Rearranging Stata s output for the analysis of epidemiological tables
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1 Rearranging Stata s output for the analysis of epidemiological tables 5ª Reunión de Usuarios Españoles de Stata Barcelona, 12/09/2012 Aurelio Tobías IDAEA-CSIC, Barcelona [email protected]
2 Background In epidemiological research we usually investigate the relationship between a binary response (C/nC) and a binary exposure (E/nE) Risk Exposure Outcome
3 Background A major capability in Stata is the analysis of epidemiological tables by using any of the epitab commands These report measures of frequency (proportion or odds), association (risk difference, relative risk, or odds ratio) and impact on public health (attributable risks)
4 . use example 1, clear Contains data from example1.dta obs: 8 vars: storage display value variable name type format label variable label y byte %8.0g cc Response x byte %8.0g yn Exposure z byte %8.0g yn Other N int %8.0g Sample size list, noobs y x z N control no no 131 control no yes 234 control yes no 650 control yes yes 295 case no no 122 case no yes 78 case yes no 660 case yes yes expand N (2612 observations created)
5 . cs y x Exposure Exposed Unexposed Total Cases Noncases Total Risk Point estimate [95% Conf. Interval] Risk difference Risk ratio Attr. frac. ex Attr. frac. pop chi2(1) = Pr>chi2 =
6 . cc y x Proportion Exposed Unexposed Total Exposed Cases Controls Total Point estimate [95% Conf. Interval] Odds ratio Attr. frac. ex Attr. frac. pop chi2(1) = Pr>chi2 =
7 . cc y x Exposed Unexposed Total Cases Controls Total Odds Point estimate [95% Conf. Interval] Odds ratio Attr. frac. ex Attr. frac. pop chi2(1) = Pr>chi2 =
8 . tabodds y x x cases controls odds [95% Conf. Interval] no yes tabodds y x, or x Odds Ratio chi2 P>chi2 [95% Conf. Interval] no yes mhodds y x Maximum likelihood estimate of the odds ratio Comparing x==1 vs. x== Odds Ratio chi2(1) P>chi2 [95% Conf. Interval]
9 Stratified analysis But... there could be more variables involved in this relationship Risk? Exposure Outcome Third variable
10 Stratified analysis Analyse the relationship between the binary response (C/nC) and the binary exposure (E/nE) for each stratum taken by a third variable (M/F) Third variable Exposure M Exposure F Risk M Risk F Outcome M Outcome F
11 Stratified analysis Analyse the relationship between the binary response (C/nC) and the binary exposure (E/nE) for each stratum taken by a third variable (M/F) Third variable Exposure M Exposure F Risk M Risk F Outcome M Outcome F Do specific-stratum estimates look similar?
12 Effect modification Variation in the magnitude of measure of effect across stratums of a third variable (subgroups of population) Can be tested for by using an statistical test for homogeneity
13 How to conduct an stratified analysis? Crude analysis Stratified analysis Do stratum-specific estimates look similar? YES NO EFFECT MODIFICATION (Report estimates by stratum)
14 How to conduct an stratified analysis? Crude analysis Stratified analysis Do stratum-specific estimates look similar? YES NO EFFECT MODIFICATION (Report estimates by stratum)
15 Confounding Distortion in the of measure of effect because of a third variable Exposure Outcome Third variable Be associated with outcome, independently of exposure Be associated with exposure, without being the consequence of exposure
16 Confounding A confounder influences (bias) the effect of a exposure in the same way for everyone Needs to be adjusted for There is not statistical test to check for confounding, it is usually assessed by comparing crude and adjusted estimates
17 How to conduct an stratified analysis? Crude analysis Stratified analysis Do stratum-specific estimates look similar? YES Adjusted analysis Do adjusted estimates look similar to crude estimates? NO EFFECT MODIFICATION (Report estimates by stratum)
18 How to conduct an stratified analysis? Crude analysis Stratified analysis Do stratum-specific estimates look similar? YES Adjusted analysis Do adjusted estimates look similar to crude estimates? NO EFFECT MODIFICATION (Report estimates by stratum) YES NO CONFOUNDING (Report adjusted estimates)
19 Stratified analysis Any of the epitab commands jointly with the by() option allow to run stratified analyses reporting; specific stratum measures of association, a test of homogeneity, as well as the crude and adjusted estimates These allow to epidemiologists to check for effect modification or to assess for confounding However users are still being confused about how Stata reports stratified analyses
