates obtainable with CPB. CPB may also limit infarct size during the postresuscitation period and requires further study.

Introduction to biostatistics: Part 5, Statistical inference techniques for hypothesis testing with nonparametric data.

Specific statistical tests are used when the null hypothesis (H0) is to be tested using nonparametric nominal or ordinal data. With nominal data, experimental results are expressed by proportions or frequencies. Chi-square or related tests (the Fisher's exact test or the rows by columns test) are appropriate for testing H0 with nominal data. Ordinal data permit arrangement of statistical results by rank. Rank-order tests used to test H0 with ordinal data include the Mann-Whitney U, Kolmogorov-Smirnov, Wilcoxon, Kruskal-Wallis, and Friedman tests. The Kruskal-Wallis and Friedman tests permit multiple intergroup comparisons. Other rank-order tests permit only single intergroup comparisons. Specific details to guide the researcher in the proper selection of these tests are presented.

Cardiopulmonary bypass in a model of acute myocardial infarction and cardiac arrest.

Cardiopulmonary bypass (CPB) reperfusion has demonstrated improved resuscitation rates in ventricular fibrillation cardiac arrest models. To investigate the effectiveness of CPB reperfusion in an ischemic cardiac arrest setting, simulating the clinical scenario of myocardial ischemia preceding sudden cardiac death, we developed a canine model of acute myocardial infarction followed by ventricular fibrillation. Sixteen dogs were randomly assigned to two groups. Group 1 (eight) had ventricular fibrillation induced without left anterior descending coronary artery occlusion. Group 2 (eight) had a thrombogenic copper coil placed in the left anterior descending artery and showed ECG evidence of acute myocardial infarction before induction of ventricular fibrillation. CPR commenced after eight minutes of ventricular fibrillation. Epinephrine 0.05 mg/kg and NaHCO3 1.0 mEq/kg were administered at ten minutes. CPB was begun at 12 minutes and continued for one hour. Myocardial ischemic and necrotic areas were determined in four-hour survivors by dual histochemical staining. All animals were resuscitated; all eight group 1 and six of eight group 2 animals survived to four hours. With the onset of CPB, coronary perfusion pressures increased significantly by 68.6 +/- 31.8 (SD) mm Hg in group 1 and 56.2 +/- 34.6 mm Hg in group 2 over those obtained with CPR (P less than .001).(ABSTRACT TRUNCATED AT 250 WORDS)

Introduction to biostatistics: Part 4, statistical inference techniques in hypothesis testing.

Statistical methods used to test the null hypothesis are termed tests of significance. Selection of an appropriate test of significance is dependent on the type of data to be analyzed and the number of groups to be compared. Parametric tests of significance are based on the parameters, mean, standard deviation, and variance, and thus are used appropriately when interval or ratio data are analyzed. The t-test and analysis of variance (ANOVA) are examples of parametric tests of significance. Assumptions regarding the data to be analyzed when using the t-test or ANOVA include normality of the populations from which the sample data are drawn, homogeneity of the variances of the populations from which the sample data are drawn, and independence of the data points within a sample group. The t-test is the appropriate test of significance to use if there are only two groups to compare. If there are three or more groups to compare, ANOVA is the appropriate test. ANOVA holds the preset alpha level constant. While ANOVA will imply a significant difference between the groups compared, a multiple comparison test will define which of the three or more groups differ significantly.

Introduction to biostatistics: Part 3, Sensitivity, specificity, predictive value, and hypothesis testing.

Diagnostic tests guide physicians in assessment of clinical disease states, just as statistical tests guide scientists in the testing of scientific hypotheses. Sensitivity and specificity are properties of diagnostic tests and are not predictive of disease in individual patients. Positive and negative predictive values are predictive of disease in patients and are dependent on both the diagnostic test used and the prevalence of disease in the population studied. These concepts are best illustrated by study of a two by two table of possible outcomes of testing, which shows that diagnostic tests may lead to correct or erroneous clinical conclusions. In a similar manner, hypothesis testing may or may not yield correct conclusions. A two by two table of possible outcomes shows that two types of errors in hypothesis testing are possible. One can falsely conclude that a significant difference exists between groups (type I error). The probability of a type I error is alpha. One can falsely conclude that no difference exists between groups (type II error). The probability of a type II error is beta. The consequence and probability of these errors depend on the nature of the research study. Statistical power indicates the ability of a research study to detect a significant difference between populations, when a significant difference truly exists. Power equals 1-beta. Because hypothesis testing yields "yes" or "no" answers, confidence intervals can be calculated to complement the results of hypothesis testing. Finally, just as some abnormal laboratory values can be ignored clinically, some statistical differences may not be relevant clinically.

Introduction to biostatistics: Part 2, Descriptive statistics.

Descriptive statistics include measures of central tendency and variability. Measures of central tendency include mean, median, and mode. The mean is the arithmetic average of data from interval or ratio scales. The median reflects the 50th percentile score. The mode is the most frequently occurring value of a data distribution. Measures of variability include range, interquartile range, standard deviation, and standard error of the mean. The range describes the spread between the extreme values of data. Interquartile range is data included between the 25th and 75th percentile of a distribution. Standard deviation describes variability of data about the sample mean, while standard error of the mean helps describe the distribution of several sample means about a true population mean. Finally, confidence intervals, which are derived from the standard error of the mean, define an interval likely to include a true population value, based on sample statistical values and probability charceristics of data distributions.

Introduction to biostatistics: Part 1, Basic concepts.

Statistical methods commonly used to analyze data presented in journal articles should be understood by both medical scientists and practicing clinicians. Inappropriate data analysis methods have been reported in 42% to 78% of original publications in critical reviews of selected medical journals. The only way to halt researchers' misuse of statistics and improve the clinician's knowledge of statistics is through education. This is the first of a six-part series of articles intended to provide the reader with a basic, yet fundamental knowledge of common biomedical statistical methods. The series will cover basic concepts of statistical analysis, descriptive statistics, statistical inference theory, comparison of means, chi 2, and correlational and regression techniques. A conceptual explanation will accompany discussion of the appropriate use of these techniques.

Autoregulation of cardiac output by passive elastic characteristics of the vascular capacitance system.

After a change in cardiac output, the magnitude of potential blood volume redistribution was investigated in 10 dogs anesthetized with chloralose. All of the venous return was pumped into a reservoir, using servocontrolled pumps to maintain fixed superior and inferior vena cava pressures. The cardiac output was set at various levels by pumping from the reservoir into the right atrium. Changes in reservoir volume were assumed to reflect the changes in vascular blood volume. After measuring the control responses, cardiovascular reflexes were blocked with hexamethonium. Reducing the cardiac output, for example, from 110 to 80 ml/(min.kg) with reflexes intact, caused a 9.2-ml/kg transfer of blood from the dog to the reservoir. With reflexes blocked, the same change in cardiac output caused 6.8 ml/kg of the blood to be transferred. Under the control conditions, throughout the range of 50-140 ml/(min.kg), an increase or decrease of cardiac output of 1 ml/(min.kg) elicited a 0.304 +/- 0.086 (mean +/- SD) ml/kg change in dog blood volume; with reflexes blocked, the flow sensitivity was 0.239 +/- 0.062 ml/kg. Thus, only 21% of the total blood volume redistribution was attributable to active reflex responses. Deterioration of the preparation may have attenuated the magnitude of active reflex activity. Neither the systemic vascular compliance of 1.80 +/- 0.35 ml/mm Hg.kg nor the fraction of venous return from the superior vena cava of 26.5 +/- 4.6% was significantly changed by reflex blockade.(ABSTRACT TRUNCATED AT 250 WORDS)