Bayesian Semiparametric Modeling for Matched Case–Control Studies with Multiple Disease States

Abstract

We present a Bayesian approach to analyze matched "case-control" data with multiple disease states. The probability of disease development is described by a multinomial logistic regression model. The exposure distribution depends on the disease state and could vary across strata. In such a model, the number of stratum effect parameters grows in direct proportion to the sample size leading to inconsistent MLEs for the parameters of interest even when one uses a retrospective conditional likelihood. We adopt a semiparametric Bayesian framework instead, assuming a Dirichlet process prior with a mixing normal distribution on the distribution of the stratum effects. We also account for possible missingness in the exposure variable in our model. The actual estimation is carried out through a Markov chain Monte Carlo numerical integration scheme. The proposed methodology is illustrated through simulation and an example of a matched study on low birth weight of newborns (Hosmer, D. A. and Lemeshow, S., 2000, Applied Logistic Regression) with two possible disease groups matched with a control group.

Bayesian inference for categorical data analysis

“…They argued that the Bayesian approach is well suited for this, since such studies do not represent randomized experiments or random samples from a real or hypothetical population of possible experiments. Later Bayesian work on case-control studies includes Ghosh and Chen (2002), Müller and Roeder (1997), Seaman and Richardson (2004), and Sinha, Mukherjee, and Ghosh (2004). For instance, Seaman and Richardson (2004) extend to Bayesian methods the equivalence between prospective and retrospective models in case-control studies.…”

Estudo caso-controle com resposta multinomial: uma proposta de análise

“…Em razão disso, 247 foram excluídos por não apresentar delineamento do tipo casocontrole; 102 pelo desfecho não ter sido subdividido, ou seja, a resposta permaneceu binária; 57 pela resposta ter sido estratificada por variáveis que não dividiam os casos em subtipos, como variáveis relacionadas à exposição, ou grupos de controles e; em 11 casos não se pôde acessar as publicações. Dos 31 trabalhos restantes, dois eram metodológicos 4,5 e serão comentados mais à frente; dois, por serem estudos caso-controle emparelhados, fizeram uso de métodos Bayesianos para a análise 6,7 ; dois fizeram apenas análi-ses descritivas 8,9 ; três consideraram o desfecho ordinal, e destes, um utilizou para a análise o modelo de Odds Proporcionais 10 e os outros dois analisaram apenas os casos por meio do modelo politômico 11,12 ; quatro trabalhos ajustaram diversos modelos binomiais (um para cada tipo de caso) 13,14,15,16 ; um utilizou um modelo denominado modified polytomous logit model 17 ; e 13 utilizaram o modelo politômico com todos os dados 18,19,20,21,22,23,24,25,26,27,28,29,30 , porém dois deles não usaram a categoria de controles para as comparações 25,28 .…”

A note on bias due to fitting prospective multivariate generalized linear models to categorical outcomes ignoring retrospective sampling schemes

“…We deliberately chose to use the cohort data to illustrate our analytical work for the following reason. If we analyze a single retrospective study with outcome-dependent sampling (as done in Reference [22]), we do not know the ''TRUTH'' about the parameter had a prospective cohort study been done, and it is impossible to empirically assess the true bias in that situation. However, the availability of the full PLCO cohort data ensures that we know the true estimates of cumulative odds ratio parameters and by repeated retrospective sampling from this full cohort we can assess the accuracy of our bias approximation and study it as a function of various sampling rates.…”

“…Our exposition is directed not towards developing new corrected point and interval estimates under retrospective sampling, but to study changes in the bias under different design and model settings. Case-control or nested case-control studies which provide data on further disease sub-classification are becoming increasingly common in practice [22]. The analytical work in the current paper provides strong evidence, why one should not rely on naive fitting of popular models for ordinal data under retrospective design and should employ a proper and valid inference procedure as developed in the papers referred above, though the adjusted estimation procedures may appear more complex than the ones readily available in standard statistical softwares.…”