Dear all



I am wondering if anyone can help me in interpreting a zero added model using MCMCglmm. I am analysing a clinical trial for counts of incidents on a psychiatric ward (per work shift).  The data has a surfeit of zeros and so I am using zero inflated models. The problem I have is trying to understand what zero added models is telling me about the zero inflation. I've looked through the excellent course notes from Jarrod Hadfield but am a bit unsure as to the take home message as this is the first time I've attempted to use these models.



Model background: Outcome data is collected at the ward level (i.e. not individual patient) and so a hurdle model seemed the most appropriate, i.e. each ward has the potential to generate an incident on any given shift. I have used the zero altered models to test for inflation as on p109 of the course notes. In this (simplified analysis with just a quick test run) I have included all factors as predictors for both parts of the model;  trial phase: period.x (baseline vs outcome) and experimental condition expconr (control vs test). Here is my model specification

 cf.za.1 <- MCMCglmm(totflct ~ -1 + trait*(expcon.r*period.x),

                      data = sw.df, family = "zapoisson",

                      random = ~idh(at.level(trait,2)):wardn + idh(at.level(trait,1)):wardn,

                     rcov = ~ trait:units,

                      #prior = zza.prior,

                      #nitt = 250000, burnin = 50000, thin = 500,

                      verbose = TRUE, pr = TRUE, pl = FALSE, saveXL = TRUE)



The outcome I'm interested in is the change between control and treatment from baseline to outcome, highlighted as the interaction term in the model below. For shifts with events there is a reduction in the rate of events for the intervention versus control shown by the negative coefficient for the expcon.r  x period.x. However, for the zero inflation test this co-efficient is positive. Just to confirm, does this mean I have zero deflation for the test condition in the outcome phase relative to the control condition, i.e. more shifts with incidents.



post.mean l-95% CI u-95% CI eff.samp

trait:units    0.4641   0.4317   0.4947    116.3



Location effects: totflct ~ -1 + trait * (expcon.r * period.x)



                                              post.mean  l-95% CI  u-95% CI eff.samp  pMCMC

traittotflct                                  1.395460  1.195803  1.602353   1000.0 <0.001 ***

traitza_totflct                               1.012971  0.742179  1.318166    468.3 <0.001 ***

expcon.rtest                                  0.052641 -0.210311  0.327396    894.5  0.690

period.xoutcome                              -0.170481 -0.251931 -0.103334    567.0 <0.001 ***

expcon.rtest:period.xoutcome                 -0.157615 -0.269555 -0.051604    513.6  0.004 **

traitza_totflct:expcon.rtest                 -0.316590 -0.762917  0.150063    748.1  0.174

traitza_totflct:period.xoutcome              -0.189739 -0.345773 -0.059751    162.4  0.008 **

traitza_totflct:expcon.rtest:period.xoutcome  0.237426  0.001023  0.450208    166.0  0.034 *



I find this a bit odd, but then you would expect more zeros for a condition with a lower mean count in 1 condition relative to the other so that would reduce zero inflation? If anyone has any insight it would be much appreciated.



Thanks

John



====================================



John Hodsoll

Institute of Psychiatry

Kings College London

London

SE5 8AF

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