20 . cc y x, by(z) Other OR [95% Conf. Interval] M-H Weight no yes Crude M-H combined Test of homogeneity (M-H) chi2(1) = Pr>chi2 = Test that combined OR = 1: Mantel-Haenszel chi2(1) = Pr>chi2 =
21 . cc y x, by(z) Other OR [95% Conf. Interval] M-H Weight no yes Crude M-H combined Test of homogeneity (M-H) chi2(1) = Pr>chi2 = Test that combined OR = 1: Mantel-Haenszel chi2(1) = Pr>chi2 = Do stratum-specific estimates look similar? Misleading p-value
22 . cc y x, by(z) Other OR [95% Conf. Interval] M-H Weight no yes Crude M-H combined Test of homogeneity (M-H) chi2(1) = Pr>chi2 = Test that combined OR = 1: H 0 : OR=1 Mantel-Haenszel chi2(1) = Pr>chi2 = Misleading p-value
23 . cc y x, by(z) Other OR [95% Conf. Interval] M-H Weight no yes Crude M-H combined Test of homogeneity (M-H) chi2(1) = Pr>chi2 = Test that combined OR = 1: Mantel-Haenszel chi2(1) = Pr>chi2 = Misleading p-values No p-values for specific-stratum and crude estimates Missing the relative change between the crude and adjusted estimates
24 . mhodds y x, by(z) Maximum likelihood estimate of the odds ratio Comparing x==1 vs. x==0 by z z Odds Ratio chi2(1) P>chi2 [95% Conf. Interval] no yes Mantel-Haenszel estimate controlling for z Odds Ratio chi2(1) P>chi2 [95% Conf. Interval] Test of homogeneity of ORs (approx): chi2(1) = Pr>chi2 =
25 . mhodds y x, by(z) Maximum likelihood estimate of the odds ratio Comparing x==1 vs. x==0 by z z Odds Ratio chi2(1) P>chi2 [95% Conf. Interval] no yes Mantel-Haenszel estimate controlling for z Odds Ratio chi2(1) P>chi2 [95% Conf. Interval] Test of homogeneity of ORs (approx): chi2(1) = Pr>chi2 = Do stratum-specific estimates look similar? Another misleading p-value
26 . mhodds y x, by(z) Maximum likelihood estimate of the odds ratio Comparing x==1 vs. x==0 by z z Odds Ratio chi2(1) P>chi2 [95% Conf. Interval] no yes Mantel-Haenszel estimate controlling for z Odds Ratio chi2(1) P>chi2 [95% Conf. Interval] Test of homogeneity of ORs (approx): chi2(1) = Pr>chi2 = Another misleading p-value Missing the crude estimate, and the relative change between the crude and adjusted estimates
27 Rearranging the output Rearrange the output of the epitab commands from the scheme of a classic epidemiological analysis Specific stratum estimates, with 95%CI and p-values Test of homogeneity (to check for effect modification) Crude and adjusted estimates, with 95%CI and p-values Relative change between them (to assess for confounding)
28 . mymhodds y x, by(z) Stratified analysis with test for effect modification z Odds Ratio [95% Conf. Interval] chi2(1) P>chi no yes Test of homogeneity of ORs (approx): chi2(1) = 48.86, P>chi2 = Adjusted analysis with assessment for confounding Odds Ratio [95% Conf. Interval] chi2(1) P>chi Crude Adjusted Adjusted/crude relative change = -0.31%
29 . use example2, clear. expand N (2612 observations created). mymhodds y x, by(z) Stratified analysis with test for effect modification z Odds Ratio [95% Conf. Interval] chi2(1) P>chi no yes Test of homogeneity of ORs (approx): chi2(1) = 0.00, P>chi2 = Adjusted analysis with assessment for confounding Odds Ratio [95% Conf. Interval] chi2(1) P>chi Crude Adjusted Adjusted/crude relative change = %
30 Rearranging the output Rearrange the output of the epitab commands from the scheme of a classic epidemiological analysis Specific stratum estimates, with 95%CI and p-values Test of homogeneity (to check for effect modification) Crude and adjusted estimates, with 95%CI and p-values Relative change between them (to assess for confounding) Furthermore, graphs are always helpful and nice!
31 . use example1, clear. expand N. mymhodds y x, by(z) graphs
32 . use example1, clear. expand N. mymhodds y x, by(z) graphs. use example2, clear. expand N. mymhodds y x, by(z) graphs
33 Conclusions Stata is mainly used in epidemiological research thanks to the epitab commands The cc command must also display the odds epitab commands with capabilities to run stratified analysis with the by() option (cs, cc, ir, and mhodds) must rearrange their output to address effect modification and confounding in a easiest way diagt (SJ4-4) command should also be included in epitab to cover all types of study designs in epidemiological research
34 Rearranging Stata s output for the analysis of epidemiological tables 5ª Reunión de Usuarios Españoles de Stata Barcelona, 12/09/2012 Aurelio Tobías IDAEA-CSIC, Barcelona [email protected]
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Statistics in Retail Finance 1 Overview > We consider how to build statistical models of default, or delinquency, and how such models are traditionally used for credit application scoring and decision