# Fitting MNAR models in missingHE" In missingHE: Missing Outcome Data in Health Economic Evaluation

BCEA::ceac.plot(NN.pat2$cea) Results under MNAR (NN.pat2) clearly suggest a higher chance for the new intervention to be cost-effective compared with those from the MAR model (NN.pat1). This is in accordance with our MNAR assumptions under which we expect, on average, lower QALYs in the control with respect to the intervention group compared with the results under MAR (when Delta_e = 0). The range of values for the sensitivity parameters under MNAR should be informed based on some external source of information (e.g. expert opinion) which can be used to guide the choice of the values and the number of scenarios to explore. ## Handling MNAR with hurdle models Even though, technically speaking, hurdle models cannot be qualified as missingness models, they can still be specified so to assess the impact of some MNAR assumptions on the posterior results. This can be achieved by making arbitrary assumptions about the number of individuals with missing outcomes who are assigned a structural value in the model. Consider first a standard hurdle model specification under MAR. We specify the model using hurdle to handle both structural ones and zeros in$e$and$c$from our economic data in MenSS (setting the arguments se = 1 and sc = 0). NN.hur1=hurdle(data = MenSS, model.eff = e ~ u.0, model.cost = c ~ 1, model.se = se ~ 1, model.sc = sc ~ 1, type = "SCAR", se = 1, sc = 0, n.iter = 1000, dist_e = "norm", dist_c = "norm") NN.hur1=hurdle(data = MenSS, model.eff = e ~ u.0, model.cost = c ~ 1, model.se = se ~ 1, model.sc = sc ~ 1, type = "SCAR", se = 1, sc = 0, n.iter = 1000, dist_e = "norm", dist_c = "norm") The model assumes that the mechanisms of the structural values in both outomes do not depend on any observed covariate, i.e. it is structural completely at random (SCAR). The function automatically assignes all individuals with an observed one and zero to the structural components of the effectiveness and cost mixture distributions, while all the remaining individuals are modelled using normal distributions. In general, we do not know to which component of the mixture individuals with a missing outcome value should be assigned, as this information cannot be obtained from the data. However, based on some external information that we may have, we can impose this assignment, which effectively corresponds to a MNAR mechanism. We can perform this type of analysis in missingHE by first creating an indicator variable (called d_e), telling for each individual whether a structural value is observed (d_e = 1) not observed (d_e = 0) or missing (d_e = NA). For example, focussing on the effectiveness variables, we can obtain this indicator by typing d_e <- ifelse(MenSS$e == 1, 1, 0)

#number of ones
sum(d_e == 1, na.rm = T)

Next, for all or some of the individuals with a missing effect value, we set the value of d_e = 1 to assign them to the structural component of the hurdle model. For example, we may believe that it is likely for all individuals aged $< 22$ to be associated with a perfect health status (i.e. e = 1). We can obtain this by typing

myd_e <- ifelse(is.na(d_e) & MenSS$age < 22, 1, d_e) #number of ones sum(myd_e == 1, na.rm = T) The number of individuals associated with$e = 1$has considerbly increased with respect to that based on the observed data alone. We can now proceed to fit our model using this new indicator variable for the structural values of$e$by setting the optional argument d_e = myd_e. NN.hur2=hurdle(data = MenSS, model.eff = e ~ u.0, model.cost = c ~ 1, model.se = se ~ 1, model.sc = sc ~ 1, type = "SCAR", se = 1, sc = 0, n.iter = 1000, dist_e = "norm", dist_c = "norm", d_e = myd_e) NN.hur2=hurdle(data = MenSS, model.eff = e ~ u.0, model.cost = c ~ 1, model.se = se ~ 1, model.sc = sc ~ 1, type = "SCAR", se = 1, sc = 0, n.iter = 1000, dist_e = "norm", dist_c = "norm", d_e = myd_e) We can inspect the posterior results by typing, print(NN.hur2) and we can look at how imputations in each treatment group are carried out based on our model using the generic plot function. plot(NN.hur2, outcome = "effects") As it is possible to see, for some individuals, imputed values are essentially equal to one with very small credible intervals. These imputations are due to the fact that the outcome values for these people are assumed to be one with almost no uncertainty. Finally, we compare the economic results from the two alternative hurdle models using the ceac.plot function from the BCEA package. par(mfrow=c(1,2)) BCEA::ceac.plot(NN.hur1$cea)
BCEA::ceac.plot(NN.hur2$cea) The probabiility of cost-effectiveness for the "standard" hurdle model (NN.hur1) remains stable around$0.6$for most willingness to pay values. However, for the MNAR model (NN.hur2), results indicate an higher chance of cost-effectiveness up to about$0.8\$ for most threshold values. This is due to the fact that, under our MNAR assumptions, the difference between the treatment groups in terms of the number of individuals assigned to a structural one is more in favour of the new intervention compared with that under MAR.

## Try the missingHE package in your browser

Any scripts or data that you put into this service are public.

missingHE documentation built on July 1, 2020, 5:50 p.m.