title: Performing meta-analysis with incomplete statistical information in clinical trials.
abstract: BACKGROUND
  Results from clinical trials are usually summarized in the form of sampling distributions. When full information (mean, SEM) about these distributions is given, performing meta-analysis is straightforward. However, when some of the sampling distributions only have mean values, a challenging issue is to decide how to use such distributions in meta-analysis. Currently, the most common approaches are either ignoring such trials or for each trial with a missing SEM, finding a similar trial and taking its SEM value as the missing SEM. Both approaches have drawbacks. As an alternative, this paper develops and tests two new methods, the first being the prognostic method and the second being the interval method, to estimate any missing SEMs from a set of sampling distributions with full information. A merging method is also proposed to handle clinical trials with partial information to simulate meta-analysis.
  
  
  METHODS
  Both of our methods use the assumption that the samples for which the sampling distributions will be merged are randomly selected from the same population. In the prognostic method, we predict the missing SEMs from the given SEMs. In the interval method, we define intervals that we believe will contain the missing SEMs and then we use these intervals in the merging process.
  
  
  RESULTS
  Two sets of clinical trials are used to verify our methods. One family of trials is on comparing different drugs for reduction of low density lipprotein cholesterol (LDL) for Type-2 diabetes, and the other is about the effectiveness of drugs for lowering intraocular pressure (IOP). Both methods are shown to be useful for approximating the conventional meta-analysis including trials with incomplete information. For example, the meta-analysis result of Latanoprost versus Timolol on IOP reduction for six months provided in 1 was 5.05 +/- 1.15 (Mean +/- SEM) with full information. If the last trial in this study is assumed to be with partial information, the traditional analysis method for dealing with incomplete information that ignores this trial would give 6.49 +/- 1.36 while our prognostic method gives 5.02 +/- 1.15, and our interval method provides two intervals as Mean in [4.25, 5.63] and SEM in [1.01, 1.24].
  
  
  CONCLUSIONS
  Both the prognostic and the interval methods are useful alternatives for dealing with missing data in meta-analysis. We recommend clinicians to use the prognostic method to predict the missing SEMs in order to perform meta-analysis and the interval method for obtaining a more cautious result.
authors.affiliation: School of Electronics, Electrical Engineering and Computer Science, Queen's University Belfast, Belfast, BT7 1NN, UK. jma03@qub.ac.uk
authors.forename: Jianbing
authors.initials: J
authors.lastname: Ma
authors.forename: Weiru
authors.initials: W
authors.lastname: Liu
authors.forename: Anthony
authors.initials: A
authors.lastname: Hunter
authors.forename: Weiya
authors.initials: W
authors.lastname: Zhang
mesh_terms: D000959:Antihypertensive Agents / Q000627:therapeutic use; D008078:Cholesterol, LDL / Q000187:drug effects; D002986:Clinical Trials as Topic; D003627:Data Interpretation, Statistical; D003924:Diabetes Mellitus, Type 2 / Q000188:drug therapy; D004359:Drug Therapy, Combination; D006801:Humans; D007004:Hypoglycemic Agents / Q000627:therapeutic use; D007429:Intraocular Pressure / Q000187:drug effects; D000077338:Latanoprost; D015201:Meta-Analysis as Topic; D008687:Metformin / Q000627:therapeutic use; D009798:Ocular Hypertension / Q000188:drug therapy; D011461:Prostaglandins F, Synthetic / Q000627:therapeutic use; D012494:Sampling Studies; D013453:Sulfonylurea Compounds / Q000627:therapeutic use; D045162:Thiazolidinediones / Q000627:therapeutic use; D013997:Time Factors; D013999:Timolol / Q000627:therapeutic use
chemical_list: D000959:Antihypertensive Agents; D008078:Cholesterol, LDL; D007004:Hypoglycemic Agents; D011461:Prostaglandins F, Synthetic; D013453:Sulfonylurea Compounds; D045162:Thiazolidinediones; D000077338:Latanoprost; D013999:Timolol; D008687:Metformin; C089946:2,4-thiazolidinedione