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Comment & Response |

Testing the Penrose Hypothesis—Reply

Adrian P. Mundt, MD1,2; Winnie S. Chow, MSc1; Stefan Priebe, FRCPsych1
[+] Author Affiliations
1Unit of Social and Community Psychiatry, World Health Organization Collaborating Centre for Mental Health Services Development, Queen Mary University of London, London, England
2Escuela de Medicina sede Puerto Montt, Universidad San Sebastián, Puerto Montt, Chile
JAMA Psychiatry. 2015;72(7):736. doi:10.1001/jamapsychiatry.2015.0217.
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In Reply We thank Tsai and Venkataramani for their comments, which raise important methodological issues and challenge the findings presented in our article.1 They reconstructed the data set and stated that the association found between psychiatric bed numbers and prison populations disappears once they adjusted for year fixed effects or linear time trends.

Yet, they did not use the same data set as in our study. They interpolated the data, ending up with 104 observations, almost twice as many as the 53 observations in our analyis.1 All the additional data points were not observed data but interpolated estimates. This changes the variance and standard errors and leads to completely different results. Computing the analysis with year fixed effects, as suggested by Tsai and Venkataramani, with the real data (available on request), the association between psychiatric bed numbers and prison population rates remains statistically significant (−3.15; 95% CI, −4.72 to −1.60). Adding a linear time trend to the original data set showed a similar result (−2.96; 95% CI, −4.66 to −1.25). We can conclude that the findings presented in our article1 are consistent with the Penrose hypothesis, whether year fixed effects are added or not.

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July 1, 2015
Alexander C. Tsai, MD, PhD; Atheendar S. Venkataramani, MD, PhD
1Chester M. Pierce, MD, Division of Global Psychiatry, Massachusetts General Hospital, Boston2Mbarara University of Science and Technology, Mbarara, Uganda3Center for Global Health, Massachusetts General Hospital, Boston
3Center for Global Health, Massachusetts General Hospital, Boston4Department of Medicine, Massachusetts General Hospital, Boston
JAMA Psychiatry. 2015;72(7):735-736. doi:10.1001/jamapsychiatry.2015.0212.
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