061110L - MEASURES OF ASSOCIATION and MEASURES OF EFFECT

Synopsis of a lecture given by Professor Omar Hasan Kasule Sr. to MPH candidates at Universiti Malaya on 10^th November 2006

1.0 GENERAL CONCEPTS

Data analysis affects practical decisions. It involves construction of hypotheses and testing them. The 2-sided test covers both p₁ > p₂ and p₂ > p₁. The 1-sided test covers either p₁ > p₂ or p₂ > p₁ and not both. The 2-sided test is preferentially used because it is more conservative. Simple manual inspection of the data is needed can help identify outliers, assess the normality of data, identify commonsense relationships, and alert the investigator to errors in computer analysis. Data models for continuous data can be straight line regression, non-linear regression, or trends. Data models for categorical data are the maximum likelihood and the logistic models.

Two procedures are employed in analytic epidemiology: test for association and measures of effect. The test for association is done first. The assessment of the effect measures is done after finding an association. Effect measures are useless in situations in which tests for association are negative. The common tests for association are: t-test, F test, chi-square, the linear correlation coefficient, and the linear regression coefficient. The effect measures commonly employed are: Odds Ratio, Risk Ratio, Rate difference. Measures of trend can discover relationships that are too small to be picked up by association and effect measures.

2.0 TESTS OF ASSOCIATION

The tests of association for continuous data are the t-test, the F-test, the correlation coefficient, and the regression coefficient. The t-test is used for two sample means. Analysis of variance, ANOVA (F test) is used for more than 2 sample means. 1-way ANOVA involves one factor (explanatory variable). 2-way ANOVA involves 2 factors. Multiple analysis of variance, MANOVA, is used to test for more than 2 factors. Linear regression is used in conjunction with the t test for data that requires modeling. Dummy variables in the regression model can be used to control for confounding factors like age and sex.

The common test of association for discrete data is the chi square test. The chisquare test is used to test association of 2 or more proportions in contingency tables. The exact test is used to test proportions for small sample sizes. The Mantel-Haenszel chi-square statistic is used to test for association in stratified 2 x 2 tables. The chi square statistic is valid in one of the following conditions: (a) if at least 80% of cells have more than 5 observed, (b) if at least 80% of cells have more than 1.0 expected, (c) if there are at least 5 observed in 80% of cells. If the observations are not independent of one another as in paired or matched  studies, the McNemar chisquare test is used instead of the usual Pearson chisquare test. The chisquare works best for approximately Gaussian distributions.

3.0 MEASURES OF EFFECT

The Mantel-Haenszel Odds Ratio is used for 2 proportions in single or stratified 2x2 contingency table. Logistic regression can be used as an alternative to the MH procedure. For paired proportions, a special form of the Manetl-Haenszel OR and a special form of logistic regression called conditional logistic regression, are used. Excessive disease risk is measured by Attributable Risk, Attributable Risk Proportion, and Population Attributable Risk. Variation of an effect measure by levels of a third variable is called effect modification by epidemiologists and interaction by statisticians. Synergism/antagonism is when the interaction between two causative factors leads to an effect more than what is expected on the basis of additivity or subtractibility. Interaction can be conceptualised at 4 levels. Statistical, biologic, public health, & decision making. The chi square for heterogeneity can be used to test for effect modification/interaction.

4.0 VALIDITY and PRECISION

An epidemiological study should be considered as a sort of measurement with parameters for validity, precision, and reliability. Validity is a measure of accuracy. Precision measures variation in the estimate. Reliability is reproducibility. Bias is defined technically as the situation in which the expectation of the parameter is not zero. Bias may move the effect parameter away from the null value or toward the null value. In negative bias the parameter estimate is below the true parameter. In positive bias the parameter estimate is above the true parameter. A study is not valid if it is biased. Systematic errors lead to bias and therefore invalid parameter estimates. Random errors lead to imprecise parameter estimates. Internal validity is concerned with the results of each individual study. Internal validity is impaired by study bias. External validity is generalizability of results. Traditionally results are generalized if the sample is representative of the population. In practice generalizability is achieved by looking at results of several studies each of which is individually internally valid. It is therefore not the objective of each individual study to be generalizable because that would require assembling a representative sample. Precision is a measure for lack of random error. An effect measure with a narrow confidence interval is said to be precise. An effect measure with a wide confidence interval in imprecise. Precision is increased in three ways: increasing the study size, increasing study efficiency, and care taken in measurement of variables to decrease mistakes.

5.0 META ANALYSIS

Meta analysis refers to methods used to combine data from more than one study to produce a quantitative summary statistic. Meta analysis enables computation of an effect estimate for a larger number of study subjects thus enabling picking up statistical significance that would be missed if analysis were based on small individual studies. Meta analysis also enables study of variation across several population subgroups since it involves several individual studies carried out in various countries and populations. Criteria must be set for what articles to include or exclude. Information is abstracted from the articles on a standardized data abstract form with standard outcome, exposure, confounder, or effect modifying variables. The first step is to display the effect measures with each article with their 95% confidence limits to get a general idea of their distribution before proceeding to compute summary measures. The summary effect measure, OR or b, is computed from the effect measures of individual studies using weighted logistic regression or computing a MH weighted average in which the weight of each measure is the inverse of its precision i.e. 1/(se)². In both the logistic or MH procedures, each study is treated as a stratum. The combined effect measure is then statistically adjusted for confounding, selection, and misclassification biases. Tests of homogeneity can be carried out before computing the summary effect measure. Sensitivity analysis is undertaken to test the robustness of the combined effect measure.