Meta-analysis of genetic association studies increases sample size and the power for mapping complex traits. Existing methods are mostly developed for datasets without missing values, i.e. the summary association statistics are measured for all variants in contributing studies. In practice, genotype imputation is not always effective. This may be the case when targeted genotyping/sequencing assays are used or when the un-typed genetic variant is rare. Therefore, contributed summary statistics often contain missing values. Existing methods for imputing missing summary association statistics and using imputed values in meta-analysis, approximate conditional analysis, or simple strategies such as complete case analysis all have theoretical limitations. Applying these approaches can bias genetic effect estimates and lead to seriously inflated type-I or type-II errors in conditional analysis, which is a critical tool for identifying independently associated variants. To address this challenge and complement imputation methods, we developed a method to combine summary statistics across participating studies and consistently estimate joint effects, even when the contributed summary statistics contain large amounts of missing values. Based on this estimator, we proposed a score statistic called PCBS (partial correlation based score statistic) for conditional analysis of single-variant and gene-level associations. Through extensive analysis of simulated and real data, we showed that the new method produces well-calibrated type-I errors and is substantially more powerful than existing approaches. We applied the proposed approach to one of the largest meta-analyses to date for the cigarettes-per-day phenotype. Using the new method, we identified multiple novel independently associated variants at known loci for tobacco use, which were otherwise missed by alternative methods. Together, the phenotypic variance explained by these variants was 1.1%, improving that of previously reported associations by 71%. These findings illustrate the extent of locus allelic heterogeneity and can help pinpoint causal variants.