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From |
Joseph Coveney <jcoveney@bigplanet.com> |

To |
Statalist <statalist@hsphsun2.harvard.edu> |

Subject |
Re: st: Comparing change in rates - frustrating problem, please help |

Date |
Sat, 31 Jan 2004 13:32:21 +0900 |

Ricardo Ovaldia wrote: >Thank you Joseph and Kieran. >I originally though to model this problem as Joseph's >"ANCOVA-like approach" but without the interaction >term (i.e.): > >xi: logistic followup i.baseline i.intervention > >If I do these, isn't the test: Beta(intervention)=0 >testing whether the intervention had an effect? I am >not certain what the interaction term adds in this >context? Please excuse me if this is a stupid >question, but I do not get it. What am I missing? Well, here's my take on it: the interaction term tests the analogue of what it would in a linear model--whether the intervention effect depends upon the level of baseline. In one sense, it seems difficult to fathom in a pre-post design: if a person doesn't wear a seatbelt prior to intevention, then the odds that that person wears a seatbelt is zero and the the intervention odds ratio for a group of like-behaving people would be infinite, regardless of whether they wore seatbelts after intervention. In another sense, however, the interaction term measures how justified you are in collapsing a 2 X 2 X 2 table (baseline X intervention X outcome) into a 2 X 2 table (intervention X outcome). In this latter sense, it would test whether ratio of the odds that a person wears a seatbelt after experimental intervention to the odds that a person wears a seatbelt after control intervention needs to take into account the odds that the person wears a seatbelt before intevention. The analogy with the linear model is seen better with -logit- and -lincom- as shown below. clear set obs 400 set seed 20040131 generate byte baseline = _n > _N / 2 generate byte treatment = mod(_n, 2) generate byte result = uniform() < 1 / 4 replace result = uniform() < 3/4 if baseline == 1 & treatment == 0 table baseline treatment, contents(mean result) generate byte iac = baseline * treatment logistic result baseline treatment iac, nolog * Creating the analogue of the "cell means model" of ANOVA egen byte group = group(baseline treatment) xi: logit result i.group, nolog * The following linearized contrast is * the interaction term (iac) in -logistic- above. lincom _Igroup_4 - _Igroup_3 - _Igroup_2 lincom _Igroup_4 - _Igroup_3 - _Igroup_2, or exit I'll take a crack at answering my own questions: >1. Which is better for binary outcomes, Kieran's repeated-measures approach >or an ANCOVA-like approach using the pretreatment values as a baseline >covariate in conventional logistic regression? The do-file below suggests >that completely different conclusions would be drawn from the same dataset >depending upon which approach is used to analyze it. It looks like the ANCOVA-like approach is the one to use, from the results of a Monte Carlo simulation under the null hypothesis. The false-positive rejection rate for the repeated-measures approach is orders of magnitude too high. (See do-file below.) >2. As Kieran mentioned, the repeated-measures approach drops one of the >"main effects" (treatment) so that the model ends up having an interaction >term in it when one of the component "main effects" terms contributing to >the interaction is not in the model. This would be a no-no from what I've >heard, at least for the analogous situation in ANOVA. But, I assume that >this *not* a problem for conditional logistic regression due to the >conditioning. Is that correct? Apparently not. (See answer for 1. above.) >2. When using the likelihood-ratio test (-lrtest-), which is the proper >model against which to compare for testing individual "main effects" of >treatment and baseline--the saturated model (*with* the interaction) or the >partially reduced model (*no* interaction term, i.e., the model that >includes only both of the main effects)? Or should we be testing a >constant-only model against one with the "main effect" in order to test that >"main effect"? Well, they test different hypotheses: one tests whether there is an effect of intervention at both levels of baseline, and the other tests whether there is an effect of intervention at *any* level of baseline. (Mentioned by Frank E. Harrell, Jr., in the context of clinical studies in hesweb1.med.virginia.edu/biostat/presentations/feh/covadj.pdf .) I knew this, but this answer doesn't really answer my question: which hypothesis ought we to be testing as a default when we believe that a baseline covariate is sufficiently important to include in a model a priori (in the protocol or statistical analysis plan)? Joseph Coveney Monte Carlo simulation evaluating null-hypothesis behavior of ANCOVA-like and repeated-measures approaches to pre-post design with binary endpoint: clear set more off set seed 20040130 * program define twolog, rclass version 8.2 tempvar a b iac pid dep per tempname A B C drop _all set obs 200 generate byte `a' = _n > _N / 2 generate byte `b' = mod(_n, 2) generate byte `iac' = `a' * `b' generate byte `dep' = uniform() > 0.5 logistic `dep' `a' `b' `iac' estimates store `A' logistic `dep' `a' `b' estimates store `B' logistic `dep' `b' lrtest `A' . return scalar ancova_iac = r(p) lrtest `B' . return scalar ancova_me = r(p) drop `iac' estimates drop _all generate int `pid' = _n rename `b' `dep'0 rename `dep' `dep'1 reshape long `dep', i(`pid') j(`per') generate byte `iac' = `a' * `per' clogit `dep' `a' `per' `iac', group(`pid') estimates store `C' clogit `dep' `per', group(`pid') lrtest `C' . return scalar rpm = r(p) end * simulate "twolog" ancova_me = r(ancova_me) rpm = r(rpm) /// ancova_iac = r(ancova_iac), reps(3000) generate byte pancova_me = ancova_me < 0.05 generate byte prpm = rpm < 0.05 generate byte pancova_iac = ancova_iac < 0.05 summarize p* exit * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**RE: st: Comparing change in rates - frustrating problem, please help***From:*"Kieran McCaul" <kieran@dph.uwa.edu.au>

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