Dataset Information

Dynamic programming procedure for searching optimal models to estimate substitution rates based on the maximum-likelihood method.

ABSTRACT: The substitution rate in a gene can provide valuable information for understanding its functionality and evolution. A widely used method to estimate substitution rates is the maximum-likelihood method implemented in the CODEML program in the PAML package. A limited number of branch models, chosen based on a priori information or an interest in a particular lineage(s), are tested, whereas a large number of potential models are neglected. A complementary approach is also needed to test all or a large number of possible models to search for the globally optional model(s) of maximum likelihood. However, the computational time for this search even in a small number of sequences becomes impractically long. Thus, it is desirable to explore the most probable spaces to search for the optimal models. Using dynamic programming techniques, we developed a simple computational method for searching the most probable optimal branch-specific models in a practically feasible computational time. We propose three search methods to find the optimal models, which explored O(n) (method 1) to O(n(2)) (method 2 and method 3) models when the given phylogeny has n branches. In addition, we derived a formula to calculate the number of all possible models, revealing the complexity of finding the optimal branch-specific model. We show that in a reanalysis of over 50 previously published studies, the vast majority obtained better models with significantly higher likelihoods than the conventional hypothesis model methods.

SUBMITTER: Zhang C

PROVIDER: S-EPMC3093512 | biostudies-literature | 2011 May

REPOSITORIES: biostudies-literature

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Dynamic programming procedure for searching optimal models to estimate substitution rates based on the maximum-likelihood method.

Zhang Chengjun C Wang Jia J Xie Weibo W Zhou Gang G Long Manyuan M Zhang Qifa Q

Proceedings of the National Academy of Sciences of the United States of America 20110426 19

The substitution rate in a gene can provide valuable information for understanding its functionality and evolution. A widely used method to estimate substitution rates is the maximum-likelihood method implemented in the CODEML program in the PAML package. A limited number of branch models, chosen based on a priori information or an interest in a particular lineage(s), are tested, whereas a large number of potential models are neglected. A complementary approach is also needed to test all or a la ...[more]

PMID: 21521791

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Project description:Longitudinal targeted maximum likelihood estimation (LTMLE) has very rarely been used to estimate dynamic treatment effects in the context of time-dependent confounding affected by prior treatment when faced with long follow-up times, multiple time-varying confounders, and complex associational relationships simultaneously. Reasons for this include the potential computational burden, technical challenges, restricted modeling options for long follow-up times, and limited practical guidance in the literature. However, LTMLE has desirable asymptotic properties, ie, it is doubly robust, and can yield valid inference when used in conjunction with machine learning. It also has the advantage of easy-to-calculate analytic standard errors in contrast to the g-formula, which requires bootstrapping. We use a topical and sophisticated question from HIV treatment research to show that LTMLE can be used successfully in complex realistic settings, and we compare results to competing estimators. Our example illustrates the following practical challenges common to many epidemiological studies: (1) long follow-up time (30 months); (2) gradually declining sample size; (3) limited support for some intervention rules of interest; (4) a high-dimensional set of potential adjustment variables, increasing both the need and the challenge of integrating appropriate machine learning methods; and (5) consideration of collider bias. Our analyses, as well as simulations, shed new light on the application of LTMLE in complex and realistic settings: We show that (1) LTMLE can yield stable and good estimates, even when confronted with small samples and limited modeling options; (2) machine learning utilized with a small set of simple learners (if more complex ones cannot be fitted) can outperform a single, complex model, which is tailored to incorporate prior clinical knowledge; and (3) performance can vary considerably depending on interventions and their support in the data, and therefore critical quality checks should accompany every LTMLE analysis. We provide guidance for the practical application of LTMLE.

Dataset Information

Dynamic programming procedure for searching optimal models to estimate substitution rates based on the maximum-likelihood method.

Publications

Dynamic programming procedure for searching optimal models to estimate substitution rates based on the maximum-likelihood method.

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